1
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Wang G, Su Q, Wang L, Plotkin JB. The evolution of social behaviors and risk preferences in settings with uncertainty. Proc Natl Acad Sci U S A 2024; 121:e2406993121. [PMID: 39018189 PMCID: PMC11287271 DOI: 10.1073/pnas.2406993121] [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: 04/08/2024] [Accepted: 06/13/2024] [Indexed: 07/19/2024] Open
Abstract
Humans update their social behavior in response to past experiences and changing environments. Behavioral decisions are further complicated by uncertainty in the outcome of social interactions. Faced with uncertainty, some individuals exhibit risk aversion while others seek risk. Attitudes toward risk may depend on socioeconomic status; and individuals may update their risk preferences over time, which will feedback on their social behavior. Here, we study how uncertainty and risk preferences shape the evolution of social behaviors. We extend the game-theoretic framework for behavioral evolution to incorporate uncertainty about payoffs and variation in how individuals respond to this uncertainty. We find that different attitudes toward risk can substantially alter behavior and long-term outcomes, as individuals seek to optimize their rewards from social interactions. In a standard setting without risk, for example, defection always overtakes a well-mixed population engaged in the classic Prisoner's Dilemma, whereas risk aversion can reverse the direction of evolution, promoting cooperation over defection. When individuals update their risk preferences along with their strategic behaviors, a population can oscillate between periods dominated by risk-averse cooperators and periods of risk-seeking defectors. Our analysis provides a systematic account of how risk preferences modulate, and even coevolve with, behavior in an uncertain social world.
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Affiliation(s)
- Guocheng Wang
- Center for Systems and Control, College of Engineering, Peking University, Beijing100871, China
- Department of Biology, University of Pennsylvania, Philadelphia, PA19104
| | - Qi Su
- Department of Automation, Shanghai Jiao Tong University, Shanghai200240, China
- Ministry of Education of China, Key Laboratory of System Control and Information Processing, Shanghai200240, China
- Shanghai Engineering Research Center of Intelligent Control and Management, Shanghai200240, China
| | - Long Wang
- Center for Systems and Control, College of Engineering, Peking University, Beijing100871, China
- Center for Multi-Agent Research, Institute for Artificial Intelligence, Peking University, Beijing100871, China
| | - Joshua B. Plotkin
- Department of Biology, University of Pennsylvania, Philadelphia, PA19104
- Center for Mathematical Biology, University of Pennsylvania, Philadelphia, PA19014
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2
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Wang C, Perc M, Szolnoki A. Evolutionary dynamics of any multiplayer game on regular graphs. Nat Commun 2024; 15:5349. [PMID: 38914550 PMCID: PMC11196707 DOI: 10.1038/s41467-024-49505-5] [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: 12/23/2023] [Accepted: 06/05/2024] [Indexed: 06/26/2024] Open
Abstract
Multiplayer games on graphs are at the heart of theoretical descriptions of key evolutionary processes that govern vital social and natural systems. However, a comprehensive theoretical framework for solving multiplayer games with an arbitrary number of strategies on graphs is still missing. Here, we solve this by drawing an analogy with the Balls-and-Boxes problem, based on which we show that the local configuration of multiplayer games on graphs is equivalent to distributing k identical co-players among n distinct strategies. We use this to derive the replicator equation for any n-strategy multiplayer game under weak selection, which can be solved in polynomial time. As an example, we revisit the second-order free-riding problem, where costly punishment cannot truly resolve social dilemmas in a well-mixed population. Yet, in structured populations, we derive an accurate threshold for the punishment strength, beyond which punishment can either lead to the extinction of defection or transform the system into a rock-paper-scissors-like cycle. The analytical solution also qualitatively agrees with the phase diagrams that were previously obtained for non-marginal selection strengths. Our framework thus allows an exploration of any multi-strategy multiplayer game on regular graphs.
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Affiliation(s)
- Chaoqian Wang
- Department of Computational and Data Sciences, George Mason University, Fairfax, VA, 22030, USA.
| | - Matjaž Perc
- Faculty of Natural Sciences and Mathematics, University of Maribor, Koroška cesta 160, 2000, Maribor, Slovenia
- Community Healthcare Center Dr. Adolf Drolc Maribor, Vošnjakova ulica 2, 2000, Maribor, Slovenia
- Complexity Science Hub Vienna, Josefstädterstraße 39, 1080, Vienna, Austria
- Department of Physics, Kyung Hee University, 26 Kyungheedae-ro, Dongdaemun-gu, Seoul, Republic of Korea
| | - Attila Szolnoki
- Institute of Technical Physics and Materials Science, Centre for Energy Research, P.O. Box 49, H-1525, Budapest, Hungary
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3
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Dong G, Sun N, Yan M, Wang F, Lambiotte R. Robustness of coupled networks with multiple support from functional components at different scales. CHAOS (WOODBURY, N.Y.) 2024; 34:043122. [PMID: 38579147 DOI: 10.1063/5.0198732] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/19/2024] [Accepted: 03/04/2024] [Indexed: 04/07/2024]
Abstract
Robustness is an essential component of modern network science. Here, we investigate the robustness of coupled networks where the functionality of a node depends not only on its connectivity, here measured by the size of its connected component in its own network, but also the support provided by at least M links from another network. We here develop a theoretical framework and investigate analytically and numerically the cascading failure process when the system is under attack, deriving expressions for the proportion of functional nodes in the stable state, and the critical threshold when the system collapses. Significantly, our results show an abrupt phase transition and we derive the minimum inner and inter-connectivity density necessary for the system to remain active. We also observe that the system necessitates an increased density of links inside and across networks to prevent collapse, especially when conditions on the coupling between the networks are more stringent. Finally, we discuss the importance of our results in real-world settings and their potential use to aid decision-makers design more resilient infrastructure systems.
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Affiliation(s)
- Gaogao Dong
- School of Mathematical Sciences, Jiangsu University, Zhenjiang 212013, Jiangsu, People's Republic of China
- Emergency Management Institute, Jiangsu University, Zhenjiang 212013, Jiangsu, People's Republic of China
- Jiangsu Key Laboratory for Numerical Simulation of Large Scale Complex Systems, Nanjing Normal University, Zhenjiang 210023, Jiangsu, People's Republic of China
| | - Nannan Sun
- School of Mathematical Sciences, Jiangsu University, Zhenjiang 212013, Jiangsu, People's Republic of China
| | - Menglong Yan
- School of Mathematical Sciences, Jiangsu University, Zhenjiang 212013, Jiangsu, People's Republic of China
| | - Fan Wang
- Department of Physics, Bar-Ilan University, Ramat-Gan 52900, Israel
| | - Renaud Lambiotte
- School of Mathematical Sciences, Jiangsu University, Zhenjiang 212013, Jiangsu, People's Republic of China
- Mathematical Institute, University of Oxford, Woodstock Rd, Oxford OX2 6GG, United Kingdom
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4
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Jing Y, Han S, Feng M, Kurths J. Co-evolution of heterogeneous cognition in spatial snowdrift game with asymmetric cost. CHAOS (WOODBURY, N.Y.) 2024; 34:023109. [PMID: 38341764 DOI: 10.1063/5.0192619] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/20/2023] [Accepted: 01/11/2024] [Indexed: 02/13/2024]
Abstract
The emergence of the evolutionary game on complex networks provides a fresh framework for studying cooperation behavior between complex populations. Numerous recent progress has been achieved in studying asymmetric games. However, there is still a substantial need to address how to flexibly express the individual asymmetric nature. In this paper, we employ mutual cognition among individuals to elucidate the asymmetry inherent in their interactions. Cognition arises from individuals' subjective assessments and significantly influences their decision-making processes. In social networks, mutual cognition among individuals is a persistent phenomenon and frequently displays heterogeneity as the influence of their interactions. This unequal cognitive dynamic will, in turn, influence the interactions, culminating in asymmetric outcomes. To better illustrate the inter-individual cognition in asymmetric snowdrift games, the concept of favor value is introduced here. On this basis, the evolution of cognition and its relationship with asymmetry degree are defined. In our simulation, we investigate how game cost and the intensity of individual cognitive changes impact the cooperation frequency. Furthermore, the temporal evolution of individual cognition and its variation under different parameters was also examined. The simulation results reveal that the emergence of heterogeneous cognition effectively addresses social dilemmas, with asymmetric interactions among individuals enhancing the propensity for cooperative choices. It is noteworthy that distinctions exist in the rules governing cooperation and cognitive evolution between regular networks and Watts-Strogatz small-world networks. In light of this, we deduce the relationship between cognition evolution and cooperative behavior in co-evolution and explore potential factors influencing cooperation within the system.
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Affiliation(s)
- Yuxuan Jing
- College of Artificial Intelligence, Southwest University, Chongqing 400715, China
| | - Songlin Han
- College of Han Hong, Southwest University, Chongqing 400715, China
| | - Minyu Feng
- College of Artificial Intelligence, Southwest University, Chongqing 400715, China
| | - Jürgen Kurths
- Potsdam Institute for Climate Impact Research, 14437 Potsdam, Germany
- Institute of Physics, Humboldt University, Berlin 12489, Germany
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5
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Colnaghi M, Santos FP, Van Lange PAM, Balliet D. Adaptations to infer fitness interdependence promote the evolution of cooperation. Proc Natl Acad Sci U S A 2023; 120:e2312242120. [PMID: 38055736 PMCID: PMC10723045 DOI: 10.1073/pnas.2312242120] [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: 07/18/2023] [Accepted: 10/30/2023] [Indexed: 12/08/2023] Open
Abstract
The evolution of cooperation is a major question in the biological and behavioral sciences. While most theoretical studies model cooperation in the context of an isolated interaction (e.g., a Prisoner's Dilemma), humans live in heterogeneous social environments, characterized by large variations in fitness interdependence-the extent to which one's fitness is affected by others. Theoretical and experimental work indicates that humans can infer, and respond to, variations in interdependence. In a heterogeneous ancestral environment, these psychological mechanisms to infer fitness interdependence could have provided a selective advantage, allowing individuals to maximize their fitness by deciding when and with whom to cooperate. Yet, to date, the link between cognitive inference, variation in fitness interdependence, and cooperation remains unclear. Here we introduce a theoretical framework to study the evolution of inference and cooperation in heterogeneous social environments, where individuals experience interactions with varying levels of corresponding interests. Using a combination of evolutionary game theory and agent-based modeling, we model the evolution of adaptive agents, who incur a cost to infer interdependence, in populations of fixed-behavior agents who always cooperate or defect. Our results indicate that natural selection could promote the evolution of psychological mechanisms to infer fitness interdependence, provided that there is enough variation in fitness interdependence to offset the cost of inference. Under certain conditions, the fixation of adaptive agents results in higher levels of cooperation. This depends crucially on the type of inference performed and the features of the interdependence landscape.
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Affiliation(s)
- Marco Colnaghi
- Department of Experimental and Applied Psychology, Institute for Brain and Behaviour Amsterdam, Vrije Universiteit Amsterdam, Amsterdam1081BT, The Netherlands
| | - Fernando P. Santos
- Informatics Institute, University of Amsterdam, Amsterdam1098XH, The Netherlands
| | - Paul A. M. Van Lange
- Department of Experimental and Applied Psychology, Institute for Brain and Behaviour Amsterdam, Vrije Universiteit Amsterdam, Amsterdam1081BT, The Netherlands
| | - Daniel Balliet
- Department of Experimental and Applied Psychology, Institute for Brain and Behaviour Amsterdam, Vrije Universiteit Amsterdam, Amsterdam1081BT, The Netherlands
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6
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Yuan Y, Wang J, Wang Z, Yang H, Xu T, Huang H. Aspiration-driven co-evolution of cooperation with individual behavioral diversity. PLoS One 2023; 18:e0291134. [PMID: 37713378 PMCID: PMC10503719 DOI: 10.1371/journal.pone.0291134] [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: 04/23/2023] [Accepted: 08/22/2023] [Indexed: 09/17/2023] Open
Abstract
In evolutionary game, aspiration-driven updates and imitation updates are the two dominant game models, and individual behavior patterns are mainly categorized into two types: node player and link player. In more recent studies, the mixture strategy of different types of players has been proven to improve cooperation substantially. Motivated by such a co-evolution mechanism, we combine aspiration dynamics with individual behavioral diversity, where self-assessed aspirations are used to update imitation strategies. In this study, the node players and the link players are capable to transform into each other autonomously, which introduces new features to cooperation in a diverse population as well. In addition, by driving all the players to form specific behavior patterns, the proposed mechanism achieves a survival environment optimization of the cooperators. As expected, the interaction between node players and link players allows the cooperator to avoid the invasion of the defector. Based on the experimental evaluation, the proposed work has demonstrated that the co-evolution mechanism has facilitated the emergence of cooperation by featuring mutual transformation between different players. We hope to inspire a new way of thinking for a promising solution to social dilemmas.
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Affiliation(s)
- Yongqiong Yuan
- Key Laboratory of Data Link, China Electronics Technology Group Corporation, Xi’an, China
| | - Jian Wang
- AVIC Chengdu Aircraft Design & Research Institute, Chengdu, China
| | - Zhigang Wang
- Key Laboratory of Data Link, China Electronics Technology Group Corporation, Xi’an, China
| | - Haochun Yang
- School of Computer Science and Engineering, Northwestern Polytechnical University, Xi’an, Shaanxi, China
| | - Tao Xu
- School of Computer Science and Engineering, Northwestern Polytechnical University, Xi’an, Shaanxi, China
| | - Huang Huang
- School of Computer Science and Engineering, Northwestern Polytechnical University, Xi’an, Shaanxi, China
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7
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Abstract
Reputation and reciprocity are key mechanisms for cooperation in human societies, often going hand in hand to favor prosocial behavior over selfish actions. Here we review recent researches at the interface of physics and evolutionary game theory that explored these two mechanisms. We focus on image scoring as the bearer of reputation, as well as on various types of reciprocity, including direct, indirect, and network reciprocity. We review different definitions of reputation and reciprocity dynamics, and we show how these affect the evolution of cooperation in social dilemmas. We consider first-order, second-order, as well as higher-order models in well-mixed and structured populations, and we review experimental works that support and inform the results of mathematical modeling and simulations. We also provide a synthesis of the reviewed researches along with an outlook in terms of six directions that seem particularly promising to explore in the future.
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Affiliation(s)
- Chengyi Xia
- School of Artificial Intelligence, Tiangong University, Tianjin 300384, China
| | - Juan Wang
- School of Electrical Engineering and Automation, Tianjin University of Technology, Tianjin 300384, China.
| | - Matjaž Perc
- Faculty of Natural Sciences and Mathematics, University of Maribor, Koroška cesta 160, 2000 Maribor, Slovenia; Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 404332, Taiwan; Alma Mater Europaea, Slovenska ulica 17, 2000 Maribor, Slovenia; Complexity Science Hub Vienna, Josefstädterstraße 39, 1080 Vienna, Austria
| | - Zhen Wang
- Center for OPTical IMagery Analysis and Learning (OPTIMAL), Northwestern Polytechnical University, Xian 710072, China.
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8
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Sheng A, Li A, Wang L. Evolutionary dynamics on sequential temporal networks. PLoS Comput Biol 2023; 19:e1011333. [PMID: 37549167 PMCID: PMC10434888 DOI: 10.1371/journal.pcbi.1011333] [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: 01/30/2023] [Revised: 08/17/2023] [Accepted: 07/06/2023] [Indexed: 08/09/2023] Open
Abstract
Population structure is a well-known catalyst for the evolution of cooperation and has traditionally been considered to be static in the course of evolution. Conversely, real-world populations, such as microbiome communities and online social networks, frequently show a progression from tiny, active groups to huge, stable communities, which is insufficient to be captured by constant structures. Here, we propose sequential temporal networks to characterize growing networked populations, and we extend the theory of evolutionary games to these temporal networks with arbitrary structures and growth rules. We derive analytical rules under which a sequential temporal network has a higher fixation probability for cooperation than its static counterpart. Under neutral drift, the rule is simply a function of the increment of nodes and edges in each time step. But if the selection is weak, the rule is related to coalescence times on networks. In this case, we propose a mean-field approximation to calculate fixation probabilities and critical benefit-to-cost ratios with lower calculation complexity. Numerical simulations in empirical datasets also prove the cooperation-promoting effect of population growth. Our research stresses the significance of population growth in the real world and provides a high-accuracy approximation approach for analyzing the evolution in real-life systems.
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Affiliation(s)
- Anzhi Sheng
- Center for Systems and Control, College of Engineering, Peking University, Beijing, China
- Department of Biology, University of Pennsylvania, Philadelphia, United States of America
| | - Aming Li
- Center for Systems and Control, College of Engineering, Peking University, Beijing, China
- Center for Multi-Agent Research, Institute for Artificial Intelligence, Peking University, Beijing, China
| | - Long Wang
- Center for Systems and Control, College of Engineering, Peking University, Beijing, China
- Center for Multi-Agent Research, Institute for Artificial Intelligence, Peking University, Beijing, China
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9
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Jiang Y, Wang X, Liu L, Wei M, Zhao J, Zheng Z, Tang S. Nonlinear eco-evolutionary games with global environmental fluctuations and local environmental feedbacks. PLoS Comput Biol 2023; 19:e1011269. [PMID: 37379330 DOI: 10.1371/journal.pcbi.1011269] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/13/2022] [Accepted: 06/13/2023] [Indexed: 06/30/2023] Open
Abstract
Environmental changes play a critical role in determining the evolution of social dilemmas in many natural or social systems. Generally, the environmental changes include two prominent aspects: the global time-dependent fluctuations and the local strategy-dependent feedbacks. However, the impacts of these two types of environmental changes have only been studied separately, a complete picture of the environmental effects exerted by the combination of these two aspects remains unclear. Here we develop a theoretical framework that integrates group strategic behaviors with their general dynamic environments, where the global environmental fluctuations are associated with a nonlinear factor in public goods game and the local environmental feedbacks are described by the 'eco-evolutionary game'. We show how the coupled dynamics of local game-environment evolution differ in static and dynamic global environments. In particular, we find the emergence of cyclic evolution of group cooperation and local environment, which forms an interior irregular loop in the phase plane, depending on the relative changing speed of both global and local environments compared to the strategic change. Further, we observe that this cyclic evolution disappears and transforms into an interior stable equilibrium when the global environment is frequency-dependent. Our results provide important insights into how diverse evolutionary outcomes could emerge from the nonlinear interactions between strategies and the changing environments.
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Affiliation(s)
- Yishen Jiang
- School of Mathematical Sciences, Beihang University, Beijing, China
- Key laboratory of Mathematics, Informatics and Behavioral Semantics (LMIB), Beihang University, Beijing, China
| | - Xin Wang
- Institute of Artificial Intelligence, Beihang University, Beijing, China
- Key laboratory of Mathematics, Informatics and Behavioral Semantics (LMIB), Beihang University, Beijing, China
- State Key Lab of Software Development Environment (NLSDE), Beihang University, Beijing, China
- Zhongguancun Laboratory, Beijing, P.R.China
- Beijing Advanced Innovation Center for Future Blockchain and Privacy Computing, Beihang University, Beijing, China
- PengCheng Laboratory, Shenzhen, China
| | - Longzhao Liu
- Institute of Artificial Intelligence, Beihang University, Beijing, China
- Key laboratory of Mathematics, Informatics and Behavioral Semantics (LMIB), Beihang University, Beijing, China
- State Key Lab of Software Development Environment (NLSDE), Beihang University, Beijing, China
- Zhongguancun Laboratory, Beijing, P.R.China
- Beijing Advanced Innovation Center for Future Blockchain and Privacy Computing, Beihang University, Beijing, China
- PengCheng Laboratory, Shenzhen, China
| | - Ming Wei
- School of Mathematical Sciences, Beihang University, Beijing, China
- Key laboratory of Mathematics, Informatics and Behavioral Semantics (LMIB), Beihang University, Beijing, China
| | - Jingwu Zhao
- School of Law, Beihang University, Beijing, China
| | - Zhiming Zheng
- Institute of Artificial Intelligence, Beihang University, Beijing, China
- Key laboratory of Mathematics, Informatics and Behavioral Semantics (LMIB), Beihang University, Beijing, China
- State Key Lab of Software Development Environment (NLSDE), Beihang University, Beijing, China
- Zhongguancun Laboratory, Beijing, P.R.China
- Beijing Advanced Innovation Center for Future Blockchain and Privacy Computing, Beihang University, Beijing, China
- PengCheng Laboratory, Shenzhen, China
- Institute of Medical Artificial Intelligence, Binzhou Medical University, Yantai, China
- School of Mathematical Sciences, Dalian University of Technology, Dalian, China
| | - Shaoting Tang
- Institute of Artificial Intelligence, Beihang University, Beijing, China
- Key laboratory of Mathematics, Informatics and Behavioral Semantics (LMIB), Beihang University, Beijing, China
- State Key Lab of Software Development Environment (NLSDE), Beihang University, Beijing, China
- Zhongguancun Laboratory, Beijing, P.R.China
- Beijing Advanced Innovation Center for Future Blockchain and Privacy Computing, Beihang University, Beijing, China
- PengCheng Laboratory, Shenzhen, China
- Institute of Medical Artificial Intelligence, Binzhou Medical University, Yantai, China
- School of Mathematical Sciences, Dalian University of Technology, Dalian, China
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10
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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: 6] [Impact Index Per Article: 6.0] [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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11
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Evolutionary dynamics under partner preferences. J Theor Biol 2023; 557:111340. [PMID: 36343667 DOI: 10.1016/j.jtbi.2022.111340] [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: 08/10/2022] [Revised: 10/13/2022] [Accepted: 10/30/2022] [Indexed: 11/06/2022]
Abstract
The fact that people often have preference rankings for their partners is a distinctive aspect of human behavior. Little is known, however, about how this talent as a powerful force shapes human behavioral traits, including those which should not have been favored by selection, such as cooperation in social dilemma situations. Here we propose a dynamic model in which network-structured individuals can switch their interaction partners within neighborhoods based on their preferences. For the partner switching, we propose two interruption regimes: dictatorial regime and negotiating regime. In the dictatorial regime, focal individuals are able to suspend interactions out of preferences unilaterally. In the negotiating regime, either focal individuals or the associated partners agree to suspend, then these interactions can be successfully suspended. We investigate the evolution of cooperation under both preference-driven partner switching regimes in the context of both the weakened variant of the donation game and the standard one. Specifically, we theoretically approximate the critical conditions for cooperation to be favored by weak selection in the weakened donation game where cooperators bear a unit cost to provide a benefit for each active neighbor and simulate the evolutionary dynamics of cooperation in the standard donation game to test the robustness of the analytical results. Under dictatorial regime, selection of cooperation becomes harder when individuals have preferences for either cooperator or defector partners, implying that the expulsion of defectors by cooperators is overwhelmed by the chasing of defectors towards cooperators. Under negotiating regime, both preferences for cooperator and defector partners can significantly favor the evolution of cooperation, yet underlying mechanisms differ greatly. For preferences over cooperator partners, cooperator-cooperator interaction relationships are reinforced and the associated mutual reciprocity can resist and assimilate defectors. For preferences over defector partners, defector-defector interaction relationships are anchored, weakening defectors' exploitation over cooperators. Cooperators are thus offered much time space to interact among cospecies and spread. Our work may help better understand the critical role of preference-based adaptive partner switching in promoting the evolution of cooperation.
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12
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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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13
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Li J, Zhao X, Li B, Rossetti CSL, Hilbe C, Xia H. Evolution of cooperation through cumulative reciprocity. NATURE COMPUTATIONAL SCIENCE 2022; 2:677-686. [PMID: 38177263 DOI: 10.1038/s43588-022-00334-w] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/06/2021] [Accepted: 09/14/2022] [Indexed: 01/06/2024]
Abstract
Reciprocity is a simple principle for cooperation that explains many of the patterns of how humans seek and receive help from each other. To capture reciprocity, traditional models often assume that individuals use simple strategies with restricted memory. These memory-1 strategies are mathematically convenient, but they miss important aspects of human reciprocity, where defections can have lasting effects. Here we instead propose a strategy of cumulative reciprocity. Cumulative reciprocators count the imbalance of cooperation across their previous interactions with their opponent. They cooperate as long as this imbalance is sufficiently small. Using analytical and computational methods, we show that this strategy can sustain cooperation in the presence of errors, that it enforces fair outcomes and that it evolves in hostile environments. Using an economic experiment, we confirm that cumulative reciprocity is more predictive of human behaviour than several classical strategies. The basic principle of cumulative reciprocity is versatile and can be extended to a range of social dilemmas.
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Affiliation(s)
- Juan Li
- Institute of Systems Engineering, Dalian University of Technology, Dalian, China
- Center for Big Data and Intelligent Decision-Making, Dalian University of Technology, Dalian, China
| | - Xiaowei Zhao
- Institute of Systems Engineering, Dalian University of Technology, Dalian, China
- School of Software Technology, Dalian University of Technology, Dalian, China
| | - Bing Li
- Institute of Systems Engineering, Dalian University of Technology, Dalian, China
| | | | - Christian Hilbe
- Max Planck Institute for Evolutionary Biology, Plön, Germany.
| | - Haoxiang Xia
- Institute of Systems Engineering, Dalian University of Technology, Dalian, China.
- Center for Big Data and Intelligent Decision-Making, Dalian University of Technology, Dalian, China.
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14
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Luo Y, Li Y, Cheng C. Cooperative evolution with opinion formation in a complex social environment. CHAOS (WOODBURY, N.Y.) 2022; 32:103123. [PMID: 36319276 DOI: 10.1063/5.0090831] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/09/2022] [Accepted: 09/09/2022] [Indexed: 06/16/2023]
Abstract
Cooperation is a significant aspect in the daily activities of human or animal populations that involves the process of agents making decisions based in part on the ideas or beliefs of cooperators. The importance of communication in the evolutionary game cannot be overstated. In this paper, we offer a co-evolutionary game model on a communication network, including expressed and private opinions. Then, we present our theoretical analysis of scenarios characterized by different parameters, elucidating the relationship between the agents' opinion formation process and the decision-making process. Finally, we run simulations with our proposed model. Surprisingly, we discover that whereas communication does not increase cooperation on Erdös-Rényi random networks, it does so on the Barabási-Albert scale-free network. Meanwhile, we discover that in the simulation results, the average of private opinions (simplified as values within [0,1]) changes in the same direction of the percentage of cooperators. Furthermore, we discover that deceivers who conceal their true private opinions may, to some extent, foster the formation of collaboration in the human population, which goes against our common sense.
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Affiliation(s)
- Yun Luo
- School of Computer Science and Technology, Zhejiang University, Hangzhou 310024, People's Republic of China
| | - Yuke Li
- School of Engineering, Westlake Institute for Advanced Study, Hangzhou 310000, People's Republic of China
| | - Chun Cheng
- School of Information Science and Technology, Nantong University, Nantong 226019, People's Republic of China
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15
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Salahshour M. Interaction between games give rise to the evolution of moral norms of cooperation. PLoS Comput Biol 2022; 18:e1010429. [PMID: 36173936 PMCID: PMC9521931 DOI: 10.1371/journal.pcbi.1010429] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/06/2021] [Accepted: 07/21/2022] [Indexed: 11/18/2022] Open
Abstract
In many biological populations, such as human groups, individuals face a complex strategic setting, where they need to make strategic decisions over a diverse set of issues and their behavior in one strategic context can affect their decisions in another. This raises the question of how the interaction between different strategic contexts affects individuals’ strategic choices and social norms? To address this question, I introduce a framework where individuals play two games with different structures and decide upon their strategy in a second game based on their knowledge of their opponent’s strategy in the first game. I consider both multistage games, where the same opponents play the two games consecutively, and reputation-based model, where individuals play their two games with different opponents but receive information about their opponent’s strategy. By considering a case where the first game is a social dilemma, I show that when the second game is a coordination or anti-coordination game, the Nash equilibrium of the coupled game can be decomposed into two classes, a defective equilibrium which is composed of two simple equilibrium of the two games, and a cooperative equilibrium, in which coupling between the two games emerge and sustain cooperation in the social dilemma. For the existence of the cooperative equilibrium, the cost of cooperation should be smaller than a value determined by the structure of the second game. Investigation of the evolutionary dynamics shows that a cooperative fixed point exists when the second game belongs to coordination or anti-coordination class in a mixed population. However, the basin of attraction of the cooperative fixed point is much smaller for the coordination class, and this fixed point disappears in a structured population. When the second game belongs to the anti-coordination class, the system possesses a spontaneous symmetry-breaking phase transition above which the symmetry between cooperation and defection breaks. A set of cooperation supporting moral norms emerges according to which cooperation stands out as a valuable trait. Notably, the moral system also brings a more efficient allocation of resources in the second game. This observation suggests a moral system has two different roles: Promotion of cooperation, which is against individuals’ self-interest but beneficial for the population, and promotion of organization and order, which is at both the population’s and the individual’s self-interest. Interestingly, the latter acts like a Trojan horse: Once established out of individuals’ self-interest, it brings the former with itself. Importantly, the fact that the evolution of moral norms depends only on the cost of cooperation and is independent of the benefit of cooperation implies that moral norms can be harmful and incur a pure collective cost, yet they are just as effective in promoting order and organization. Finally, the model predicts that recognition noise can have a surprisingly positive effect on the evolution of moral norms and facilitates cooperation in the Snow Drift game in structured populations. How do moral norms spontaneously evolve in the presence of selfish incentives? An answer to this question is provided by the observation that moral systems have two distinct functions: Besides encouraging self-sacrificing cooperation, they also bring organization and order into the societies. In contrast to the former, which is costly for the individuals but beneficial for the group, the latter is beneficial for both the group and the individuals. A simple evolutionary model suggests this latter aspect is what makes a moral system evolve based on the individuals’ self-interest. However, a moral system behaves like a Trojan horse: Once established out of the individuals’ self-interest to promote order and organization, it also brings self-sacrificing cooperation.
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Affiliation(s)
- Mohammad Salahshour
- Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany
- Max Planck Institute of Animal Behavior, Radolfzell, Germany
- Centre for the Advanced Study of Collective Behaviour, University of Konstanz, Konstanz, Germany
- Department of Biology, University of Konstanz, Konstanz, Germany
- * E-mail:
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16
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Zeng Z, Li Q, Feng M. Spatial evolution of cooperation with variable payoffs. CHAOS (WOODBURY, N.Y.) 2022; 32:073118. [PMID: 35907736 DOI: 10.1063/5.0099444] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/17/2022] [Accepted: 06/16/2022] [Indexed: 06/15/2023]
Abstract
In the evolution of cooperation, the individuals' payoffs are commonly random in real situations, e.g., the social networks and the economic regions, leading to unpredictable factors. Therefore, there are chances for each individual to obtain the exceeding payoff and risks to get the low payoff. In this paper, we consider that each individual's payoff follows a specific probability distribution with a fixed expectation, where the normal distribution and the exponential distribution are employed in our model. In the simulations, we perform the models on the weak prisoner's dilemmas (WPDs) and the snowdrift games (SDGs), and four types of networks, including the hexagon lattice, the square lattice, the small-world network, and the triangular lattice are considered. For the individuals' normally distributed payoff, we find that the higher standard deviation usually inhibits the cooperation for the WPDs but promotes the cooperation for the SDGs. Besides, with a higher standard deviation, the cooperation clusters are usually split for the WPDs but constructed for the SDGs. For the individuals' exponentially distributed payoff, we find that the small-world network provides the best condition for the emergence of cooperators in WPDs and SDGs. However, when playing SDGs, the small-world network allows the smallest space for the pure cooperative state while the hexagon lattice allows the largest.
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Affiliation(s)
- Ziyan Zeng
- The College of Artificial Intelligence, Southwest University, No.2 Tiansheng Road, Beibei, Chongqing 400715, China
| | - Qin Li
- School of Public Policy and Administration, Chongqing University, No.174 Shazhengjie, Shapingba, Chongqing 400044, China
| | - Minyu Feng
- The College of Artificial Intelligence, Southwest University, No.2 Tiansheng Road, Beibei, Chongqing 400715, China
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17
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Braga I, Wardil L. When stochasticity leads to cooperation. Phys Rev E 2022; 106:014112. [PMID: 35974527 DOI: 10.1103/physreve.106.014112] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/04/2022] [Accepted: 06/17/2022] [Indexed: 06/15/2023]
Abstract
The evolution of cooperation has gained more attention after Smith introduced game theory in the study of evolutionary biology. Subsequent works have extensively explained this phenomenon, consistently showing the importance of spatial structure for the evolution of cooperation. Here we analyze the effect of stochasticity on the evolution of cooperation in group-structured populations. We find a simple formula for the fixation probability of cooperators and show that cooperation can be favored by selection if a condition similar to Hamilton's rule is satisfied, which is also valid for strong selection and high migration. In fact, cooperation can be favored even in the absence of population viscosity and in the limit of an infinite number of finite-size groups. We discuss the importance of stochastic fluctuations in helping cooperation. We argue that this may be a general principle because fluctuations favoring the cooperators are often much more impactful than those favoring the defectors.
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Affiliation(s)
- Ian Braga
- Departamento de Física, Universidade Federal de Minas Gerais, 31270-901 Belo Horizonte, Minas Gerais, Brazil
| | - Lucas Wardil
- Departamento de Física, Universidade Federal de Minas Gerais, 31270-901 Belo Horizonte, Minas Gerais, Brazil
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18
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Chen F, Wu T, Wang L. Evolutionary dynamics of zero-determinant strategies in repeated multiplayer games. J Theor Biol 2022; 549:111209. [PMID: 35779706 DOI: 10.1016/j.jtbi.2022.111209] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/21/2021] [Revised: 06/01/2022] [Accepted: 06/23/2022] [Indexed: 12/01/2022]
Abstract
Several studies have confirmed the existence of zero-determinant (ZD) strategies in repeated social dilemmas since Press and Dyson's ingenious discovery of ZD strategies in iterated prisoner's dilemmas. However, less research studies evolutionary performance of multiplayer ZD strategies, especially from a theoretical perspective. Here, we use a state-clustering method to theoretically analyze evolutionary dynamics of two representative ZD strategies: generous ZD strategies and extortionate ZD strategies. We consider two new settings for multiplayer ZD strategies: competitions with all ZD strategies and competitions with all memory-one strategies, apart from the competitions between these strategies and some classical ones. Moreover, we investigate the influence of the level of generosity and extortion on evolutionary dynamics of generous and extortionate ZD strategies, which was commonly ignored in previous studies. Theoretical results show that players with limited generosity are at an advantageous place and extortioners extorting more severely hold their ground more readily. Our results may provide new insights into better understanding evolutionary dynamics of ZD strategies in repeated multiplayer games.
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Affiliation(s)
- Fang Chen
- Center for Systems and Control, College of Engineering, Peking University, Beijing, China
| | - Te Wu
- Center for Complex Systems, Xidian University, Xi'an, China
| | - Long Wang
- Center for Systems and Control, College of Engineering, Peking University, Beijing, China; Center for Multi-Agent Research, Institute for Artificial Intelligence, Peking University, Beijing, China.
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19
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Abstract
'Personal responsibility', one of the basic principles of social governance, requires one to be accountable for what one does. However, personal responsibility is far from the only norm ruling human interactions, especially in social and economic activities. In many collective communities such as among enterprise colleagues and family members, one's personal interests are often bound to others'-once one member breaks the rule, a group of people have to bear the punishment or sanction. Such a mechanism is termed 'joint liability'. Although many real-world cases have evidenced that joint liability can help to maintain collective collaboration, a deep and systematic theoretical analysis on how and when it promotes cooperation remains lacking. Here, we use evolutionary game theory to model an interacting system with joint liability, where one's losing credit could deteriorate the reputation of the whole group. We provide the analytical condition to predict when cooperation evolves and analytically prove that in the presence of punishment, being jointly liable greatly promotes cooperation. Our work stresses that joint liability is of great significance in promoting current economic prosperity.
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Affiliation(s)
- Guocheng Wang
- Center for Systems and Control, College of Engineering, Peking University, Beijing 100871, People's Republic of China
| | - Qi Su
- Center for Mathematical Biology, University of Pennsylvania, Philadelphia, PA 19104, USA.,Department of Mathematics, University of Pennsylvania, Philadelphia, PA 19104, USA.,Department of Biology, University of Pennsylvania, Philadelphia, PA 19104, USA
| | - Long Wang
- Center for Systems and Control, College of Engineering, Peking University, Beijing 100871, People's Republic of China.,Center for Multi-Agent Research, Institute for Artificial Intelligence, Peking University, Beijing 100871, People's Republic of China
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20
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Barfuss W, Mann RP. Modeling the effects of environmental and perceptual uncertainty using deterministic reinforcement learning dynamics with partial observability. Phys Rev E 2022; 105:034409. [PMID: 35428165 DOI: 10.1103/physreve.105.034409] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/25/2021] [Accepted: 02/24/2022] [Indexed: 11/07/2022]
Abstract
Assessing the systemic effects of uncertainty that arises from agents' partial observation of the true states of the world is critical for understanding a wide range of scenarios, from navigation and foraging behavior to the provision of renewable resources and public infrastructures. Yet previous modeling work on agent learning and decision-making either lacks a systematic way to describe this source of uncertainty or puts the focus on obtaining optimal policies using complex models of the world that would impose an unrealistically high cognitive demand on real agents. In this work we aim to efficiently describe the emergent behavior of biologically plausible and parsimonious learning agents faced with partially observable worlds. Therefore we derive and present deterministic reinforcement learning dynamics where the agents observe the true state of the environment only partially. We showcase the broad applicability of our dynamics across different classes of partially observable agent-environment systems. We find that partial observability creates unintuitive benefits in several specific contexts, pointing the way to further research on a general understanding of such effects. For instance, partially observant agents can learn better outcomes faster, in a more stable way, and even overcome social dilemmas. Furthermore, our method allows the application of dynamical systems theory to partially observable multiagent leaning. In this regard we find the emergence of catastrophic limit cycles, a critical slowing down of the learning processes between reward regimes, and the separation of the learning dynamics into fast and slow directions, all caused by partial observability. Therefore, the presented dynamics have the potential to become a formal, yet practical, lightweight and robust tool for researchers in biology, social science, and machine learning to systematically investigate the effects of interacting partially observant agents.
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Affiliation(s)
- Wolfram Barfuss
- Institute for Theoretical Physics, University of Tübingen, 72076 Tübingen, Germany.,Department of Statistics, School of Mathematics, University of Leeds, Leeds LS2 9JT, United Kingdom
| | - Richard P Mann
- Department of Statistics, School of Mathematics, University of Leeds, Leeds LS2 9JT, United Kingdom
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21
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Amaral MA, de Oliveira MM. Criticality and Griffiths phases in random games with quenched disorder. Phys Rev E 2022; 104:064102. [PMID: 35030882 DOI: 10.1103/physreve.104.064102] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/24/2021] [Accepted: 11/22/2021] [Indexed: 11/07/2022]
Abstract
The perceived risk and reward for a given situation can vary depending on resource availability, accumulated wealth, and other extrinsic factors such as individual backgrounds. Based on this general aspect of everyday life, here we use evolutionary game theory to model a scenario with randomly perturbed payoffs in a prisoner's dilemma game. The perception diversity is modeled by adding a zero-average random noise in the payoff entries and a Monte Carlo simulation is used to obtain the population dynamics. This payoff heterogeneity can promote and maintain cooperation in a competitive scenario where only defectors would survive otherwise. In this work, we give a step further, understanding the role of heterogeneity by investigating the effects of quenched disorder in the critical properties of random games. We observe that payoff fluctuations induce a very slow dynamic, making the cooperation decay behave as power laws with varying exponents, instead of the usual exponential decay after the critical point, showing the emergence of a Griffiths phase. We also find a symmetric Griffiths phase near the defector's extinction point when fluctuations are present, indicating that Griffiths phases may be frequent in evolutionary game dynamics and play a role in the coexistence of different strategies.
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Affiliation(s)
- Marco A Amaral
- Instituto de Artes, Humanidades e Ciências, Universidade Federal do Sul da Bahia, Teixeira de Freitas-BA, 45996-108 Brazil
| | - Marcelo M de Oliveira
- Departamento de Física e Matemática, Universidade Federal de São João del Rei, Ouro Branco-MG, 36420-000 Brazil
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22
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Su Q, McAvoy A, Mori Y, Plotkin JB. Evolution of prosocial behaviours in multilayer populations. Nat Hum Behav 2022; 6:338-348. [PMID: 34980900 DOI: 10.1038/s41562-021-01241-2] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/29/2020] [Accepted: 10/22/2021] [Indexed: 01/16/2023]
Abstract
Human societies include diverse social relationships. Friends, family, business colleagues and online contacts can all contribute to one's social life. Individuals may behave differently in different domains, but success in one domain may engender success in another. Here, we study this problem using multilayer networks to model multiple domains of social interactions, in which individuals experience different environments and may express different behaviours. We provide a mathematical analysis and find that coupling between layers tends to promote prosocial behaviour. Even if prosociality is disfavoured in each layer alone, multilayer coupling can promote its proliferation in all layers simultaneously. We apply this analysis to six real-world multilayer networks, ranging from the socio-emotional and professional relationships in a Zambian community, to the online and offline relationships within an academic university. We discuss the implications of our results, which suggest that small modifications to interactions in one domain may catalyse prosociality in a different domain.
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Affiliation(s)
- Qi Su
- Department of Biology, University of Pennsylvania, PA, USA. .,Center for Mathematical Biology, University of Pennsylvania, PA, USA. .,Department of Mathematics, University of Pennsylvania, PA, USA.
| | - Alex McAvoy
- Center for Mathematical Biology, University of Pennsylvania, PA, USA. .,Department of Mathematics, University of Pennsylvania, PA, USA.
| | - Yoichiro Mori
- Department of Biology, University of Pennsylvania, PA, USA.,Center for Mathematical Biology, University of Pennsylvania, PA, USA.,Department of Mathematics, University of Pennsylvania, PA, USA
| | - Joshua B Plotkin
- Department of Biology, University of Pennsylvania, PA, USA.,Center for Mathematical Biology, University of Pennsylvania, PA, USA.,Department of Mathematics, University of Pennsylvania, PA, USA
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23
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Shi J, Liu J, Perc M, Deng Z, Wang Z. Neighborhood size effects on the evolution of cooperation under myopic dynamics. CHAOS (WOODBURY, N.Y.) 2021; 31:123113. [PMID: 34972342 DOI: 10.1063/5.0073632] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/01/2021] [Accepted: 11/23/2021] [Indexed: 06/14/2023]
Abstract
We study the evolution of cooperation in 2×2 social dilemma games in which players are located on a two-dimensional square lattice. During the evolution, each player modifies her strategy by means of myopic update dynamic to maximize her payoff while composing neighborhoods of different sizes, which are characterized by the corresponding radius, r. An investigation of the sublattice-ordered spatial structure for different values of r reveals that some patterns formed by cooperators and defectors can help the former to survive, even under untoward conditions. In contrast to individuals who resist the invasion of defectors by forming clusters due to network reciprocity, innovators spontaneously organize a socially divisive structure that provides strong support for the evolution of cooperation and advances better social systems.
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Affiliation(s)
- Juan Shi
- School of Automation, Northwestern Polytechnical University, Shaanxi 710072, China
| | - Jinzhuo Liu
- School of Software, Yunnan University, Kunming, Yunnan 650504, China
| | - Matjaž Perc
- Faculty of Natural Sciences and Mathematics, University of Maribor, Koroška cesta 160, 2000 Maribor, Slovenia
| | - Zhenghong Deng
- School of Automation, Northwestern Polytechnical University, Shaanxi 710072, China
| | - Zhen Wang
- School of Artificial Intelligence, Optics and Electronics (iOPEN), Northwestern Polytechnical University, Shaanxi 710072, China
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24
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Sadhukhan S, Chattopadhyay R, Chakraborty S. Amplitude death in coupled replicator map lattice: Averting migration dilemma. Phys Rev E 2021; 104:044304. [PMID: 34781425 DOI: 10.1103/physreve.104.044304] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/26/2021] [Accepted: 09/20/2021] [Indexed: 11/07/2022]
Abstract
Populations composed of a collection of subpopulations (demes) with random migration between them are quite common occurrences. The emergence and sustenance of cooperation in such a population is a highly researched topic in the evolutionary game theory. If the individuals in every deme are considered to be either cooperators or defectors, the migration dilemma can be envisaged: The cooperators would not want to migrate to a defector-rich deme as they fear of facing exploitation; but without migration, cooperation cannot be established throughout the network of demes. With a view to studying the aforementioned scenario, in this paper, we set up a theoretical model consisting of a coupled map lattice of replicator maps based on two-player-two-strategy games. The replicator map considered is capable of showing a variety of evolutionary outcomes, like convergent (fixed point) outcomes and nonconvergent (periodic and chaotic) outcomes. Furthermore, this coupled network of the replicator maps undergoes the phenomenon of amplitude death leading to nonoscillatory stable synchronized states. We specifically explore the effect of (i) the nature of coupling that models migration between the maps, (ii) the heterogenous demes (in the sense that not all the demes have the same game being played by the individuals), (iii) the degree of the network, and (iv) the cost associated with the migration. In the course of investigation, we are intrigued by the effectiveness of the random migration in sustaining a uniform cooperator fraction across a population irrespective of the details of the replicator dynamics and the interaction among the demes.
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Affiliation(s)
- Shubhadeep Sadhukhan
- Department of Physics, Indian Institute of Technology Kanpur, Uttar Pradesh 208016, India
| | - Rohitashwa Chattopadhyay
- The Institute of Mathematical Sciences, CIT Campus, Taramani, Chennai 600113, India.,Homi Bhabha National Institute, Anushaktinagar, Mumbai 400 094, India
| | - Sagar Chakraborty
- Department of Physics, Indian Institute of Technology Kanpur, Uttar Pradesh 208016, India
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25
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Johnson T, Smirnov O. Temporal assortment of cooperators in the spatial prisoner's dilemma. Commun Biol 2021; 4:1283. [PMID: 34773077 PMCID: PMC8589994 DOI: 10.1038/s42003-021-02804-9] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/11/2020] [Accepted: 10/25/2021] [Indexed: 11/09/2022] Open
Abstract
We study a spatial, one-shot prisoner's dilemma (PD) model in which selection operates on both an organism's behavioral strategy (cooperate or defect) and its decision of when to implement that strategy, which we depict as an organism's choice of one point in time, out of a set of discrete time slots, at which to carry out its PD strategy. Results indicate selection for cooperators across various time slots and parameter settings, including parameter settings in which cooperation would not evolve in an exclusively spatial model-as in work investigating exogenously imposed temporal networks. Moreover, in the presence of time slots, cooperators' portion of the population grows even under different combinations of spatial structure, transition rules, and update dynamics, though rates of cooperator fixation decline under pairwise comparison and synchronous updating. These findings indicate that, under certain evolutionary processes, merely existing in time and space promotes the evolution of cooperation.
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Affiliation(s)
- Tim Johnson
- Atkinson Graduate School of Management, Willamette University, Salem, OR, 97301, USA.
- Center for Governance and Public Policy Research, Willamette University, Salem, OR, 97301, USA.
| | - Oleg Smirnov
- Department of Political Science, Stony Brook University, Stony Brook, NY, 11794, USA
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26
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Arefin MR, Tanimoto J. Imitation and aspiration dynamics bring different evolutionary outcomes in feedback-evolving games. Proc Math Phys Eng Sci 2021. [DOI: 10.1098/rspa.2021.0240] [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
Feedback-evolving games characterize the interplay between the evolution of strategies and environments. Rich dynamics have been derived for such games under the premise of the replicator equation, which unveils persistent oscillations between cooperation and defection. Besides replicator dynamics, here we have employed aspiration dynamics, in which individuals, instead of comparing payoffs with opposite strategies, assess their payoffs by self-evaluation to update strategies. We start with a brief review of feedback-evolving games with replicator dynamics and then comprehensively discuss such games with aspiration dynamics. Interestingly, the tenacious cycles, as perceived in replicator dynamics, cannot be observed in aspiration dynamics. Our analysis reveals that a parameter
θ
—which depicts the strength of cooperation in enhancing the environment—plays a pivotal role in comprehending the dynamics. In particular, with the symmetric aspiration level, if replete and depleted states, respectively, experience Prisoner's Dilemma and Trivial games, the rich environment is achievable only when
θ
> 1. The case
θ
< 1 never allows us to reach the replete state, even with a higher cooperation level. Furthermore, if cooperators aspire less than defectors, then the enhanced state can be achieved with a relatively lower
θ
value compared with the opposite scenario because too much expectation from cooperation can be less beneficial.
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Affiliation(s)
- Md. Rajib Arefin
- Interdisciplinary Graduate School of Engineering Sciences, Kyushu University, Kasuga-koen, Kasuga-shi, Fukuoka 816-8580, Japan
- Department of Mathematics, University of Dhaka, 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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27
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Wang G, Su Q, Wang L. Evolution of state-dependent strategies in stochastic games. J Theor Biol 2021; 527:110818. [PMID: 34181968 DOI: 10.1016/j.jtbi.2021.110818] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/11/2021] [Revised: 06/06/2021] [Accepted: 06/22/2021] [Indexed: 10/21/2022]
Abstract
In a population of interacting individuals, the environment for interactions often changes due to individuals' behaviors, which in turn drive the evolution of individuals' behaviors. The interplay between the environment and individuals' behaviors has been demonstrated to remarkably influence the evolutionary outcomes. In reality, in highly cognitive species such as social primates and human beings, individuals are often capable of perceiving the environment change and then differentiate their strategies across different environment states. We propose a model of environmental feedback with state-dependent strategies: individuals have perceptions of distinct environment states and therefore take distinct sub-strategies under each of them; based on the sub-strategy, individuals then decide their behaviors; their behaviors subsequently modify the environment state. We use the theory of stochastic games and evolutionary dynamics to analyze this idea. We find that when environment changes slower than behaviors, state-dependent strategies (i.e. taking different sub-strategies under different environment states) can outperform state-independent strategies (i.e. taking an identical sub-strategy under all environment states), such as Win-Stay, Lose-Shift, the most leading strategy among state-independent strategies. The intuition is that delayed environmental feedback provides chances for individuals with state-dependent strategies to exploit those with state-independent strategies. Our results hold (1) in both well-mixed and structured populations; (2) when the environment switches between two or more states. Furthermore, the environment changing rate decides if state-dependent strategies benefit global cooperation. The evolution sees the rise of the cooperation level for fast environment switching and the decrease otherwise. Our work stresses that individuals' perceptions of different environment states are beneficial to their survival and social prosperity in a changing world.
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Affiliation(s)
- Guocheng Wang
- Center for Systems and Control, College of Engineering, Peking University, Beijing 100871, China
| | - Qi Su
- Center for Mathematical Biology, University of Pennsylvania, Philadelphia, PA 19104, USA; Department of Mathematics, University of Pennsylvania, Philadelphia, PA19104, USA; Department of Biology, University of Pennsylvania, Philadelphia, PA 19104, USA
| | - Long Wang
- Center for Systems and Control, College of Engineering, Peking University, Beijing 100871, China; Center for Multi-Agent Research, Institute for Artificial Intelligence, Peking University, Beijing 100871, China.
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28
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Huang F, Cao M, Wang L. Learning enables adaptation in cooperation for multi-player stochastic games. J R Soc Interface 2020; 17:20200639. [PMID: 33202177 DOI: 10.1098/rsif.2020.0639] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/08/2023] Open
Abstract
Interactions among individuals in natural populations often occur in a dynamically changing environment. Understanding the role of environmental variation in population dynamics has long been a central topic in theoretical ecology and population biology. However, the key question of how individuals, in the middle of challenging social dilemmas (e.g. the 'tragedy of the commons'), modulate their behaviours to adapt to the fluctuation of the environment has not yet been addressed satisfactorily. Using evolutionary game theory, we develop a framework of stochastic games that incorporates the adaptive mechanism of reinforcement learning to investigate whether cooperative behaviours can evolve in the ever-changing group interaction environment. When the action choices of players are just slightly influenced by past reinforcements, we construct an analytical condition to determine whether cooperation can be favoured over defection. Intuitively, this condition reveals why and how the environment can mediate cooperative dilemmas. Under our model architecture, we also compare this learning mechanism with two non-learning decision rules, and we find that learning significantly improves the propensity for cooperation in weak social dilemmas, and, in sharp contrast, hinders cooperation in strong social dilemmas. Our results suggest that in complex social-ecological dilemmas, learning enables the adaptation of individuals to varying environments.
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Affiliation(s)
- Feng Huang
- Center for Systems and Control, College of Engineering, Peking University, Beijing 100871, People's Republic of China.,Center for Data Science and System Complexity, Faculty of Science and Engineering, University of Groningen, Groningen 9747 AG, The Netherlands
| | - Ming Cao
- Center for Data Science and System Complexity, Faculty of Science and Engineering, University of Groningen, Groningen 9747 AG, The Netherlands
| | - Long Wang
- Center for Systems and Control, College of Engineering, Peking University, Beijing 100871, People's Republic of China
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29
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Arend RJ. The expected prisoner's dilemma - With rationally arising cooperation. PLoS One 2020; 15:e0239299. [PMID: 32997678 PMCID: PMC7526889 DOI: 10.1371/journal.pone.0239299] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/17/2020] [Accepted: 09/03/2020] [Indexed: 11/19/2022] Open
Abstract
Currently, there is no satisfying answer to how cooperation arises rationally in a single-play prisoner's dilemma game with complete information. When player types are known, as well as payoffs and actions, economic analysis through payoff-optimizing computation does not provide a clear path for cooperation. We propose a new form of game-the 'expected' game-and illustrate its implications for theory and practice based on the prisoner's dilemma example. We prove that cooperation can be a rational choice for players in reality in such games defined by a weighted set of payoffs of two or more different reference games.
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Affiliation(s)
- Richard J. Arend
- School of Business, College of Management & Human Service, University of Southern Maine, Portland, ME, United States of America
- * E-mail:
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Taitelbaum A, West R, Assaf M, Mobilia M. Population Dynamics in a Changing Environment: Random versus Periodic Switching. PHYSICAL REVIEW LETTERS 2020; 125:048105. [PMID: 32794803 DOI: 10.1103/physrevlett.125.048105] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/13/2020] [Revised: 05/13/2020] [Accepted: 06/23/2020] [Indexed: 06/11/2023]
Abstract
Environmental changes greatly influence the evolution of populations. Here, we study the dynamics of a population of two strains, one growing slightly faster than the other, competing for resources in a time-varying binary environment modeled by a carrying capacity switching either randomly or periodically between states of abundance and scarcity. The population dynamics is characterized by demographic noise (birth and death events) coupled to a varying environment. We elucidate the similarities and differences of the evolution subject to a stochastically and periodically varying environment. Importantly, the population size distribution is generally found to be broader under intermediate and fast random switching than under periodic variations, which results in markedly different asymptotic behaviors between the fixation probability of random and periodic switching. We also determine the detailed conditions under which the fixation probability of the slow strain is maximal.
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Affiliation(s)
- Ami Taitelbaum
- Racah Institute of Physics, Hebrew University of Jerusalem, Jerusalem 91904, Israel
| | - Robert West
- Department of Applied Mathematics, School of Mathematics, University of Leeds, Leeds LS2 9JT, United Kingdom
| | - Michael Assaf
- Racah Institute of Physics, Hebrew University of Jerusalem, Jerusalem 91904, Israel
| | - Mauro Mobilia
- Department of Applied Mathematics, School of Mathematics, University of Leeds, Leeds LS2 9JT, United Kingdom
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Amaral MA, Javarone MA. Strategy equilibrium in dilemma games with off-diagonal payoff perturbations. Phys Rev E 2020; 101:062309. [PMID: 32688499 DOI: 10.1103/physreve.101.062309] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/01/2020] [Accepted: 06/03/2020] [Indexed: 06/11/2023]
Abstract
We analyze the strategy equilibrium of dilemma games considering a payoff matrix affected by small and random perturbations on the off-diagonal. Notably, a recent work [Proc. R. Soc. A 476, 20200116 (2020)1364-502110.1098/rspa.2020.0116] reported that while cooperation is sustained by perturbations acting on the main diagonal, a less clear scenario emerges when perturbations act on the off-diagonal. Thus, the second case represents the core of this investigation, aimed at completing the description of the effects that payoff perturbations have on the dynamics of evolutionary games. Our results, achieved by analyzing the proposed model under a variety of configurations as different update rules, suggest that off-diagonal perturbations actually constitute a nontrivial form of noise. In particular, the most interesting effects are detected near the phase transition, as perturbations tend to move the strategy distribution towards nonordered states of equilibrium, supporting cooperation when defection is pervading the population, and supporting defection in the opposite case. To conclude, we identified a form of noise that, under controlled conditions, could be used to enhance cooperation and greatly delay its extinction.
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Affiliation(s)
- Marco A Amaral
- Instituto de Humanidades, Artes e Ciências, Universidade Federal do Sul da Bahia-BA, 45996-108, Brazil
| | - Marco A Javarone
- Department of Mathematics, University College London, London WC1E 6BT, United Kingdom
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Social goods dilemmas in heterogeneous societies. Nat Hum Behav 2020; 4:819-831. [DOI: 10.1038/s41562-020-0881-2] [Citation(s) in RCA: 23] [Impact Index Per Article: 5.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/18/2019] [Accepted: 04/07/2020] [Indexed: 12/16/2022]
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Amaral MA, Javarone MA. Heterogeneity in evolutionary games: an analysis of the risk perception. Proc Math Phys Eng Sci 2020; 476:20200116. [PMID: 32523420 DOI: 10.1098/rspa.2020.0116] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/21/2020] [Accepted: 03/24/2020] [Indexed: 11/12/2022] Open
Abstract
In this study, we analyse the relationship between heterogeneity and cooperation. Previous investigations suggest that this relation is non-trivial, as some authors found that heterogeneity sustains cooperation, while others obtained different results. Among the possible forms of heterogeneity, we focus on the individual perception of risks and rewards related to a generic event, which can appear in a number of social and biological systems. The modelling approach is based on the framework of evolutionary game theory. To represent this kind of heterogeneity, we implement small and local perturbations on the pay-off matrix of simple two-strategy games, such as the Prisoner's Dilemma. So, while usually the pay-off is considered to be a global and time-invariant structure, i.e. it is the same for all individuals of a population at any time, in our model its value is continuously affected by small variations, in both time and space (i.e. position on a lattice). We found that such perturbations can be beneficial or detrimental to cooperation, depending on their setting. Notably, cooperation is strongly supported when perturbations act on the main diagonal of the pay-off matrix, whereas when they act on the off-diagonal the resulting effect is more difficult to quantify. To conclude, the proposed model shows a rich spectrum of possible equilibria, whose interpretation might offer insights and enrich the description of several systems.
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Affiliation(s)
- Marco A Amaral
- Instituto de Humanidades, Artes e Ciências, Universidade Federal do Sul da Bahia, Teixeira de Freitas, Bahia 45988, Brazil
| | - Marco A Javarone
- Department of Mathematics, University College London, London, UK
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Zhang Y, Shao C, He S, Gao J. Resilience centrality in complex networks. Phys Rev E 2020; 101:022304. [PMID: 32168562 DOI: 10.1103/physreve.101.022304] [Citation(s) in RCA: 13] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/10/2019] [Accepted: 01/11/2020] [Indexed: 11/07/2022]
Abstract
Resilience describes a system's ability to adjust its activity to retain the basic functionality when errors or failures occur in components (nodes) of the network. Due to the complexity of a system's structure, different components in the system exhibit diversity in the ability to affect the resilience of the system, bringing us a great challenge to protect the system from collapse. A fundamental problem is therefore to propose a physically insightful centrality index, with which to quantify the resilience contribution of a node in any systems effectively. However, existing centrality indexes are not suitable for the problem because they only consider the network structure of the system and ignore the impact of underlying dynamic characteristics. To break the limits, we derive a new centrality index: resilience centrality from the 1D dynamic equation of systems, with which we can quantify the ability of nodes to affect the resilience of the system accurately. Resilience centrality unveils the long-sought relations between the ability of nodes in a system's resilience and network structure of the system: the capacity is mainly determined by the degree and weighted nearest-neighbor degree of the node, in which weighted nearest-neighbor degree plays a prominent role. Further, we demonstrate that weighted nearest-neighbor degree has a positive impact on resilience centrality, while the effect of the degree depends on a specific parameter, average weighted degree β_{eff}, in the 1D dynamic equation. To test the performance of our approach, we construct four real networks from data, which corresponds to two complex systems with entirely different dynamic characteristics. The simulation results demonstrate the effectiveness of our resilience centrality, providing us theoretical insights into the protection of complex systems from collapse.
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Affiliation(s)
- Yongtao Zhang
- State Key Laboratory of Industrial Control Technology, Department of Control Science and Engineering, Zhejiang University, Hangzhou 310027, China
| | - Cunqi Shao
- State Key Laboratory of Industrial Control Technology, Department of Control Science and Engineering, Zhejiang University, Hangzhou 310027, China
| | - Shibo He
- State Key Laboratory of Industrial Control Technology, Department of Control Science and Engineering, Zhejiang University, Hangzhou 310027, China
| | - Jianxi Gao
- Department of Computer Science, Rensselaer Polytechnic Institute, Troy, New York 12180, USA
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