1
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Hu D, Liu J, Liu C, Chu C. Dynamic incentives and environmental feedback in public goods games: Promoting cooperation through critical thresholds. CHAOS (WOODBURY, N.Y.) 2025; 35:023117. [PMID: 39899572 DOI: 10.1063/5.0235953] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/30/2024] [Accepted: 01/09/2025] [Indexed: 02/05/2025]
Abstract
Understanding the emergence and maintenance of cooperation in multiplayer games is a significant challenge across various theoretical disciplines. In this paper, we introduce an innovative model to study the impacts of environmental feedback in systems with critical thresholds. Different from prior studies on public goods games with environmental feedback, we propose that the system holds expectations for collective behavior, and the dynamic incentives are equal for all group members. Our findings reveal that dynamic incentives driven by environmental feedback significantly enhance cooperation, particularly in scenarios with low synergy factors. As incentives increase, the system shifts from the non-cooperative to cooperative state. Moreover, a faster rate of incentive growth leads to a higher level of cooperation, demonstrating a strong positive correlation between dynamic incentive levels and overall cooperation within the system. Counterintuitively, our study finds that introducing dynamic incentives from environmental feedback not only effectively promotes cooperation under high expectation levels but also surprisingly increases the success rate of cooperation as expectations rise.
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Affiliation(s)
- Die Hu
- School of Mechanical Engineering, Northwestern Polytechnical University, Xi'an 710072, China
- Department of Computing, Hong Kong Polytechnic University, Hong Kong China
| | - Jinzhuo Liu
- School of Software, Yunnan University, Kunming 650091, China
- School of Artificial Intelligence, Optics and Electronics, Northwestern Polytechnical University, Xi'an 710072, China
| | - Chen Liu
- School of Ecology and Environment, Northwestern Polytechnical University, Xi'an 710072, China
| | - Chen Chu
- School of Artificial Intelligence, Optics and Electronics, Northwestern Polytechnical University, Xi'an 710072, China
- Department of Statistics, School of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming 650091, China
- Yunnan Key Laboratory of Service Computing, Yunnan University of Finance and Economics, Kunming 650091, China
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2
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Si Z, He Z, Shen C, Tanimoto J. Cooperative bots exhibit nuanced effects on cooperation across strategic frameworks. J R Soc Interface 2025; 22:20240427. [PMID: 39876789 PMCID: PMC11775664 DOI: 10.1098/rsif.2024.0427] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/24/2024] [Revised: 09/19/2024] [Accepted: 10/25/2024] [Indexed: 01/31/2025] Open
Abstract
The positive impact of cooperative bots on cooperation within evolutionary game theory is well-documented. However, prior studies predominantly use discrete strategic frameworks with deterministic actions. This article explores continuous and mixed strategic approaches. Continuous strategies use intermediate probabilities for varying degrees of cooperation and focus on expected payoffs, while mixed strategies calculate immediate payoffs from actions taken within these probabilities. Using the prisoner's dilemma game, this study examines the effects of cooperative bots on human cooperation in both well-mixed and structured populations across these strategic approaches. Our findings reveal that cooperative bots significantly enhance cooperation in both population types under weak imitation scenarios, where players are less concerned with material gains. Conversely, under strong imitation scenarios, cooperative bots do not alter the defective equilibrium in well-mixed populations but have varied impacts in structured populations. Specifically, they disrupt cooperation under discrete and continuous strategies but facilitate it under mixed strategies. These results highlight the nuanced effects of cooperative bots within different strategic frameworks and underscore the need for careful deployment, as their effectiveness is highly sensitive to how humans update their actions and their chosen strategic approach.
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Affiliation(s)
- Zehua Si
- Interdisciplinary Graduate School of Engineering Sciences, Kyushu University, Fukuoka816-8580, Japan
| | - Zhixue He
- Interdisciplinary Graduate School of Engineering Sciences, Kyushu University, Fukuoka816-8580, Japan
- School of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming, 650221, People’s Republic of China
| | - Chen Shen
- Faculty of Engineering Sciences, Kyushu University, Kasuga-koen, Kasuga-shi, Fukuoka816-8580, Japan
| | - Jun Tanimoto
- Interdisciplinary Graduate School of Engineering Sciences, Kyushu University, Fukuoka816-8580, Japan
- Faculty of Engineering Sciences, Kyushu University, Kasuga-koen, Kasuga-shi, Fukuoka816-8580, Japan
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3
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Gao J, Geng Y, Jiang X, Li J, Yan Y. Social dilemma for 30 years: Progress, framework, and future based on CiteSpace analysis. Medicine (Baltimore) 2024; 103:e41138. [PMID: 39969365 PMCID: PMC11688041 DOI: 10.1097/md.0000000000041138] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 05/05/2024] [Accepted: 10/31/2024] [Indexed: 02/20/2025] Open
Abstract
Social dilemmas have been a popular research topic in the past 30 years, yet there is still a lack of interdisciplinary reviews. This study represents the first attempt to conduct a bibliometric analysis of social dilemma research over the past 30 years, aiming to identify the research status, research hotspots, and future trends in this domain. We conduct an interdisciplinary analysis of 3630 articles from 1993 to 2023 using CiteSpace software. We find that: (1) this research domain exhibits a fluctuating upward trend and possesses evident interdisciplinary characteristics. (2) Collaboration among authors, institutional and regional, is much more prevalent, especially in the evolutionary dynamics of human behavior, cooperation, and reinforcement learning. (3) The current hot trend in this field of research is to investigate the influencing factors and solutions for social dilemmas. Researchers have shown great interest in value orientation, social norms, fairness, punishment, and rewards in promoting cooperation. (4) In the future, this field will cover different disciplines, develop theoretical frameworks grounded in bounded rationality, explore the boundary conditions of effective strategies, and integrate emerging technologies. This study serves as a valuable reference for scholars seeking to navigate social dilemma research while also providing insights for managers aiming to devise practical solutions to social dilemmas.
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Affiliation(s)
- Juan Gao
- School of Business, Shanghai Dianji University, Shanghai, China
| | - Yuqing Geng
- School of Business, Shanghai Dianji University, Shanghai, China
| | - Xinying Jiang
- School of Business, Shanghai Dianji University, Shanghai, China
| | - Jianyi Li
- Nursing Department, Guizhou Nursing Vocational College, Guizhou, China
| | - Yan Yan
- School of Business, Shanghai Dianji University, Shanghai, China
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4
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Zhang Y, Zhu Q, Li Z. The Nature and Motivation of Human Cooperation from Variant Public Goods Games. HUMAN NATURE (HAWTHORNE, N.Y.) 2024; 35:411-429. [PMID: 39585563 DOI: 10.1007/s12110-024-09483-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Accepted: 11/13/2024] [Indexed: 11/26/2024]
Abstract
This study aims to reveal the nature and motivation of human cooperation. By adopting the public goods game paradigm of competition and repetition, and introducing factors such as punishment and heterogeneous contributions, an experiment was conducted at Nanjing University in China, where 224 undergraduate students participated in seven games, including intragroup and intergroup competition. Meanwhile, participants' social value orientation (SVO) was measured. The results indicated that cooperation (non-zero contribution) was the common choice for participants, but their contributions varied across rounds and games. Individuals generally act as conditional free-riders in intragroup competition games, i.e., they use the "small for big" strategy. In contrast, individuals generally act as conditional cooperators in intergroup competitive games, i.e., they use the "tit for tat" strategy. Although SVO should theoretically be related to contribution, analysis revealed that participants' contributions were not significantly dominated by SVO, but were primarily driven by self-interest. Specifically, individuals switch back and forth between conditional cooperators and conditional free-riders to seek maximum self-interest. Our results not only reveal the complexity and strategic nature of human behavior in competitive contexts but also highlight the central role of self-interest in driving individual decision-making, reflecting the balance between individuals' pursuit of self-interest and adaptation to the environment in social interactions.
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Affiliation(s)
- Yigui Zhang
- Lab of Animal Behavior & Conservation, School of Life Sciences, Nanjing University, Nanjing, 210023, Jiangsu, China
| | - Qin Zhu
- Lab of Animal Behavior & Conservation, School of Life Sciences, Nanjing University, Nanjing, 210023, Jiangsu, China
| | - Zhongqiu Li
- Lab of Animal Behavior & Conservation, School of Life Sciences, Nanjing University, Nanjing, 210023, Jiangsu, China.
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5
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Basak A, Sengupta S. Evolution of cooperation in multichannel games on multiplex networks. PLoS Comput Biol 2024; 20:e1012678. [PMID: 39700300 PMCID: PMC11698529 DOI: 10.1371/journal.pcbi.1012678] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/23/2024] [Revised: 01/03/2025] [Accepted: 11/27/2024] [Indexed: 12/21/2024] Open
Abstract
Humans navigate diverse social relationships and concurrently interact across multiple social contexts. An individual's behavior in one context can influence behavior in other contexts. Different payoffs associated with interactions in the different domains have motivated recent studies of the evolution of cooperation through the analysis of multichannel games where each individual is simultaneously engaged in multiple repeated games. However, previous investigations have ignored the potential role of network structure in each domain and the effect of playing against distinct interacting partners in different domains. Multiplex networks provide a useful framework to represent social interactions between the same set of agents across different social contexts. We investigate the role of multiplex network structure and strategy linking in multichannel games on the spread of cooperative behavior in all layers of the multiplex. We find that multiplex structure along with strategy linking enhances the cooperation rate in all layers of the multiplex compared to a well-mixed population in Prisoners' Dilemma games, provided the network structure is identical across layers. The effectiveness of strategy linking in enhancing cooperation depends on the degree of similarity of the network structure across the layers and perception errors due to imperfect memory. Higher cooperation rates are achieved when the degree of structural overlap of the different layers is sufficiently large, and the probability of perception error is relatively low. Our work reveals how the social network structure in different layers of a multiplex can affect the spread of cooperation by limiting the ability of individuals to link strategies across different social domains.
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Affiliation(s)
- Amit Basak
- Department of Physical Sciences, Indian Institute of Science Education and Research Kolkata, Mohanpur Campus, West Bengal, India
| | - Supratim Sengupta
- Department of Physical Sciences, Indian Institute of Science Education and Research Kolkata, Mohanpur Campus, West Bengal, India
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6
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Lu S, Wang Y. Adjustment of link weights based on tolerance promotes cooperation in spatial prisoner's dilemma game. Biosystems 2024; 246:105362. [PMID: 39510493 DOI: 10.1016/j.biosystems.2024.105362] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/29/2024] [Revised: 11/03/2024] [Accepted: 11/03/2024] [Indexed: 11/15/2024]
Abstract
Understanding and explaining cooperative behavior in human society has become an open question. In this paper, we propose a dynamic adjustment of pair relationships in a spatial prisoner's dilemma game. Unlike previous studies that individuals dynamically adjust the intensity of interaction with their opponents at each step, this work consider tolerance, in which the intensity of interaction is adjusted when the time of successive defections by an individual exceeds a tolerance threshold T. We find that although the proposed mechanism can significantly improve cooperation compared to traditional versions, a higher tolerance for continuous defection behavior is not conducive to the evolution of cooperation. Furthermore, an environmental adaptor that dynamically adjusts the paired relationship with the opponent at all times is beneficial for the evolution of cooperation. And the higher the degree of adjustment in the paired relationship, the lower the probability of continuous exploitation by defector. We hope that our work can provide some insights into explaining the existence and maintenance of cooperation.
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Affiliation(s)
- Shounan Lu
- School of Mathematical Sciences, Laboratory of Mathematics and Complex Systems, MOE, Beijing Normal University, 100875, Beijing, China.
| | - Yang Wang
- School of Business, Shanghai Dianji University, 201306, Shanghai, China
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7
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Han TA, Duong MH, Perc M. Evolutionary mechanisms that promote cooperation may not promote social welfare. J R Soc Interface 2024; 21:20240547. [PMID: 39592014 PMCID: PMC11597467 DOI: 10.1098/rsif.2024.0547] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/10/2024] [Revised: 09/11/2024] [Accepted: 10/08/2024] [Indexed: 11/28/2024] Open
Abstract
Understanding the emergence of prosocial behaviours among self-interested individuals is an important problem in many scientific disciplines. Various mechanisms have been proposed to explain the evolution of such behaviours, primarily seeking the conditions under which a given mechanism can induce highest levels of cooperation. As these mechanisms usually involve costs that alter individual pay-offs, it is, however, possible that aiming for highest levels of cooperation might be detrimental for social welfare-the latter broadly defined as the total population pay-off, taking into account all costs involved for inducing increased prosocial behaviours. Herein, by comparing stochastic evolutionary models of two well-established mechanisms of prosocial behaviour-namely, peer and institutional incentives-we demonstrate that the objectives of maximizing cooperation and of maximizing social welfare are often misaligned. First, while peer punishment is often more effective than peer reward in promoting cooperation-especially with a higher impact-to-cost ratio-the opposite is true for social welfare. In fact, welfare typically decreases (increases) with this ratio for punishment (reward). Second, for institutional incentives, while maintaining similar levels of cooperation, rewards result in positive social welfare across a much broader range of parameters. Furthermore, both types of incentives often achieve optimal social welfare when their impact is moderate rather than maximal, indicating that careful planning is essential for costly institutional mechanisms to optimize social outcomes. These findings are consistent across varying mutation rates, selection intensities and game configurations. Overall, we argue for the need of adopting social welfare as the main optimization objective when designing and implementing evolutionary mechanisms for social and collective goods.
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Affiliation(s)
- The Anh Han
- School of Computing Engineering and Digital Technologies, Teesside University, Middlesbrough, UK
| | - Manh Hong Duong
- School of Mathematics, University of Birmingham, Birmingham, UK
| | - Matjaz Perc
- Faculty of Natural Sciences and Mathematics, University of Maribor, Maribor, Slovenia
- Community Healthcare Center Dr. Adolf Drolc Maribor, Maribor, Slovenia
- Complexity Science Hub Vienna, Vienna, Austria
- Department of Physics, Kyung Hee University, Seoul, Republic of Korea
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8
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Ito H, Yamamichi M. A complete classification of evolutionary games with environmental feedback. PNAS NEXUS 2024; 3:pgae455. [PMID: 39678038 PMCID: PMC11639210 DOI: 10.1093/pnasnexus/pgae455] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 05/31/2024] [Accepted: 10/02/2024] [Indexed: 12/17/2024]
Abstract
A tragedy of the commons, in which rational behavior of individuals to maximize their own payoffs depletes common resources, is one of the most important research topics in game theory. To better understand the social dilemma problem, recent studies have developed a theoretical framework of feedback-evolving game where individual behavior affects an environmental (renewable) resource and the environmental resource changes individual payoffs. While previous studies assumed that the frequency of defectors increases (prisoner's dilemma [PD] game) when the environmental resource is abundant to investigate an oscillating tragedy of the commons, it is also possible for other types of game to produce the social dilemma. In this paper, we extend the feedback-evolving game by considering not only PD game, but also the other three game structures when the environmental resource is replete for a reasonably complete classification. The three games are Chicken game where defectors and cooperators coexist through minority advantage, Stag-Hunt (SH) game with minority disadvantage, and Trivial game where the frequency of cooperators increases. In addition, we utilize a dilemma phase plane to visually track (transient) dynamics of game structure changes. We found that an emergent initial condition dependence (i.e. bistability) is pervasive in the feedback-evolving game when the three games are involved. We also showed that persistent oscillation dynamics arise even with Chicken or SH games in replete environments. Our generalized analysis will be an important step to further extend the theoretical framework of feedback-evolving game to various game situations with environmental feedback.
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Affiliation(s)
- Hiromu Ito
- Department of International Health and Medical Anthropology, Institute of Tropical Medicine, Nagasaki University, Nagasaki 852-8523, Japan
| | - Masato Yamamichi
- Center for Frontier Research, National Institute of Genetics, 1111 Yata, Mishima, Shizuoka 411-8540, Japan
- Genetics Program, Graduate Institute for Advanced Studies, SOKENDAI (The Graduate University for Advanced Studies), 1111 Yata, Mishima, Shizuoka 411-8540, Japan
- Department of International Health and Medical Anthropology, Institute of Tropical Medicine, Nagasaki University, Nagasaki 852-8523, Japan
- School of the Environment, The University of Queensland, St. Lucia, Brisbane, QLD 4072, Australia
- Institute for Multidisciplinary Sciences, Yokohama National University, 79-5 Tokiwadai, Hodogaya, Yokohama, Kanagawa 240-8501, Japan
- Department of Ecosystem Studies, Graduate School of Agricultural and Life Sciences, The University of Tokyo, 1-1-1 Yayoi, Bunkyo-ku, Tokyo 113-8657, Japan
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9
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Fahimur Rahman Shuvo M, Kabir KMA. Investigating the impact of environmental feedback on the optional prisoner's dilemma for insights into cyclic dominance and evolution of cooperation. ROYAL SOCIETY OPEN SCIENCE 2024; 11:240717. [PMID: 39445094 PMCID: PMC11495962 DOI: 10.1098/rsos.240717] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 05/03/2024] [Revised: 06/28/2024] [Accepted: 08/27/2024] [Indexed: 10/25/2024]
Abstract
This study incorporates environmental feedback into the optional prisoner's dilemma and rock-paper-scissors games to examine the mutual influence of eco-evolutionary outcomes and strategy dynamics. A novel game-theoretic model is developed that integrates the optional prisoner's dilemma and rock-paper-scissors games by incorporating an environmental state variable. By adjusting feedback parameters, chaos, oscillations and coexistence are observed that surpass the usual outcomes of social dilemmas when the environment transitions between depleted and replenished states. Defection is no longer advantageous in evolution; cooperation, abstention and cyclic dominance arise. The observed transitions align with natural economics, ecology and sociology phenomena. The inclusion of abstention options and environmental feedback has a significant impact on collective outcomes when compared with conventional games. This has important implications for studying adaptation and decision-making in situations with ecological constraints.
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Affiliation(s)
- Md. Fahimur Rahman Shuvo
- Department of Mathematics, Bangladesh University of Engineering and Technology, Dhaka1000, Bangladesh
| | - K. M. Ariful Kabir
- Department of Mathematics, Bangladesh University of Engineering and Technology, Dhaka1000, Bangladesh
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10
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Guo ZX, Feng TJ, Tao Y, Wang RW, Zheng XD. Evolutionary dynamics of cooperation coupled with ecological feedback compensation. Biosystems 2024; 244:105282. [PMID: 39147308 DOI: 10.1016/j.biosystems.2024.105282] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/16/2024] [Revised: 08/01/2024] [Accepted: 08/02/2024] [Indexed: 08/17/2024]
Abstract
A simple theoretical model (or a demonstrative example) was developed to illustrate how the evolution of cooperation can be affected by the density-dependent survival competition, in which we assume that the fertility of an individual depends only on the pairwise interaction between him and other individuals based on Prisoner's Dilemma game, while its viability is only related to the density-dependent survival competitiveness. Our results show that not only cooperation could be evolutionarily stable if the advantage of cooperators in viability can compensate for the cost they pay for their fertility, but also the long-term stable coexistence of cooperation and defection is possible if none of cooperation and defection is evolutionarily stable. Moreover, for the stochastic evolutionary dynamics in a finite population, our analysis shows that the increase (or decrease) of the survival competitiveness of cooperators (or defectors) should be conductive to the evolutionary emergence of cooperation.
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Affiliation(s)
- Zi-Xuan Guo
- School of Ecology and Environment, Northwestern Polytechnical University, Xi'an 710072, China
| | - Tian-Jiao Feng
- Key Laboratory of Animal Ecology and Conservation Biology, Institute of Zoology, Chinese Academy of Sciences, Beijing 100101, China; National Fisheries Technology Extension Center, Ministry of Agriculture and Rural Affairs, Beijing 100125, China
| | - Yi Tao
- School of Ecology and Environment, Northwestern Polytechnical University, Xi'an 710072, China; Key Laboratory of Animal Ecology and Conservation Biology, Institute of Zoology, Chinese Academy of Sciences, Beijing 100101, China
| | - Rui-Wu Wang
- School of Ecology and Environment, Northwestern Polytechnical University, Xi'an 710072, China
| | - Xiu-Deng Zheng
- Key Laboratory of Animal Ecology and Conservation Biology, Institute of Zoology, Chinese Academy of Sciences, Beijing 100101, China.
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11
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Sakamoto Y, Ueda M. Pink-noise dynamics in an evolutionary game on a regular graph. Phys Rev E 2024; 110:034110. [PMID: 39425391 DOI: 10.1103/physreve.110.034110] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/26/2023] [Accepted: 07/16/2024] [Indexed: 10/21/2024]
Abstract
We consider a multiplayer prisoner's dilemma game on a square lattice and regular graphs based on the pairwise-Fermi update rule, and we obtain heatmaps of the fraction of cooperators and the correlation of neighboring pairs. In the heatmap, we find a mixed region where cooperators and defectors coexist, and the correlation between neighbors is significantly enhanced. Moreover, we observe pink-noise behavior in the mixed region, where the power spectrum can be fitted by a power-law function of frequency. We also find that the pink-noise behavior can be reproduced in a simple random-walk model. In particular, we propose a modified random-walk model which can reproduce not only the pink-noise behavior but also the deviation from it observed in a low-frequency region.
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Affiliation(s)
| | - Masahito Ueda
- Department of Physics, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan
- Institute for Physics of Intelligence, Graduate School of Science, The University of Tokyo, Bunkyo-ku, Tokyo 113-0033, Japan
- RIKEN Center for Emergent Matter Science (CEMS), Wako, Saitama 351-0198, Japan
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12
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Khatun K, Shen C, Shi L, Tanimoto J. Stability of pairwise social dilemma games: Destructive agents, constructive agents, and their joint effects. Phys Rev E 2024; 110:034307. [PMID: 39425340 DOI: 10.1103/physreve.110.034307] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/21/2024] [Accepted: 08/09/2024] [Indexed: 10/21/2024]
Abstract
Destructive agents, who opt out of the game and indiscriminately harm others, paradoxically foster cooperation, representing an intriguing variant of the voluntary participation strategy. Yet, their impact on cooperation remains inadequately understood, particularly in the context of pairwise social dilemma games and in comparison to their counterparts, constructive agents, who opt out of the game but indiscriminately benefit others. Furthermore, little is known about the combined effects of both agent types on cooperation dynamics. Using replicator dynamics in infinite and well-mixed populations, we find that contrary to their role in facilitating cooperation in multiplayer games, destructive agents fail to encourage cooperation in pairwise social dilemmas. Instead, they replace defection in the prisoners' dilemma and stag-hunt games. Similarly, in the chicken game, they can destabilize or replace the mixed equilibrium of cooperation and defection, undermining cooperation in the harmony (trivial) game. Conversely, constructive agents, when their payoffs exceed their contributions to opponents, can exhibit effects similar to destructive agents. However, if their payoffs are lower, while they destabilize defection in prisoners' dilemma and stag-hunt games, they do not disrupt the cooperation equilibrium in harmony games and have a negligible impact on the coexistence of cooperation in chicken games. The combination of destructive and constructive agents does not facilitate cooperation, but instead generates complex evolutionary dynamics, including bistable, tristable, and quadstable states, with outcomes contingent on their relative payoffs and game types. These results, taken together, enhance our understanding of the impact of the voluntary participation mechanism on cooperation, contributing to a more comprehensive understanding of its influence.
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13
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Lin X, Li J, Fan S. Memory and target payoff enhance cooperation in evolutionary social dilemmas. CHAOS (WOODBURY, N.Y.) 2024; 34:083104. [PMID: 39088347 DOI: 10.1063/5.0220490] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/26/2024] [Accepted: 07/13/2024] [Indexed: 08/03/2024]
Abstract
We proposed a neighbor selection mechanism based on memory and target payoff, where the target payoff is the maximum value of the group's average expected payoff. According to this mechanism, individuals prioritize selecting neighbors whose average payoffs in the last M rounds are close to the target payoff for strategy learning, aiming to maximize the group's expected payoff. Simulation results on the grid-based Prisoner's Dilemma and Snowdrift games demonstrate that this mechanism can significantly improve the group's payoff and cooperation level. Furthermore, the longer the memory length, the higher the group's payoff and cooperation level. Overall, the combination of memory and target payoff can lead to the emergence and persistence of cooperation in social dilemmas as individuals are motivated to cooperate based on both their past experiences and future goals. This interplay highlights the significance of taking into account numerous variables in comprehending and promoting cooperation within evolutionary frameworks.
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Affiliation(s)
- Xinle Lin
- Jinan University-University of Birmingham Joint Institute, Jinan University, Guangzhou 511443, China
| | - Jianhe Li
- PSBC Consumer Finance, Guangzhou 511458, China
| | - Suohai Fan
- School of Information Science and Technology, Jinan University, Guangzhou 510632, China
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14
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Ge X, He X, Yang J, Zhao Y, Liu Y, Li L. Impact of discrepant accumulations strategy on collective cooperation in multilayer networks. Sci Rep 2024; 14:16932. [PMID: 39043873 PMCID: PMC11266721 DOI: 10.1038/s41598-024-67871-4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/24/2024] [Accepted: 07/16/2024] [Indexed: 07/25/2024] Open
Abstract
Understanding large-scale cooperation among related individuals has been one of the largest challenges. Since humans are in multiple social networks, the theoretical framework of multilayer networks is perfectly suited for studying this fascinating aspect of our biology. To that effect, we here study the cooperation in evolutionary game on interdependent networks. Importantly, a part of players are set to adopt Discrepant Accumulations Strategy. Players employing this mechanism not only use their payoffs in the multilayer network as the basis for the updating process as in previous experiments, but also take into account the similarities and differences in strategies across different layers. Monte Carlo simulations demonstrate that considering the similarities and differences in strategies across layers when calculating fitness can significantly enhance the cooperation level in the system. By examining the behavior of different pairing modes within cooperators and defectors, the equilibrium state can be attributed to the evolution of correlated pairing modes between interdependent networks. Our results provide a theoretical analysis of the group cooperation induced by the Discrepant Accumulations Strategy. And we also discuss potential implications of these findings for future human experiments concerning the cooperation on multilayer networks.
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Affiliation(s)
- Xin Ge
- College of Information Science and Technology, Dalian Maritime University, Dalian, 116026, China.
| | - Xi He
- College of Information Science and Technology, Dalian Maritime University, Dalian, 116026, China
| | - Jian Yang
- College of Information Science and Technology, Dalian Maritime University, Dalian, 116026, China
| | - Yixiang Zhao
- College of Information Science and Technology, Dalian Maritime University, Dalian, 116026, China
| | - Yue Liu
- College of Information Science and Technology, Dalian Maritime University, Dalian, 116026, China
| | - Lili Li
- College of Marine Electrical Engineering, Dalian Maritime University, Dalian, 116026, China
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15
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Gao L, Pan Q, He M. Two-stage strategy update rule based on learning cost in weak prisoner's dilemma. CHAOS (WOODBURY, N.Y.) 2024; 34:073144. [PMID: 39042507 DOI: 10.1063/5.0220267] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/23/2024] [Accepted: 07/09/2024] [Indexed: 07/25/2024]
Abstract
When players are dissatisfied with their actual payoffs, they will change the actuality by learning strategy of neighbors. The more effort players put in, the more likely they are to succeed in learning. Inspired by this, this paper proposes a two-stage strategy update rule based on learning cost. The players first decide whether to learn strategy according to the updating willingness. If the players imitate the strategy of neighbors, they need to pay the learning cost. Results show that for the well-mixed population, if the updating willingness is homogeneous and remains unchanged, reducing the updating willingness or increasing the learning cost can extend the life cycle of cooperators. If the updating willingness is heterogeneous and dynamically adjusted based on the difference between the actual payoff and the expected payoff, increasing aspiration value and learning cost promotes cooperation. For the structured population, if the updating willingness is homogeneous and remains unchanged, the moderate learning cost is beneficial for cooperators to resist the temptation of defection, and reducing updating willingness makes the system maintain cooperation within a larger parameter range. If the updating willingness is heterogeneous and dynamically adjusted, the larger learning cost and the appropriate aspiration value promote cooperation. This study highlights the complex dynamics of cooperation in paid strategy learning, contributing to the theory of cooperation in the evolutionary game.
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Affiliation(s)
- Liyan Gao
- School of Mathematical Science, Dalian University of Technology, Dalian 116024, China
- School of Physics, Dalian University of Technology, Dalian 116024, China
| | - Qiuhui Pan
- School of Mathematical Science, Dalian University of Technology, Dalian 116024, China
- School of Innovation and Entrepreneurship, Dalian University of Technology, Dalian 116024, China
| | - Mingfeng He
- School of Mathematical Science, Dalian University of Technology, Dalian 116024, China
- School of Innovation and Entrepreneurship, Dalian University of Technology, Dalian 116024, China
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16
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Sadekar O, Civilini A, Gómez-Gardeñes J, Latora V, Battiston F. Evolutionary game selection creates cooperative environments. Phys Rev E 2024; 110:014306. [PMID: 39161008 DOI: 10.1103/physreve.110.014306] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/22/2023] [Accepted: 07/01/2024] [Indexed: 08/21/2024]
Abstract
The emergence of collective cooperation in competitive environments is a well-known phenomenon in biology, economics, and social systems. While most evolutionary game models focus on the evolution of strategies for a fixed game, how strategic decisions coevolve with the environment has so far mostly been overlooked. Here, we consider a game selection model where not only the strategies but also the game can change over time following evolutionary principles. Our results show that coevolutionary dynamics of games and strategies can induce novel collective phenomena, fostering the emergence of cooperative environments. When the model is taken on structured populations the architecture of the interaction network can significantly amplify pro-social behavior, with a critical role played by network heterogeneity and the presence of clustered groups of similar players, distinctive features observed in real-world populations. By unveiling the link between the evolution of strategies and games for different structured populations, our model sheds new light on the origin of social dilemmas ubiquitously observed in real-world social systems.
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Affiliation(s)
| | | | - Jesús Gómez-Gardeñes
- Department of Condensed Matter Physics, University of Zaragoza, 50009 Zaragoza, Spain
- GOTHAM Laboratory, Institute of Biocomputation and Physics of Complex Systems (BIFI), University of Zaragoza, 50018 Zaragoza, Spain
- Center for Computational Social Science, University of Kobe, 657-8501 Kobe, Japan
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17
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Ariful Kabir KM, Tanimoto J. Assessing the instantaneous social dilemma on social distancing attitudes and vaccine behavior in disease control. Sci Rep 2024; 14:14244. [PMID: 38902279 PMCID: PMC11190193 DOI: 10.1038/s41598-024-64143-z] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/13/2024] [Accepted: 06/05/2024] [Indexed: 06/22/2024] Open
Abstract
In the face of infectious disease outbreaks, the collective behavior of a society can has a profound impact on the course of the epidemic. This study investigates the instantaneous social dilemma presented by individuals' attitudes toward vaccine behavior and its influence on social distancing as a critical component in disease control strategies. The research employs a multifaceted approach, combining modeling techniques and simulation to comprehensively assess the dynamics between social distancing attitudes and vaccine uptake during disease outbreaks. With respect to modeling, we introduce a new vaccination game (VG) where, unlike conventional VG models, a 2-player and 2-strategy payoff structure is aptly embedded in the individual behavior dynamics. Individuals' willingness to adhere to social distancing measures, such as mask-wearing and physical distancing, is strongly associated with their inclination to receive vaccines. The study reveals that a positive attitude towards social distancing tends to align with a higher likelihood of vaccine acceptance, ultimately contributing to more effective disease control. As the COVID-19 pandemic has demonstrated, swift and coordinated public health measures are essential to curbing the spread of infectious diseases. This study underscores the urgency of addressing the instantaneous social dilemma posed by individuals' attitudes. By understanding the intricate relationship between these factors, policymakers, and healthcare professionals can develop tailored strategies to promote both social distancing compliance and vaccine acceptance, thereby enhancing our ability to control and mitigate the impact of disease outbreaks in the future.
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Affiliation(s)
- K M Ariful Kabir
- Department of Mathematics, Bangladesh University of Engineering and Technology, Dhaka, 1000, Bangladesh.
| | - Jun Tanimoto
- Interdisciplinary Graduate School of Engineering Sciences, Kyushu University, Kasuga-Koen, Kasuga-Shi, Fukuoka, 816-8580, Japan
- Faculty of Engineering Sciences, Kyushu University, Kasuga-Koen, Kasuga-Shi, Fukuoka, 816-8580, Japan
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18
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Wang L, Liu Y, Guo R, Zhang L, Liu L, Hua S. The paradigm of tax-reward and tax-punishment strategies in the advancement of public resource management dynamics. Proc Biol Sci 2024; 291:20240182. [PMID: 38864335 DOI: 10.1098/rspb.2024.0182] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/30/2024] [Accepted: 03/28/2024] [Indexed: 06/13/2024] Open
Abstract
In contemporary society, the effective utilization of public resources remains a subject of significant concern. A common issue arises from defectors seeking to obtain an excessive share of these resources for personal gain, potentially leading to resource depletion. To mitigate this tragedy and ensure sustainable development of resources, implementing mechanisms to either reward those who adhere to distribution rules or penalize those who do not, appears advantageous. We introduce two models: a tax-reward model and a tax-punishment model, to address this issue. Our analysis reveals that in the tax-reward model, the evolutionary trajectory of the system is influenced not only by the tax revenue collected but also by the natural growth rate of the resources. Conversely, the tax-punishment model exhibits distinct characteristics when compared with the tax-reward model, notably the potential for bistability. In such scenarios, the selection of initial conditions is critical, as it can determine the system's path. Furthermore, our study identifies instances where the system lacks stable points, exemplified by a limit cycle phenomenon, underscoring the complexity and dynamism inherent in managing public resources using these models.
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Affiliation(s)
- Lichen Wang
- College of Science, Northwest A&F University, Yangling 712100, People's Republic of China
| | - Yuyuan Liu
- College of Science, Northwest A&F University, Yangling 712100, People's Republic of China
| | - Ruqiang Guo
- College of Science, Northwest A&F University, Yangling 712100, People's Republic of China
| | - Liang Zhang
- College of Science, Northwest A&F University, Yangling 712100, People's Republic of China
| | - Linjie Liu
- College of Science, Northwest A&F University, Yangling 712100, People's Republic of China
- College of Economics and Management, Northwest A&F University, Yangling 712100, People's Republic of China
| | - Shijia Hua
- College of Science, Northwest A&F University, Yangling 712100, People's Republic of China
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19
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Nabi KN, Kabir KMA. Modelling the dynamic vaccination game with evolutionary feedback: exploring pairwise interactions and vaccine strategies. ROYAL SOCIETY OPEN SCIENCE 2024; 11:rsos.240460. [PMID: 39100173 PMCID: PMC11295992 DOI: 10.1098/rsos.240460] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 12/01/2023] [Revised: 04/24/2024] [Accepted: 05/13/2024] [Indexed: 08/06/2024]
Abstract
A novel approach rooted in co-evolutionary game theory has been introduced to investigate how the interaction between human decision-making and the dynamics of the epidemic environment can shape vaccine acceptance during disease outbreaks. This innovative framework combines two key game concepts: the cooperation-defection game and the cost-benefit vaccination game. By doing so, it enables us to delve into the various factors that influence the success of a vaccination campaign amid an outbreak. Within this framework, individuals engage in a thorough evaluation of the risks, benefits and incentives associated with either cooperating by getting vaccinated or defecting by refusing the vaccine. Additionally, it involves a careful analysis of the costs and benefits linked to vaccine acceptance. The outcomes of this study stress the importance of two main factors: the effectiveness of the vaccine and the prevalence of a cooperative culture within society. This insight into the strategic interactions between individuals and their decisions about vaccination holds significant implications for public health policymakers. It equips to boost vaccination coverage and address vaccine hesitancy within society ultimately contributing to better public health outcomes during epidemic outbreaks.
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Affiliation(s)
- Khondoker Nazmoon Nabi
- Department of Mathematics, Bangladesh University of Engineering and Technology, Dhaka1000, Bangladesh
| | - K. M. Ariful Kabir
- Department of Mathematics, Bangladesh University of Engineering and Technology, Dhaka1000, Bangladesh
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20
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Shi L, He Z, Shen C, Tanimoto J. Enhancing social cohesion with cooperative bots in societies of greedy, mobile individuals. PNAS NEXUS 2024; 3:pgae223. [PMID: 38881842 PMCID: PMC11179109 DOI: 10.1093/pnasnexus/pgae223] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 03/11/2024] [Accepted: 05/24/2024] [Indexed: 06/18/2024]
Abstract
Addressing collective issues in social development requires a high level of social cohesion, characterized by cooperation and close social connections. However, social cohesion is challenged by selfish, greedy individuals. With the advancement of artificial intelligence (AI), the dynamics of human-machine hybrid interactions introduce new complexities in fostering social cohesion. This study explores the impact of simple bots on social cohesion from the perspective of human-machine hybrid populations within network. By investigating collective self-organizing movement during migration, results indicate that cooperative bots can promote cooperation, facilitate individual aggregation, and thereby enhance social cohesion. The random exploration movement of bots can break the frozen state of greedy population, help to separate defectors in cooperative clusters, and promote the establishment of cooperative clusters. However, the presence of defective bots can weaken social cohesion, underscoring the importance of carefully designing bot behavior. Our research reveals the potential of bots in guiding social self-organization and provides insights for enhancing social cohesion in the era of human-machine interaction within social networks.
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Affiliation(s)
- Lei Shi
- School of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming 650221, China
- Interdisciplinary Research Institute of data science, Shanghai Lixin University of Accounting and Finance, Shanghai 201209, China
| | - Zhixue He
- School of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming 650221, China
- Interdisciplinary Graduate School of Engineering Sciences, Kyushu University, Fukuoka 816-8580, Japan
| | - Chen Shen
- Faculty of Engineering Sciences, Kyushu University, Fukuoka 816-8580, Japan
| | - Jun Tanimoto
- Faculty of Engineering Sciences, Kyushu University, Fukuoka 816-8580, Japan
- Interdisciplinary Graduate School of Engineering Sciences, Kyushu University, Fukuoka 816-8580, Japan
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21
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Pulcu E. Individualistic attitudes in Iterated Prisoner's Dilemma undermine evolutionary fitness and may drive cooperative human players to extinction. ROYAL SOCIETY OPEN SCIENCE 2024; 11:230867. [PMID: 38550758 PMCID: PMC10977385 DOI: 10.1098/rsos.230867] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 06/21/2023] [Revised: 12/22/2023] [Accepted: 02/09/2024] [Indexed: 04/26/2024]
Abstract
Inarguably, humans perform the richest plethora of prosocial behaviours in the animal kingdom, and these are important for understanding how humans navigate their social environment. The success and failure of strategies human players devise also have implications for determining long-term socio-economic/evolutionary fitness. Following the footsteps of Press and Dyson (2012), I implemented their evolutionary game-theoretic modelling from Iterated Prisoner's Dilemma (a behavioural economic probe of interpersonal cooperation) and re-analysed already published data on human proposer behaviour in the Ultimatum Game (a behavioural economic probe of altruistic punishment) involving 50 human participants versus stochastic computerized opponents with prosocial and individualistic social value orientations. Although the results indicate that it is more likely to break cycles of mutual defection in ecosystems in which humans interact with individualistic opponents, analysis of social-economic fitness at the Markov stationary states suggested that this comes at an evolutionary cost. Overall, human players acted in a significantly more cooperative manner than their opponents, but they failed to overcome extortion from individualistic agents, risking 'extinction' in 70% of the cases. These findings demonstrate human players might be short-sighted, and social interactive decision strategies they devise while adjusting to different types of opponents may not be optimal in the long run.
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Affiliation(s)
- Erdem Pulcu
- Department of Psychiatry, Psychopharmacology and Emotion Research Lab, Computational Psychiatry Lab, University of Oxford, Oxford, UK
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22
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Shen C, He Z, Shi L, Wang Z, Tanimoto J. Prosocial punishment bots breed social punishment in human players. J R Soc Interface 2024; 21:20240019. [PMID: 38471533 PMCID: PMC10932715 DOI: 10.1098/rsif.2024.0019] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/10/2024] [Accepted: 02/14/2024] [Indexed: 03/14/2024] Open
Abstract
Prosocial punishment, an important factor to stabilize cooperation in social dilemma games, often faces challenges like second-order free-riders-who cooperate but avoid punishing to save costs-and antisocial punishers, who defect and retaliate against cooperators. Addressing these challenges, our study introduces prosocial punishment bots that consistently cooperate and punish free-riders. Our findings reveal that these bots significantly promote the emergence of prosocial punishment among normal players due to their 'sticky effect'-an unwavering commitment to cooperation and punishment that magnetically attracts their opponents to emulate this strategy. Additionally, we observe that the prevalence of prosocial punishment is greatly enhanced when normal players exhibit a tendency to follow a 'copying the majority' strategy, or when bots are strategically placed in high-degree nodes within scale-free networks. Conversely, bots designed for defection or antisocial punishment diminish overall cooperation levels. This stark contrast underscores the critical role of strategic bot design in enhancing cooperative behaviours in human/AI interactions. Our findings open new avenues in evolutionary game theory, demonstrating the potential of human-machine collaboration in solving the conundrum of punishment.
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Affiliation(s)
- Chen Shen
- Faculty of Engineering Sciences, Kyushu University, Fukuoka, 816-8580, Japan
| | - Zhixue He
- Interdisciplinary Graduate School of Engineering Sciences, Kyushu University, Fukuoka, 816-8580, Japan
- School of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming 650221, People’s Republic of China
| | - Lei Shi
- School of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming 650221, People’s Republic of China
| | - Zhen Wang
- Center for OPTical IMagery Analysis and Learning (OPTIMAL), Northwestern Polytechnical University, Xi’an 710072, People’s Republic of China
- School of Mechanical Engineering, Northwestern Polytechnical University, Xi’an 710072, People’s Republic of China
| | - Jun Tanimoto
- Faculty of Engineering Sciences, Kyushu University, Fukuoka, 816-8580, Japan
- Interdisciplinary Graduate School of Engineering Sciences, Kyushu University, Fukuoka, 816-8580, Japan
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23
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Guo H, Shen C, Zou R, Tao P, Shi Y, Wang Z, Xing J. Complex pathways to cooperation emergent from asymmetry in heterogeneous populations. CHAOS (WOODBURY, N.Y.) 2024; 34:023139. [PMID: 38416672 DOI: 10.1063/5.0188177] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/20/2023] [Accepted: 02/02/2024] [Indexed: 03/01/2024]
Abstract
Cooperation within asymmetric populations has garnered significant attention in evolutionary games. This paper explores cooperation evolution in populations with weak and strong players, using a game model where players choose between cooperation and defection. Asymmetry stems from different benefits for strong and weak cooperators, with their benefit ratio indicating the degree of asymmetry. Varied rankings of parameters including the asymmetry degree, cooperation costs, and benefits brought by weak players give rise to scenarios including the prisoner's dilemma (PDG) for both player types, the snowdrift game (SDG), and mixed PDG-SDG interactions. Our results indicate that in an infinite well-mixed population, defection remains the dominant strategy when strong players engage in the prisoner's dilemma game. However, if strong players play snowdrift games, global cooperation increases with the proportion of strong players. In this scenario, strong cooperators can prevail over strong defectors when the proportion of strong players is low, but the prevalence of cooperation among strong players decreases as their proportion increases. In contrast, within a square lattice, the optimum global cooperation emerges at intermediate proportions of strong players with moderate degrees of asymmetry. Additionally, weak players protect cooperative clusters from exploitation by strong defectors. This study highlights the complex dynamics of cooperation in asymmetric interactions, contributing to the theory of cooperation in asymmetric games.
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Affiliation(s)
- Hao Guo
- Department of Computer Science and Technology, Tsinghua University, Beijing 100084, China
| | - Chen Shen
- Faculty of Engineering Sciences, Kyushu University, Fukuoka 816-8580, Japan
| | - Rongcheng Zou
- School of Automation, Northwestern Polytechnical University, Xi'an 710072, China
| | - Pin Tao
- Department of Computer Science and Technology, Tsinghua University, Beijing 100084, China
| | - Yuanchun Shi
- Department of Computer Science and Technology, Tsinghua University, Beijing 100084, China
| | - Zhen Wang
- School of Artificial Intelligence, Optics and Electronics (iOPEN), Northwestern Polytechnical University, Xi'an 710072, China
| | - Junliang Xing
- Department of Computer Science and Technology, Tsinghua University, Beijing 100084, China
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24
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Alfaro G, Sanjuán MAF. Hamming distance as a measure of spatial chaos in evolutionary games. Phys Rev E 2024; 109:014203. [PMID: 38366401 DOI: 10.1103/physreve.109.014203] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/08/2023] [Accepted: 12/05/2023] [Indexed: 02/18/2024]
Abstract
From a context of evolutionary dynamics, social games can be studied as complex systems that may converge to a Nash equilibrium. Nonetheless, they can behave in an unpredictable manner when looking at the spatial patterns formed by the agents' strategies. This is known in the literature as spatial chaos. In this paper we analyze the problem for a deterministic prisoner's dilemma and a public goods game and calculate the Hamming distance that separates two solutions that start at very similar initial conditions for both cases. The rapid growth of this distance indicates the high sensitivity to initial conditions, which is a well-known indicator of chaotic dynamics.
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Affiliation(s)
- Gaspar Alfaro
- Nonlinear Dynamics, Chaos and Complex Systems Group, Departamento de Física, Universidad Rey Juan Carlos, Tulipán s/n, Móstoles, 28933 Madrid, Spain
| | - Miguel A F Sanjuán
- Nonlinear Dynamics, Chaos and Complex Systems Group, Departamento de Física, Universidad Rey Juan Carlos, Tulipán s/n, Móstoles, 28933 Madrid, Spain
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25
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Guo H, Shen C, Hu S, Xing J, Tao P, Shi Y, Wang Z. Facilitating cooperation in human-agent hybrid populations through autonomous agents. iScience 2023; 26:108179. [PMID: 37920671 PMCID: PMC10618689 DOI: 10.1016/j.isci.2023.108179] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/19/2023] [Revised: 07/10/2023] [Accepted: 10/09/2023] [Indexed: 11/04/2023] Open
Abstract
Cooperative AI has shown its effectiveness in solving the conundrum of cooperation. Understanding how cooperation emerges in human-agent hybrid populations is a topic of significant interest, particularly in the realm of evolutionary game theory. In this article, we scrutinize how cooperative and defective Autonomous Agents (AAs) influence human cooperation in social dilemma games with a one-shot setting. Focusing on well-mixed populations, we find that cooperative AAs have a limited impact in the prisoner's dilemma games but facilitate cooperation in the stag hunt games. Surprisingly, defective AAs can promote complete dominance of cooperation in the snowdrift games. As the proportion of AAs increases, both cooperative and defective AAs have the potential to cause human cooperation to disappear. We then extend our investigation to consider the pairwise comparison rule and complex networks, elucidating that imitation strength and population structure are critical for the emergence of human cooperation in human-agent hybrid populations.
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Affiliation(s)
- Hao Guo
- School of Artificial Intelligence, Optics and Electronics (iOPEN), Northwestern Polytechnical University, Xi’an 710072, China
- Department of Computer Science and Technology, Tsinghua University, Beijing 100084, China
| | - Chen Shen
- Faculty of Engineering Sciences, Kyushu University, Kasuga-koen, Kasuga-shi, Fukuoka 816-8580, Japan
| | - Shuyue Hu
- Shanghai Artificial Intelligence Laboratory, Shanghai, China
| | - Junliang Xing
- Department of Computer Science and Technology, Tsinghua University, Beijing 100084, China
| | - Pin Tao
- Department of Computer Science and Technology, Tsinghua University, Beijing 100084, China
| | - Yuanchun Shi
- Department of Computer Science and Technology, Tsinghua University, Beijing 100084, China
| | - Zhen Wang
- School of Artificial Intelligence, Optics and Electronics (iOPEN), Northwestern Polytechnical University, Xi’an 710072, China
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26
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Fischer I, Savranevski L. The effect of similarity perceptions on human cooperation and confrontation. Sci Rep 2023; 13:19849. [PMID: 37963961 PMCID: PMC10645908 DOI: 10.1038/s41598-023-46609-8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/22/2022] [Accepted: 11/02/2023] [Indexed: 11/16/2023] Open
Abstract
By assuring aversive actions are followed by similarly aversive reactions, legislators of antiquity aimed to reduce belligerence and aggression. In the present study we show how similarity perceptions drive cooperation and confrontation across several strategic decision types. Examining the choices made in three one-shot symmetric conflict games: the prisoner's dilemma, the chicken, and the battle of the sexes, we show how a short encounter with a stranger accounts for the formation of subjective similarity perceptions, which together with the expected payoffs of the game determine the choice of the preferred alternative. We describe the role of similarity perceptions for all two-by-two games, specifically for a subset of fifty-seven games that are sensitive to similarity perceptions with the opponent. We then suggest that this mechanism, by which individuals maximize expected payoffs, is key to the understanding of the evolution of cooperation and confrontation.
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Affiliation(s)
- Ilan Fischer
- School of Psychological Sciences, University of Haifa, Haifa, Israel.
| | - Lior Savranevski
- School of Psychological Sciences, University of Haifa, Haifa, Israel
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27
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Ariful Kabir KM. Behavioral vaccination policies and game-environment feedback in epidemic dynamics. Sci Rep 2023; 13:14520. [PMID: 37666863 PMCID: PMC10477251 DOI: 10.1038/s41598-023-41420-x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/09/2023] [Accepted: 08/26/2023] [Indexed: 09/06/2023] Open
Abstract
Many policymakers have adopted voluntary vaccination policies to alleviate the consequences of contagious diseases. Such policies have several well-established feathers, i.e. they are seasonal, depending on an individual's decision, adaptive, and control epidemic activity. Here, we study ideas from behavioral epidemiology embedded with a vaccination game and pairwise two-player two-strategy game to represent the environmental feedback in an SVIR model by using a composite information index including disease incidence, vaccine factors and cooperative behavior on a global time scale (repeated season). In its turn, the information index's game dynamics to participate in the vaccine program (cooperation) is supposed to reflect the feedback-evolving dynamics of competitive cognitions and the environment. The assuming model is described by two different evolutionary game systems connected by an unknown external public opinion environment feedback. The embedded model is described by an inherited system showing a behavioral aspect, i.e. pairwise game indicates an individual's cooperative behavior, and a vaccine game refers to vaccine-cost influence. This is a novel attempt to stabilize the two different decision processes to pool them into a single index. Extensive simulations suggest a rich spectrum of achievable results, including epidemic control, human behavior, social dilemma, and policy suggestions.
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Affiliation(s)
- K M Ariful Kabir
- Department of Mathematics, Bangladesh University of Engineering and Technology, Dhaka, 1000, Bangladesh.
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28
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Xing Z, Yang Y, Hu Z. Nash equilibrium realization of population games based on social learning processes. MATHEMATICAL BIOSCIENCES AND ENGINEERING : MBE 2023; 20:17116-17137. [PMID: 37920049 DOI: 10.3934/mbe.2023763] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/04/2023]
Abstract
In the two-population game model, we assume the players have certain imitative learning abilities. To simulate the learning process of the game players, we propose a new swarm intelligence algorithm by combining the particle swarm optimization algorithm, where each player can be considered a particle. We conduct simulations for three typical games: the prisoner's dilemma game (with only one pure-strategy Nash equilibrium), the coin-flip game (with only one fully-mixed Nash equilibrium), and the coordination game (with two pure-strategy Nash equilibria and one fully-mixed Nash equilibrium). The results show that when the game has a pure strategy Nash equilibrium, the algorithm converges to that equilibrium. However, if the game does not have a pure strategy Nash equilibrium, it exhibits periodic convergence to the only mixed-strategy Nash equilibrium. Furthermore, the magnitude of the periodical convergence is inversely proportional to the introspection rate. After conducting experiments, our algorithm outperforms the Meta Equilibrium Q-learning algorithm in realizing mixed-strategy Nash equilibrium.
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Affiliation(s)
- Zhiyan Xing
- School of Mathematics and Statistics, Guizhou University, Guiyang 550025, China
| | - Yanlong Yang
- School of Mathematics and Statistics, Guizhou University, Guiyang 550025, China
| | - Zuopeng Hu
- School of Mathematics and Statistics, Guizhou University, Guiyang 550025, China
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29
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El-Salam SMA, El-Seidy E, Abdel-Malek AR. Evaluating zero-determinant strategies’ effects on cooperation and conflict resolution in repeated games. CHAOS, SOLITONS & FRACTALS 2023; 174:113779. [DOI: 10.1016/j.chaos.2023.113779] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 09/02/2023]
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30
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Sharma G, Guo H, Shen C, Tanimoto J. Small bots, big impact: solving the conundrum of cooperation in optional Prisoner's Dilemma game through simple strategies. J R Soc Interface 2023; 20:20230301. [PMID: 37464799 PMCID: PMC10354466 DOI: 10.1098/rsif.2023.0301] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/24/2023] [Accepted: 06/28/2023] [Indexed: 07/20/2023] Open
Abstract
Cooperation plays a crucial role in both nature and human society, and the conundrum of cooperation attracts the attention from interdisciplinary research. In this study, we investigated the evolution of cooperation in optional Prisoner's Dilemma games by introducing simple bots. We focused on one-shot and anonymous games, where the bots could be programmed to always cooperate, always defect, never participate or choose each action with equal probability. Our results show that cooperative bots facilitate the emergence of cooperation among ordinary players in both well-mixed populations and a regular lattice under weak imitation scenarios. Introducing loner bots has no impact on the emergence of cooperation in well-mixed populations, but it facilitates the dominance of cooperation in regular lattices under strong imitation scenarios. However, too many loner bots on a regular lattice inhibit the spread of cooperation and can eventually result in a breakdown of cooperation. Our findings emphasize the significance of bot design in promoting cooperation and offer useful insights for encouraging cooperation in real-world scenarios.
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Affiliation(s)
- Gopal Sharma
- Interdisciplinary Graduate School of Engineering Sciences, Kyushu University, Fukuoka, 816-8580, Japan
| | - Hao Guo
- School of Mechanical Engineering, Northwestern Polytechnical University, Xi’an 710072, People’s Republic of China
- School of Artificial Intelligence, Optics and Electronics (iOPEN), Northwestern Polytechnical University, Xi’an 710072, People’s Republic of China
| | - Chen Shen
- Faculty of Engineering Sciences, Kyushu University, Kasuga-koen, Kasuga-shi, Fukuoka 816-8580, Japan
| | - Jun Tanimoto
- Interdisciplinary Graduate School of Engineering Sciences, Kyushu University, Fukuoka, 816-8580, Japan
- Faculty of Engineering Sciences, Kyushu University, Kasuga-koen, Kasuga-shi, Fukuoka 816-8580, Japan
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31
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Murase Y, Baek SK. Grouping promotes both partnership and rivalry with long memory in direct reciprocity. PLoS Comput Biol 2023; 19:e1011228. [PMID: 37339134 PMCID: PMC10313083 DOI: 10.1371/journal.pcbi.1011228] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/11/2023] [Revised: 06/30/2023] [Accepted: 05/30/2023] [Indexed: 06/22/2023] Open
Abstract
Biological and social scientists have long been interested in understanding how to reconcile individual and collective interests in the iterated Prisoner's Dilemma. Many effective strategies have been proposed, and they are often categorized into one of two classes, 'partners' and 'rivals.' More recently, another class, 'friendly rivals,' has been identified in longer-memory strategy spaces. Friendly rivals qualify as both partners and rivals: They fully cooperate with themselves, like partners, but never allow their co-players to earn higher payoffs, like rivals. Although they have appealing theoretical properties, it is unclear whether they would emerge in an evolving population because most previous works focus on the memory-one strategy space, where no friendly rival strategy exists. To investigate this issue, we have conducted evolutionary simulations in well-mixed and group-structured populations and compared the evolutionary dynamics between memory-one and longer-memory strategy spaces. In a well-mixed population, the memory length does not make a major difference, and the key factors are the population size and the benefit of cooperation. Friendly rivals play a minor role because being a partner or a rival is often good enough in a given environment. It is in a group-structured population that memory length makes a stark difference: When longer-memory strategies are available, friendly rivals become dominant, and the cooperation level nearly reaches a maximum, even when the benefit of cooperation is so low that cooperation would not be achieved in a well-mixed population. This result highlights the important interaction between group structure and memory lengths that drive the evolution of cooperation.
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Affiliation(s)
- Yohsuke Murase
- RIKEN Center for Computational Science, Kobe, Japan
- Max Planck Research Group ‘Dynamics of Social Behavior,’ Max Planck Institute for Evolutionary Biology, Plön, Germany
| | - Seung Ki Baek
- Department of Scientific Computing, Pukyong National University, Busan, Korea
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32
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Wang SY, Yao X, Yang YM, Chen D, Wang RW, Xie FJ. Super-rational aspiration promotes cooperation in the asymmetric game with peer exit punishment and reward. Heliyon 2023; 9:e16729. [PMID: 37346327 PMCID: PMC10279827 DOI: 10.1016/j.heliyon.2023.e16729] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/31/2022] [Revised: 05/19/2023] [Accepted: 05/25/2023] [Indexed: 06/23/2023] Open
Abstract
Super-rational aspiration induced strategy updating with exit rights has been considered in some previous studies, in which the players adjust strategies in line with their payoffs and aspirations, and they have access to exit the game. However, exit payoffs for exiting players are automatically allocated, which is clearly contrary to reality. In this study, evolutionary cooperation dynamics with super-rational aspiration and asymmetry in the Prisoner's Dilemma game is investigated, where exit payoffs are implemented by local peers. The results show that for different population structures, the asymmetry of the system is always contributive to the participation of the players. Furthermore, we show that under different exit payoffs, super-rationality and asymmetry are conductive to the evolution of cooperation.
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Affiliation(s)
- Si-Yi Wang
- School of Modern Posts, Xi’an University of Posts & Telecommunications, Xi’an, Shaanxi, 710061, China
| | - Xin Yao
- School of Modern Posts, Xi’an University of Posts & Telecommunications, Xi’an, Shaanxi, 710061, China
| | - Yi-Mei Yang
- Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an, 710129, China
| | - Daniel Chen
- The High School Affiliated to Renmin University of China, Beijing, 100097, China
| | - Rui-Wu Wang
- School of Ecology and Environment, Northwestern Polytechnical University, Xi'an, 710129, China
| | - Feng-Jie Xie
- School of Modern Posts, Xi’an University of Posts & Telecommunications, Xi’an, Shaanxi, 710061, China
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33
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Ariful Kabir K, Shahidul Islam MD, Nijhum S. Exploring the performance of volatile mutations on evolutionary game dynamics in complex networks. Heliyon 2023; 9:e16790. [PMID: 37313171 PMCID: PMC10258425 DOI: 10.1016/j.heliyon.2023.e16790] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/12/2023] [Revised: 05/25/2023] [Accepted: 05/28/2023] [Indexed: 06/15/2023] Open
Abstract
The typical framework of replicator dynamics in evolutionary game theory assumes that all mutations are equally likely, meaning that the mutation of an evolving inhabitant only contributes constantly. However, in natural systems in biological and social sciences, mutations can arise due to their repetitive regeneration. The phenomenon of changing strategies (updating), typically prolonged sequences repeated many times, is defined as a volatile mutation that has been overlooked in evolutionary game theory. Implementing a repeated time framework introduces a dynamic mutation aspect incorporated with the pairwise Fermi rule. Network structure, ubiquitous in many natural and artificial systems, has significantly affected the dynamics and outcomes of evolutionary games. We examine the evolution of the pairwise game in terms of dilemma strength. It is revealed that mutation intensity can influence evolutionary dynamics. We also demonstrated that the obtained outcomes run by the deterministic and multi-agent simulation (MAS) process present similar stability regions for both linear and non-linear dynamics, even in various game classes. In particular, the most stimulating effect is detected for the relationship between the fraction of cooperation and the fraction of the mutated individuals, as inclination tends to provide an increasing tendency and supporting defection in the opposite case. In conclusion, we identified a form of volatile mutation as a form of noise that, under certain situations, could be used to enhance cooperation in social systems and design strategies for promoting cooperation in networked environments.
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Affiliation(s)
- K.M. Ariful Kabir
- Department of Mathematics, Bangladesh University of Engineering and Technology, Dhaka, 1000, Bangladesh
| | - MD Shahidul Islam
- Department of Computer Science and Engineering, Green University of Bangladesh, Dhaka, Bangladesh
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Liu L, Chen X, Szolnoki A. Coevolutionary dynamics via adaptive feedback in collective-risk social dilemma game. eLife 2023; 12:82954. [PMID: 37204305 DOI: 10.7554/elife.82954] [Citation(s) in RCA: 11] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/24/2022] [Accepted: 04/26/2023] [Indexed: 05/20/2023] Open
Abstract
Human society and natural environment form a complex giant ecosystem, where human activities not only lead to the change in environmental states, but also react to them. By using collective-risk social dilemma game, some studies have already revealed that individual contributions and the risk of future losses are inextricably linked. These works, however, often use an idealistic assumption that the risk is constant and not affected by individual behaviors. Here, we develop a coevolutionary game approach that captures the coupled dynamics of cooperation and risk. In particular, the level of contributions in a population affects the state of risk, while the risk in turn influences individuals' behavioral decision-making. Importantly, we explore two representative feedback forms describing the possible effect of strategy on risk, namely, linear and exponential feedbacks. We find that cooperation can be maintained in the population by keeping at a certain fraction or forming an evolutionary oscillation with risk, independently of the feedback type. However, such evolutionary outcome depends on the initial state. Taken together, a two-way coupling between collective actions and risk is essential to avoid the tragedy of the commons. More importantly, a critical starting portion of cooperators and risk level is what we really need for guiding the evolution toward a desired direction.
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Affiliation(s)
- Linjie Liu
- College of Science, Northwest A & F University, Yangling, China
- School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, China
| | - Xiaojie Chen
- School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, China
| | - Attila Szolnoki
- Institute of Technical Physics and Materials Science, Centre for Energy Research, Budapest, Hungary
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35
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Hu K, Wang P, He J, Perc M, Shi L. Complex evolutionary interactions in multiple populations. Phys Rev E 2023; 107:044301. [PMID: 37198848 DOI: 10.1103/physreve.107.044301] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/01/2022] [Accepted: 03/22/2023] [Indexed: 05/19/2023]
Abstract
In competitive settings that entail several populations, individuals often engage in intra- and interpopulation interactions that determine their fitness and evolutionary success. With this simple motivation, we here study a multipopulation model where individuals engage in group interactions within their own population and in pairwise interactions with individuals from different populations. We use the evolutionary public goods game and the prisoner's dilemma game to describe these group and pairwise interactions, respectively. We also take into account asymmetry in the extent to which group and pairwise interactions determine the fitness of individuals. We find that interactions across multiple populations reveal new mechanisms through which the evolution of cooperation can be promoted, but this depends on the level of interaction asymmetry. If inter- and intrapopulation interactions are symmetric, the sole presence of multiple populations promotes the evolution of cooperation. Asymmetry in the interactions can further promote cooperation at the expense of the coexistence of the competing strategies. An in-depth analysis of the spatiotemporal dynamics reveals loop-dominated structures and pattern formation that can explain the various evolutionary outcomes. Thus, complex evolutionary interactions in multiple populations reveal an intricate interplay between cooperation and coexistence, and they also open up the path toward further explorations of multipopulation games and biodiversity.
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Affiliation(s)
- Kaipeng Hu
- School of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming 650221, China
| | - Pengyue Wang
- School of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming 650221, China
| | - Junzhou He
- School of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming 650221, China
| | - Matjaž Perc
- Faculty of Natural Sciences and Mathematics, University of Maribor, 2000 Maribor, Slovenia
- Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 404332, Taiwan
- Alma Mater Europaea, 2000 Maribor, Slovenia
- Complexity Science Hub Vienna, 1080 Vienna, Austria
- Department of Physics, Kyung Hee University, 26 Kyungheedae-ro, Dongdaemun-gu, Seoul, Republic of Korea
| | - Lei Shi
- School of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming 650221, China
- Interdisciplinary Research Institute of Data Science, Shanghai Lixin University of Accounting and Finance, Shanghai 201209, China
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36
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Lu S, Zhu G, Zhang L. The promoting effect of adaptive persistence aspiration on the cooperation based on the consideration of payoff and environment in prisoner's dilemma game. Biosystems 2023; 226:104868. [PMID: 36841505 DOI: 10.1016/j.biosystems.2023.104868] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/05/2023] [Revised: 02/19/2023] [Accepted: 02/20/2023] [Indexed: 02/26/2023]
Abstract
This work explores whether holding the last aspiration for a period of time can promote cooperation. Specifically, an evolutionary spatial prisoner's dilemma game mode is proposed, in which the players adjust strategies and aspirations by considering the payoff and environment. Therefore, the core is to allow players to hold the current aspiration for a period of time. Through numerical calculation, this study finds that the existence of an appropriate duration of aspiration can promote cooperation when b is less than a certain value. Moreover, the cooperation is gradually enhanced with the increase of T-max (maximum aspiration duration) when b is greater than it, but the enhancing effect is limited. It is also found that an appropriate value α (sensitivity to environmental change) can promote cooperation at different b intervals. Besides, this system indicates good robustness. Overall, this study provides a new perspective on exploring cooperative evolution based on aspiration.
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Affiliation(s)
- Shounan Lu
- School of Science, Beijing University of Posts and Telecommunications, Beijing, 100876, China.
| | - Ge Zhu
- School of Information Management, Beijing Information Science and Technology University, Beijing, 100192, China; Owen Graduate School of Management, Vanderbilt University, Nashville, 37203, USA
| | - Lianzhong Zhang
- School of Physics, Nankai University, Tianjin, 300071, China.
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37
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Zheng Y. University teachers' scientific research innovation incentive based on the three-party evolutionary game of the state, the colleges, and scientific researchers. Front Psychol 2023; 13:973333. [PMID: 36710812 PMCID: PMC9878385 DOI: 10.3389/fpsyg.2022.973333] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/20/2022] [Accepted: 12/19/2022] [Indexed: 01/13/2023] Open
Abstract
Scientific research in colleges and universities is of great significance to national innovation. Based on the evolutionary game theory, this paper constructs a theoretical model of the state, universities, and researchers. This paper also conducts numerical simulation on the model. The results reveal that when the scientific researchers' success rate reaches a certain threshold, more and more scientific researchers will choose to invest in scientific research. Then, universities and the state will hold a long-term incentive attitude toward scientific research and scientific innovation. The study further found that the greater the success rate of researchers, the faster universities and the state will actively encourage scientific research.
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38
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Wang Y, Meng X. Evolutionary game dynamics of cooperation in prisoner's dilemma with time delay. MATHEMATICAL BIOSCIENCES AND ENGINEERING : MBE 2023; 20:5024-5042. [PMID: 36896534 DOI: 10.3934/mbe.2023233] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/18/2023]
Abstract
Cooperation is an indispensable behavior in biological systems. In the prisoner's dilemma, due to the individual's selfish psychology, the defector is in the dominant position finally, which results in a social dilemma. In this paper, we discuss the replicator dynamics of the prisoner's dilemma with penalty and mutation. We first discuss the equilibria and stability of the prisoner's dilemma with a penalty. Then, the critical delay of the bifurcation with the payoff delay as the bifurcation parameter is obtained. In addition, considering the case of player mutation based on penalty, we analyze the two-delay system containing payoff delay and mutation delay and find the critical delay of Hopf bifurcation. Theoretical analysis and numerical simulations show that cooperative and defective strategies coexist when only a penalty is added. The larger the penalty is, the more players tend to cooperate, and the critical time delay of the time-delay system decreases with the increase in penalty. The addition of mutation has little effect on the strategy chosen by players. The two-time delay also causes oscillation.
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Affiliation(s)
- Yifei Wang
- College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, PR China
| | - Xinzhu Meng
- College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, PR China
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39
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Impact of social reward on the evolution of cooperation in voluntary prisoner's dilemma. Biosystems 2023; 223:104821. [PMID: 36464161 DOI: 10.1016/j.biosystems.2022.104821] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/26/2022] [Revised: 11/26/2022] [Accepted: 11/28/2022] [Indexed: 12/02/2022]
Abstract
The existence and sustainability of cooperation is a critical issue in nature and social systems. Reward is an essential mechanism to enhance cooperation. Meanwhile, some individuals loathe competition and then choose to escape and become a loner in competition. In this scenario, we propose a four-strategy networked evolutionary game model involving rewarders, loners, cooperators, and defectors. The classical square lattice and the Erdös-Rényi random network are adopted to describe the interaction between individuals. The four-strategy model is an extension of the classic prisoner's dilemma game model. The simulation results show that the introduction of new strategic choices can significantly improve cooperation in the population. The promotion level of cooperation is directly correlated with reward intensity and negatively correlated with reward cost. With regard to the evolution of altruistic behaviors, the fixed income from interactions with loners has an impact that is connected to the temptation to defect. Furthermore, by analyzing characteristic snapshots of four strategies, we further dissect the essence of the evolution of cooperation. As the temptation value increases, cooperators and rewarders first form compact clusters, then more and more loners join to resist the intrusion of defectors. Eventually, the three strategies coexist stably in a spatially structured population. Our research may shed some light on exploring the nature of cooperation and solving social dilemmas in the future.
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40
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Ito H, Wada T, Ichinose G, Tanimoto J, Yoshimura J, Yamamoto T, Morita S. Social dilemma in the excess use of antimicrobials incurring antimicrobial resistance. Sci Rep 2022; 12:21084. [PMID: 36473931 PMCID: PMC9726979 DOI: 10.1038/s41598-022-25632-1] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/19/2022] [Accepted: 12/02/2022] [Indexed: 12/12/2022] Open
Abstract
The emergence of antimicrobial resistance (AMR) caused by the excess use of antimicrobials has come to be recognized as a global threat to public health. There is a 'tragedy of the commons' type social dilemma behind this excess use of antimicrobials, which should be recognized by all stakeholders. To address this global threat, we thus surveyed eight countries/areas to determine whether people recognize this dilemma and showed that although more than half of the population pays little, if any, attention to it, almost 20% recognize this social dilemma, and 15-30% of those have a positive attitude toward solving that dilemma. We suspect that increasing individual awareness of this social dilemma contributes to decreasing the frequency of AMR emergencies.
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Affiliation(s)
- Hiromu Ito
- grid.174567.60000 0000 8902 2273Department of International Health and Medical Anthropology, Institute of Tropical Medicine, Nagasaki University, Nagasaki, Japan
| | - Takayuki Wada
- Graduate School of Human Life and Ecology, Osaka Metropolitan University, Osaka, Japan
| | - Genki Ichinose
- grid.263536.70000 0001 0656 4913Graduate School of Science and Technology and Department of Mathematical and Systems Engineering, Shizuoka University, Shizuoka, Japan
| | - Jun Tanimoto
- grid.177174.30000 0001 2242 4849Department of Energy and Environmental Engineering, Interdisciplinary Graduate School of Engineering Sciences, Kyushu University, Fukuoka, Japan ,grid.177174.30000 0001 2242 4849Department of Advanced Environmental Science and Engineering, Faculty of Engineering Sciences, Kyushu University, Fukuoka, Japan
| | - Jin Yoshimura
- grid.174567.60000 0000 8902 2273Department of International Health and Medical Anthropology, Institute of Tropical Medicine, Nagasaki University, Nagasaki, Japan ,grid.263536.70000 0001 0656 4913Graduate School of Science and Technology and Department of Mathematical and Systems Engineering, Shizuoka University, Shizuoka, Japan ,grid.136304.30000 0004 0370 1101Marine Biosystems Research Center, Chiba University, Chiba, Japan ,grid.265074.20000 0001 1090 2030Department of Biological Science, Tokyo Metropolitan University, Tokyo, Japan ,grid.26999.3d0000 0001 2151 536XUniversity Museum, The University of Tokyo, Tokyo, Japan
| | - Taro Yamamoto
- grid.174567.60000 0000 8902 2273Department of International Health and Medical Anthropology, Institute of Tropical Medicine, Nagasaki University, Nagasaki, Japan
| | - Satoru Morita
- grid.263536.70000 0001 0656 4913Graduate School of Science and Technology and Department of Mathematical and Systems Engineering, Shizuoka University, Shizuoka, Japan
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41
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Song Z, Guo H, Jia D, Perc M, Li X, Wang Z. Reinforcement learning facilitates an optimal interaction intensity for cooperation. Neurocomputing 2022. [DOI: 10.1016/j.neucom.2022.09.109] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
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42
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Guo H, Wang Z, Song Z, Yuan Y, Deng X, Li X. Effect of state transition triggered by reinforcement learning in evolutionary prisoner’s dilemma game. Neurocomputing 2022. [DOI: 10.1016/j.neucom.2022.08.023] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/14/2022]
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43
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Abd El-Naby AEHEH, Elrayes HA, Tarabia AMK, Elgazzar AS. Influence of the Asymmetry of the Strategy Spaces on the Properties of the Quantum Prisoner’s Dilemma. JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN 2022; 91. [DOI: 10.7566/jpsj.91.094801] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/15/2022] [Accepted: 07/11/2022] [Indexed: 09/01/2023]
Affiliation(s)
| | - Heba A. Elrayes
- Mathematics Department, Faculty of Science, Damietta University, New Damietta, Egypt
| | - Ahmed M. K. Tarabia
- Mathematics Department, Faculty of Science, Damietta University, New Damietta, Egypt
| | - Ahmed S. Elgazzar
- Mathematics Department, Faculty of Science, Arish University, 45516 Arish, Egypt
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44
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Danovski K, Brede M. On the evolutionary language game in structured and adaptive populations. PLoS One 2022; 17:e0273608. [PMID: 36040912 PMCID: PMC9426894 DOI: 10.1371/journal.pone.0273608] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/31/2022] [Accepted: 08/07/2022] [Indexed: 11/18/2022] Open
Abstract
We propose an evolutionary model for the emergence of shared linguistic convention in a population of agents whose social structure is modelled by complex networks. Through agent-based simulations, we show a process of convergence towards a common language, and explore how the topology of the underlying networks affects its dynamics. We find that small-world effects act to speed up convergence, but observe no effect of topology on the communicative efficiency of common languages. We further explore differences in agent learning, discriminating between scenarios in which new agents learn from their parents (vertical transmission) versus scenarios in which they learn from their neighbors (oblique transmission), finding that vertical transmission results in faster convergence and generally higher communicability. Optimal languages can be formed when parental learning is dominant, but a small amount of neighbor learning is included. As a last point, we illustrate an exclusion effect leading to core-periphery networks in an adaptive networks setting when agents attempt to reconnect towards better communicators in the population.
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Affiliation(s)
- Kaloyan Danovski
- Electronics and Computer Science, University of Southampton, Southampton, Hampshire, United Kingdom
- * E-mail:
| | - Markus Brede
- Electronics and Computer Science, University of Southampton, Southampton, Hampshire, United Kingdom
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45
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Roy S, Nag Chowdhury S, Mali PC, Perc M, Ghosh D. Eco-evolutionary dynamics of multigames with mutations. PLoS One 2022; 17:e0272719. [PMID: 35944035 PMCID: PMC9362954 DOI: 10.1371/journal.pone.0272719] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/20/2022] [Accepted: 07/25/2022] [Indexed: 11/30/2022] Open
Abstract
Most environments favor defection over cooperation due to natural selection. Nonetheless, the emergence of cooperation is omnipresent in many biological, social, and economic systems, quite contrary to the well-celebrated Darwinian theory of evolution. Much research has been devoted to better understanding how and why cooperation persists among self-interested individuals despite their competition for limited resources. Here we go beyond a single social dilemma since individuals usually encounter various social challenges. In particular, we propose and study a mathematical model incorporating both the prisoner’s dilemma and the snowdrift game. We further extend this model by considering ecological signatures like mutation and selfless one-sided contribution of altruist free space. The nonlinear evolutionary dynamics that results from these upgrades offer a broader range of equilibrium outcomes, and it also often favors cooperation over defection. With the help of analytical and numerical calculations, our theoretical model sheds light on the mechanisms that maintain biodiversity, and it helps to explain the evolution of social order in human societies.
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Affiliation(s)
- Sourav Roy
- Department of Mathematics, Jadavpur University, Kolkata, West Bengal, India
| | - Sayantan Nag Chowdhury
- Physics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata, West Bengal, India
| | | | - Matjaž Perc
- Faculty of Natural Sciences and Mathematics, University of Maribor, Maribor, Slovenia
- Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan
- Alma Mater Europaea, Maribor, Slovenia
- Complexity Science Hub Vienna, Vienna, Austria
| | - Dibakar Ghosh
- Physics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata, West Bengal, India
- * E-mail:
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46
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Chen Z, Yang C. Cognitive-Behavioral Differences Between Officials and Folks in China's Targeted Poverty Alleviation: An Evolutionary Game Theory Perspective. Front Psychol 2022; 13:916030. [PMID: 35846654 PMCID: PMC9278326 DOI: 10.3389/fpsyg.2022.916030] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/08/2022] [Accepted: 05/30/2022] [Indexed: 11/13/2022] Open
Abstract
China has historically eliminated absolute poverty and built a comprehensive well-off society through targeted poverty alleviation, at the end of which, however, many issues are worthy of scholars' attention kept emerging. A significant one was cognitive-behavioral differences between officials and folks regarding the procedure, standards, and methods of removing the poverty hats, which formed a new social dilemma called the official-folk game. Officials did not carry out targeted poverty alleviation work in strict accordance with the criteria specified by the government. In comparison, folks who have reached poverty elimination standards were unwilling to take off their poverty hats after targeted assistance due to the fear of returning to poverty. To fully explain this social dilemma, this study analyzes the causes of cognitive-behavioral differences between officials and folks in China's targeted poverty alleviation from the perspective of evolutionary game theory. The results show that bounded rational officials and folks will eventually get caught up in the prisoner's dilemma without exogenous factors' intervention. Furthermore, the study proposes that the government establish reasonable punishment, incentives, and supervision mechanisms to guide officials and folks and eliminate their cognitive-behavioral differences by investigating the influence of exogenous policy factors on the evolutionarily stable strategy (ESS) of the official-folk game. This finding not only reveals the formation mechanism of the cognitive-behavioral differences between officials and folks and presents an effective solution at the individual level but also provides a reference for other developing countries to overcome similar social dilemmas in the process of eliminating absolute poverty.
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Affiliation(s)
- Zhi Chen
- Institute of Economic Research, Hubei Academy of Social Sciences, Wuhan, China
| | - Chao Yang
- Institute of Economic Research, Hubei Academy of Social Sciences, Wuhan, China
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47
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Liu L, Chen X. Indirect exclusion can promote cooperation in repeated group interactions. Proc Math Phys Eng Sci 2022. [DOI: 10.1098/rspa.2022.0290] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
Social exclusion has been regarded as one of the most effective measures to promote the evolution of cooperation. In real society, the way in which social exclusion works can be direct or indirect. However, thus far there is no related work to explore how indirect exclusion influences the evolution of cooperation from a theoretical perspective. Here, we introduce indirect exclusion into the repeated public goods game where the game organizer probabilistically selects cooperators after the first game round to participate in the following possible game interactions. We then investigate the evolutionary dynamics of cooperation both in infinite and finite well-mixed populations. Through theoretical analysis and numerical calculations, we find that the introduction of indirect exclusion can induce the stable coexistence of cooperators and defectors or the dominance of cooperators, which thus effectively promotes the evolution of cooperation. Besides, we show that the identifying probability of the organizer has a nonlinear effect on public cooperation when its value is lower than an intermediate value, while the higher identifying probability can maintain a high level of cooperation. Furthermore, our results show that increasing the average rounds of game interactions can effectively promote the evolution of cooperation.
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Affiliation(s)
- Linjie Liu
- College of Science, Northwest A & F University, Yangling 712100, People’s Republic of China
- School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu 611731, People’s Republic of China
| | - Xiaojie Chen
- School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu 611731, People’s Republic of China
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48
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Shi Z, Wei W, Li B, Li C, Li H, Zheng Z. Two-layer network model of public goods games with intervention and corruption. CHAOS (WOODBURY, N.Y.) 2022; 32:063138. [PMID: 35778150 DOI: 10.1063/5.0088493] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/17/2022] [Accepted: 05/16/2022] [Indexed: 06/15/2023]
Abstract
Public goods games are widely used to model social dilemmas involving multiple agents. Though defection is the only rational choice for an individual in a public goods game, cooperative behavior is observed in a variety of social dilemmas, which is the subject of our research. Punishing defectors has been shown to be an effective mechanism for promoting cooperation, but it relies on the third-party umpire being fair. In this article, an umpire intervention model with corruption is proposed to explore the impact of corruption on punishment mechanisms. In our model, players and umpires operate in a multilayer network. The players play public goods games, which are overseen by umpires. Fair umpires punish defectors, whereas corrupt umpires take bribes from defectors rather than meting out a punishment. We separately explore the effects of the fraction of fair umpires ρ, the spatial distribution, and the fine cost α and bribe cost β. Our Monte Carlo simulation shows that the above factors have a significant impact on cooperation. Intervention by an umpire always improves social efficiency, even for an entirely corrupt system. Moreover, relatively developed systems can resist corruption. Staggered and centralized distributions always have opposite effects on cooperative behavior, and these effects depend on ρ and r. We also find that whether cooperators fully occupy the player layer depends only on whether β reaches a certain threshold.
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Affiliation(s)
- Zhenyu Shi
- School of Mathematical Sciences, Beihang University, Beijing 100191, China
| | - Wei Wei
- School of Mathematical Sciences, Beihang University, Beijing 100191, China
| | - Baifeng Li
- School of Mathematical Sciences, Beihang University, Beijing 100191, China
| | - Chao Li
- Department of Mathematics and Computer Science, Hengshui University, Hengshui 053000, China
| | - Haibin Li
- Key Laboratory of Mathematics Informatics Behavioral Semantics, Ministry of Education, Beijing 100191, China
| | - Zhiming Zheng
- School of Mathematical Sciences, Beihang University, Beijing 100191, China
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49
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Cuaresma DCN, Chiba E, Tubay JM, Rabajante JF, Gavina MKA, Yoshimura J, Ito H, Okabe T, Morita S. Optimal strategies and cost-benefit analysis of the [Formula: see text]-player weightlifting game. Sci Rep 2022; 12:8482. [PMID: 35589925 PMCID: PMC9120137 DOI: 10.1038/s41598-022-12394-z] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/05/2022] [Accepted: 04/27/2022] [Indexed: 11/08/2022] Open
Abstract
The study of cooperation has been extensively studied in game theory. Especially, two-player two-strategy games have been categorized according to their equilibrium strategies and fully analysed. Recently, a grand unified game covering all types of two-player two-strategy games, i.e., the weightlifting game, was proposed. In the present study, we extend this two-player weightlifting game into an [Formula: see text]-player game. We investigate the conditions for pure strategy Nash equilibria and for Pareto optimal strategies, expressed in terms of the success probability and benefit-to-cost ratio of the weightlifting game. We also present a general characterization of [Formula: see text]-player games in terms of the proposed game. In terms of a concrete example, we present diagrams showing how the game category varies depending on the benefit-to-cost ratio. As a general rule, cooperation becomes difficult to achieve as group size increases because the success probability of weightlifting saturates towards unity. The present study provides insights into achieving behavioural cooperation in a large group by means of a cost-benefit analysis.
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Affiliation(s)
- Diane Carmeliza N. Cuaresma
- Graduate School of Science and Technology, Shizuoka University, Hamamatsu, Shizuoka 423-8561 Japan
- Institute of Mathematical Sciences and Physics, College of Arts and Sciences, University of the Philippines Los Baños, 4031 Laguna, Philippines
| | - Erika Chiba
- Graduate School of Informatics, Nagoya University, Furo-cho, Chikusa-ku, Nagoya, 464-8601 Japan
| | - Jerrold M. Tubay
- Institute of Mathematical Sciences and Physics, College of Arts and Sciences, University of the Philippines Los Baños, 4031 Laguna, Philippines
| | - Jomar F. Rabajante
- Institute of Mathematical Sciences and Physics, College of Arts and Sciences, University of the Philippines Los Baños, 4031 Laguna, Philippines
| | - Maica Krizna A. Gavina
- Institute of Mathematical Sciences and Physics, College of Arts and Sciences, University of the Philippines Los Baños, 4031 Laguna, Philippines
| | - Jin Yoshimura
- Graduate School of Science and Technology, Shizuoka University, Hamamatsu, Shizuoka 423-8561 Japan
- Department of International Health and Medical Anthropology, Institute of Tropical Medicine, Nagasaki University, Nagasaki, 852-8523 Japan
- Department of Biological Sciences, Tokyo Metropolitan University, Hachioji, Tokyo, 192-0397 Japan
- The University Museum, University of Tokyo, Bunkyo-ku, Tokyo, 113-0033 Japan
| | - Hiromu Ito
- Department of International Health and Medical Anthropology, Institute of Tropical Medicine, Nagasaki University, Nagasaki, 852-8523 Japan
| | - Takuya Okabe
- Graduate School of Integrated Science and Technology, Shizuoka University, Hamamatsu, Shizuoka 423-8561 Japan
| | - Satoru Morita
- Graduate School of Science and Technology, Shizuoka University, Hamamatsu, Shizuoka 423-8561 Japan
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50
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Dhakal S, Chiong R, Chica M, Han TA. Evolution of cooperation and trust in an N-player social dilemma game with tags for migration decisions. ROYAL SOCIETY OPEN SCIENCE 2022; 9:212000. [PMID: 35582657 PMCID: PMC9091842 DOI: 10.1098/rsos.212000] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 01/09/2022] [Accepted: 04/11/2022] [Indexed: 05/03/2023]
Abstract
We present an evolutionary game model that integrates the concept of tags, trust and migration to study how trust in social and physical groups influence cooperation and migration decisions. All agents have a tag, and they gain or lose trust in other tags as they interact with other agents. This trust in different tags determines their trust in other players and groups. In contrast to other models in the literature, our model does not use tags to determine the cooperation/defection decisions of the agents, but rather their migration decisions. Agents decide whether to cooperate or defect based purely on social learning (i.e. imitation from others). Agents use information about tags and their trust in tags to determine how much they trust a particular group of agents and whether they want to migrate to that group. Comprehensive experiments show that the model can promote high levels of cooperation and trust under different game scenarios, and that curbing the migration decisions of agents can negatively impact both cooperation and trust in the system. We also observed that trust becomes scarce in the system as the diversity of tags increases. This work is one of the first to study the impact of tags on trust in the system and migration behaviour of the agents using evolutionary game theory.
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Affiliation(s)
- Sandeep Dhakal
- School of Information and Physical Sciences, The University of Newcastle, Callaghan, New South Wales 2308, Australia
| | - Raymond Chiong
- School of Information and Physical Sciences, The University of Newcastle, Callaghan, New South Wales 2308, Australia
| | - Manuel Chica
- School of Information and Physical Sciences, The University of Newcastle, Callaghan, New South Wales 2308, Australia
- Department of Computer Science and Artificial Intelligence, Andalusian Research Institute in Data Science and Computational Intelligence, DaSCI, University of Granada, 18071 Granada, Spain
| | - The Anh Han
- Department of Computing and Games, Teesside University, Middlesbrough, Tees Valley, UK
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