1
|
Botta R, Blanco G, Schaerer CE. Discipline and punishment in panoptical public goods games. Sci Rep 2024; 14:7903. [PMID: 38570552 PMCID: PMC10991498 DOI: 10.1038/s41598-024-57842-0] [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: 11/17/2023] [Accepted: 03/22/2024] [Indexed: 04/05/2024] Open
Abstract
In Public Goods Games (PGG), the temptation to free-ride on others' contributions poses a significant threat to the sustainability of cooperative societies. Therefore, societies strive to mitigate this through incentive systems, employing rewards and punishments to foster cooperative behavior. Thus, peer punishment, in which cooperators sanction defectors, as well as pool punishment, where a centralized punishment institution executes the punishment, is deeply analyzed in previous works. Although the literature indicates that these methods may enhance cooperation on social dilemmas under particular contexts, there are still open questions, for instance, the structural connection between graduated punishment and the monitoring of public goods games. Our investigation proposes a compulsory PGG framework under Panoptical surveillance. Inspired by Foucault's theories on disciplinary mechanisms and biopower, we present a novel mathematical model that scrutinizes the balance between the severity and scope of punishment to catalyze cooperative behavior. By integrating perspectives from evolutionary game theory and Foucault's theories of power and discipline, this research uncovers the theoretical foundations of mathematical frameworks involved in punishment and discipline structures. We show that well-calibrated punishment and discipline schemes, leveraging the panoptical effect for universal oversight, can effectively mitigate the free-rider dilemma, fostering enhanced cooperation. This interdisciplinary approach not only elucidates the dynamics of cooperation in societal constructs but also underscores the importance of integrating diverse methodologies to address the complexities of fostering cooperative evolution.
Collapse
Affiliation(s)
- Rocio Botta
- Polytechnic School, National University of Asuncion, San Lorenzo, Paraguay.
| | - Gerardo Blanco
- Pontificia Universidad Católica de Valparaíso, Valparaíso, Chile
| | | |
Collapse
|
2
|
Kurokawa S. Evolution of spite in an n-player game with an opting-out option. J Theor Biol 2023; 572:111585. [PMID: 37516345 DOI: 10.1016/j.jtbi.2023.111585] [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: 03/05/2023] [Revised: 07/19/2023] [Accepted: 07/24/2023] [Indexed: 07/31/2023]
Abstract
The evolution of altruism and spite is facilitated by positive and negative assortments, respectively. Animals repeatedly meet the same opponents and can choose to keep or terminate the interaction. Previous studies have showed that if the probability that the interaction stops depends on how the pairs are, then a positive assortment can emerge, encouraging the evolution of altruism in dyadic interactions and in interactions involving more than two individuals. In contrast, according to another previous study if the probability that the interaction stops depends on how the pairs are, then a negative assortment can emerge, encouraging the evolution of spite in dyadic interactions. Is the evolution of spite facilitated by interactions involving more than two individuals, in addition to dyadic interactions? The present study shows that the evolution of spite in interactions involving many individuals is possible by studying the repeated n-player game played using spiteful and nonspiteful strategies with opting-out options. These results suggest that spite in large groups may evolve through an opt-out mechanism. It also promotes the investigation about whether there are any examples of spiteful behavior in large groups that have evolved through negative assortment in opt-out options in nature.
Collapse
Affiliation(s)
- Shun Kurokawa
- School of Knowledge Science, Japan Advanced Institute of Science and Technology, 1-1 Asahidai, Nomi, Ishikawa 923-1292, Japan.
| |
Collapse
|
3
|
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 DOI: 10.1098/rsif.2023.0301] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [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.
Collapse
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
| |
Collapse
|
4
|
Zhang M, Huang Y, Jin Y, Bao Y. Government regulation strategy, leading firms' innovation strategy, and following firms imitation strategy: An analysis based on evolutionary game theory. PLoS One 2023; 18:e0286730. [PMID: 37289768 PMCID: PMC10249874 DOI: 10.1371/journal.pone.0286730] [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: 01/11/2023] [Accepted: 05/22/2023] [Indexed: 06/10/2023] Open
Abstract
In the innovation ecosystem, the knowledge-based game behavior of each subject not only pertains to its own survival and development but also affects evolution of the innovation ecosystem. The present study investigates the choice of government's regulation strategy, leading firms' innovation protection strategy and following firms' imitation strategy from the perspective of group evolutionary game. Based on the cost-benefit perspective, an asymmetric tripartite evolutionary game model and a simulation model are constructed to analyze the strategies and stability of the evolutionary equilibrium of each subject. We focus mainly on the protection intensity of innovation achievements by leading enterprises and the difficulty of imitation and substitution by following enterprises. The cost of patent operation and maintenance, government subsidies, and the relative difficulty of technology substitution and imitation were identified as the key factors affecting the evolutionary equilibrium of the system. Based on different scenarios resulting from the aforementioned factors, four equilibrium states are observed in the system, namely {no government regulation, technology secrecy, substitution}, {no government regulation, technology secrecy, imitation}, {no government regulation, patent application, imitation}, and {government regulation, patent application, imitation}. Finally, the study suggests corresponding recommendations for the three parties, which can help governments as well as the leading and following firms to choose appropriate behavioral strategies. At the same time, this study offers positive insights to participants in the global innovation ecosystem.
Collapse
Affiliation(s)
- Mengke Zhang
- School of Management, Beijing Union University, Beijing, China
| | - Yan Huang
- School of Management, Beijing Union University, Beijing, China
| | - Yifan Jin
- School of Management, Beijing Union University, Beijing, China
| | - Yuan Bao
- School of Management, Beijing Union University, Beijing, China
| |
Collapse
|
5
|
Liu J, Peng Y, Zhu P, Yu Y. The Polarization of the Coupling Strength of Interdependent Networks Stimulates Cooperation. ENTROPY 2022; 24:e24050694. [PMID: 35626577 PMCID: PMC9141804 DOI: 10.3390/e24050694] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 03/15/2022] [Revised: 04/27/2022] [Accepted: 05/09/2022] [Indexed: 11/16/2022]
Abstract
We introduce a mixed network coupling mechanism and study its effects on how cooperation evolves in interdependent networks. This mechanism allows some players (conservative-driven) to establish a fixed-strength coupling, while other players (radical-driven) adjust their coupling strength through the evolution of strategy. By means of numerical simulation, a hump-like relationship between the level of cooperation and conservative participant density is revealed. Interestingly, interspecies interactions stimulate polarization of the coupling strength of radical-driven players, promoting cooperation between two types of players. We thus demonstrate that a simple mixed network coupling mechanism substantially expands the scope of cooperation among structured populations.
Collapse
Affiliation(s)
- Jinzhuo Liu
- School of Software, Yunnan University, Kunming 650504, China; (J.L.); (Y.P.)
- School of Artificial Intelligence, Optics and Electronics (iOPEN), Northwestern Polytechnical University, Xi’an 710072, China;
| | - Yunchen Peng
- School of Software, Yunnan University, Kunming 650504, China; (J.L.); (Y.P.)
| | - Peican Zhu
- School of Artificial Intelligence, Optics and Electronics (iOPEN), Northwestern Polytechnical University, Xi’an 710072, China;
| | - Yong Yu
- School of Software, Yunnan University, Kunming 650504, China; (J.L.); (Y.P.)
- Correspondence:
| |
Collapse
|
6
|
The Effect of Bounded Rationality on Human Cooperation with Voluntary Participation. MATHEMATICS 2022. [DOI: 10.3390/math10091550] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/27/2023]
Abstract
The evolution of human cooperation is an important issue concerning social science. A deep understanding of human bounded rationality is a prerequisite for promoting collective cooperation and solving social dilemmas. Here we construct an asymmetric micro-dynamic based on bounded rationality from a micro perspective by combining behavioral economics and cognitive psychology with evolutionary game theory. Asynchronously updated Monte Carlo simulations were conducted where individuals were located on a square lattice to play a voluntary public goods game. The results showed that “free riding” behaviors can be effectively suppressed in most situations. The cooperation level can be obviously enhanced in a population comprising easily satisfied cooperators and greedy defectors. Moreover, essential conditions for the stability of the system are further discussed at the microscopic level, and altruistic behavior can be explained that an individual with lower expectations for or underestimation of a single game is more likely to cooperate. We argue that, compared to traditional approaches, the integration of interdisciplinary ideas should be taken more seriously.
Collapse
|
7
|
Wang SY, Liu YP, Li ML, Li C, Wang RW. Super-rational aspiration induced strategy updating helps resolve the tragedy of the commons in a cooperation system with exit rights. Biosystems 2021; 208:104496. [PMID: 34332036 DOI: 10.1016/j.biosystems.2021.104496] [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: 04/19/2021] [Revised: 06/30/2021] [Accepted: 07/23/2021] [Indexed: 10/20/2022]
Abstract
Avoiding the tragedy of the commons requires altruists to incur some losses to benefit the group. Although specific rules and self-enforcing agreements could help maintain the cooperation system stable, the costly recognition and free-rider problem are still questioned these two cooperation maintenance mechanisms. We here considered the situation of both exit costs and exit benefits in the asymmetric prisoner's dilemma game and introduced a super-rational aspiration induced strategy updating, where players adjust strategies in line with their payoffs and aspirations. If their payoffs reach or exceed the aspiration levels, which may be rational or super-rational, they keep their strategies. Otherwise, they imitate a local neighbor's strategy. We explored this rule in the structured and well-mixed population. The results show that super-rationality and asymmetry could together promote cooperation when exit costs exist. With exit benefit, super-rationality promotes cooperation in both structures and asymmetry only works in the well-mixed population. This suggests that the introduced strategy updating rule could sustain cooperation among egoists with exit rights.
Collapse
Affiliation(s)
- Si-Yi Wang
- School of Ecology and Environment, Northwestern Polytechnical University, Xi'an, 710129, China; Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an, 710129, China
| | - Yan-Ping Liu
- School of Ecology and Environment, Northwestern Polytechnical University, Xi'an, 710129, China; Center for Quantitative Biology, College of Science, Gansu Agricultural University, Lanzhou, 730070, China
| | - Min-Lan Li
- School of Ecology and Environment, Northwestern Polytechnical University, Xi'an, 710129, China; Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an, 710129, China
| | - Cong Li
- School of Ecology and Environment, Northwestern Polytechnical University, Xi'an, 710129, China.
| | - Rui-Wu Wang
- School of Ecology and Environment, Northwestern Polytechnical University, Xi'an, 710129, China.
| |
Collapse
|
8
|
Shen C, Jusup M, Shi L, Wang Z, Perc M, Holme P. Exit rights open complex pathways to cooperation. J R Soc Interface 2021; 18:20200777. [PMID: 33435841 DOI: 10.1098/rsif.2020.0777] [Citation(s) in RCA: 18] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
We study the evolutionary dynamics of the Prisoner's Dilemma game in which cooperators and defectors interact with another actor type called exiters. Rather than being exploited by defectors, exiters exit the game in favour of a small pay-off. We find that this simple extension of the game allows cooperation to flourish in well-mixed populations when iterations or reputation are added. In networked populations, however, the exit option is less conducive to cooperation. Instead, it enables the coexistence of cooperators, defectors, and exiters through cyclic dominance. Other outcomes are also possible as the exit pay-off increases or the network structure changes, including network-wide oscillations in actor abundances that may cause the extinction of exiters and the domination of defectors, although game parameters should favour exiting. The complex dynamics that emerges in the wake of a simple option to exit the game implies that nuances matter even if our analyses are restricted to incentives for rational behaviour.
Collapse
Affiliation(s)
- Chen Shen
- School of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming 650221, People's Republic of China.,Tokyo Tech World Hub Research Initiative, Institute of Innovative Research, Tokyo Institute of Technology, Tokyo 152-8550, Japan
| | - Marko Jusup
- Tokyo Tech World Hub Research Initiative, Institute of Innovative Research, Tokyo Institute of Technology, Tokyo 152-8550, Japan
| | - 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) and School of Mechanical Engineering, Northwestern Polytechnical University, Xi'an 710072, People's Republic of 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, Republic of China.,Complexity Science Hub Vienna, 1080 Vienna, Austria
| | - Petter Holme
- Tokyo Tech World Hub Research Initiative, Institute of Innovative Research, Tokyo Institute of Technology, Tokyo 152-8550, Japan
| |
Collapse
|
9
|
Coalition-structured governance improves cooperation to provide public goods. Sci Rep 2020; 10:9194. [PMID: 32514093 PMCID: PMC7280206 DOI: 10.1038/s41598-020-65960-8] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/15/2020] [Accepted: 05/12/2020] [Indexed: 11/09/2022] Open
Abstract
While the benefits of common and public goods are shared, they tend to be scarce when contributions are provided voluntarily. Failure to cooperate in the provision or preservation of these goods is fundamental to sustainability challenges, ranging from local fisheries to global climate change. In the real world, such cooperative dilemmas occur in multiple interactions with complex strategic interests and frequently without full information. We argue that voluntary cooperation enabled across overlapping coalitions (akin to polycentricity) not only facilitates a higher generation of non-excludable public goods, but it may also allow evolution toward a more cooperative, stable, and inclusive approach to governance. Contrary to any previous study, we show that these merits of multi-coalition governance are far more general than the singular examples occurring in the literature, and they are robust under diverse conditions of excludability, congestion of the non-excludable public good, and arbitrary shapes of the return-to-contribution function. We first confirm the intuition that a single coalition without enforcement and with players pursuing their self-interest without knowledge of returns to contribution is prone to cooperative failure. Next, we demonstrate that the same pessimistic model but with a multi-coalition structure of governance experiences relatively higher cooperation by enabling recognition of marginal gains of cooperation in the game at stake. In the absence of enforcement, public-goods regimes that evolve through a proliferation of voluntary cooperative forums can maintain and increase cooperation more successfully than singular, inclusive regimes.
Collapse
|
10
|
Guo H, Song Z, Geček S, Li X, Jusup M, Perc M, Moreno Y, Boccaletti S, Wang Z. A novel route to cyclic dominance in voluntary social dilemmas. J R Soc Interface 2020; 17:20190789. [PMID: 32126192 DOI: 10.1098/rsif.2019.0789] [Citation(s) in RCA: 28] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
Cooperation is the backbone of modern human societies, making it a priority to understand how successful cooperation-sustaining mechanisms operate. Cyclic dominance, a non-transitive set-up comprising at least three strategies wherein the first strategy overrules the second, which overrules the third, which, in turn, overrules the first strategy, is known to maintain biodiversity, drive competition between bacterial strains, and preserve cooperation in social dilemmas. Here, we present a novel route to cyclic dominance in voluntary social dilemmas by adding to the traditional mix of cooperators, defectors and loners, a fourth player type, risk-averse hedgers, who enact tit-for-tat upon paying a hedging cost to avoid being exploited. When this cost is sufficiently small, cooperators, defectors and hedgers enter a loop of cyclic dominance that preserves cooperation even under the most adverse conditions. By contrast, when the hedging cost is large, hedgers disappear, consequently reverting to the traditional interplay of cooperators, defectors, and loners. In the interim region of hedging costs, complex evolutionary dynamics ensues, prompting transitions between states with two, three or four competing strategies. Our results thus reveal that voluntary participation is but one pathway to sustained cooperation via cyclic dominance.
Collapse
Affiliation(s)
- Hao Guo
- School of Mechanical Engineering, Northwestern Polytechnical University, Xi'an 710072, People's Republic of China.,Center for OPTical IMagery Analysis and Learning (OPTIMAL), Northwestern Polytechnical University, Xi'an 710072, People's Republic of China
| | - Zhao Song
- School of Mechanical Engineering, Northwestern Polytechnical University, Xi'an 710072, People's Republic of China.,Center for OPTical IMagery Analysis and Learning (OPTIMAL), Northwestern Polytechnical University, Xi'an 710072, People's Republic of China
| | - Sunčana Geček
- Division for Marine and Environmental Research, Ruđer Bošković Institute, HR-10002 Zagreb, Croatia
| | - Xuelong Li
- Center for OPTical IMagery Analysis and Learning (OPTIMAL), Northwestern Polytechnical University, Xi'an 710072, People's Republic of China.,School of Computer Science, Northwestern Polytechnical University, Xi'an 710072, People's Republic of China
| | - Marko Jusup
- Tokyo Tech World Research Hub Initiative (WRHI), Institute of Innovative Research, Tokyo Institute of Technology, Tokyo 152-8550, Japan
| | - Matjaž Perc
- Faculty of Natural Sciences and Mathematics, University of Maribor, Koroška cesta 160, 2000 Maribor, Slovenia.,Complexity Science Hub Vienna, Josefstädterstraße 39, Vienna 1080, Austria.,Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan
| | - Yamir Moreno
- Institute for Biocomputation and Physics of Complex Systems (BIFI), University of Zaragoza, 50009 Zaragoza, Spain.,ISI Foundation, Turin 10126, Italy
| | - Stefano Boccaletti
- Unmanned Systems Research Institute, Northwestern Polytechnical University, Xi'an 710072, People's Republic of China.,CNR-Institute of Complex Systems, Via Madonna del Piano 10, 50019 Sesto Fiorentino, Florence, Italy.,Moscow Institute of Physics and Technology, National Research University, Moscow Region 141701, Russia
| | - Zhen Wang
- School of Mechanical Engineering, Northwestern Polytechnical University, Xi'an 710072, People's Republic of China.,Center for OPTical IMagery Analysis and Learning (OPTIMAL), Northwestern Polytechnical University, Xi'an 710072, People's Republic of China
| |
Collapse
|
11
|
Souza PVS, Silva R, Bauch C, Girardi D. Cooperation in a generalized age-structured spatial game. J Theor Biol 2020; 484:109995. [PMID: 31491496 DOI: 10.1016/j.jtbi.2019.109995] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/03/2019] [Revised: 08/18/2019] [Accepted: 09/02/2019] [Indexed: 11/24/2022]
Abstract
The emergence and prevalence of cooperative behavior within a group of selfish individuals remains a puzzle for evolutionary game theory precisely because it conflicts directly with the central idea of natural selection. Accordingly, in recent years, the search for an understanding of how cooperation can be stimulated, even when it conflicts with individual interest, has intensified. We investigate the emergence of cooperation in an age-structured evolutionary spatial game. In it, players age with time and the payoff that they receive after each round depends on their age. We find that the outcome of the game is strongly influenced by the type of distribution used to modify the payoffs according to the age of each player. The results show that, under certain circumstances, cooperators may not only survive but dominate the population.
Collapse
Affiliation(s)
- Paulo Victor Santos Souza
- Departamento de Ciências Exatas e Licenciaturas, Universidade Federal Fluminense, 27213-145, Volta Redonda, Rio de Janeiro, Brazil.
| | - Rafael Silva
- Rua Antônio Barreiros, 212 Aterrado 27215350 Volta Redonda Brazil
| | - Chris Bauch
- Department of Applied Mathematics, University of Waterloo, 200 University Avenue West, Waterloo, Ontario, N2L 3G1, Canada
| | - Daniel Girardi
- Department of Applied Mathematics, University of Waterloo, 200 University Avenue West, Waterloo, Ontario, N2L 3G1, Canada
| |
Collapse
|
12
|
Zhu P, Song Z, Guo H, Wang Z, Zhao T. Adaptive willingness resolves social dilemma in network populations. CHAOS (WOODBURY, N.Y.) 2019; 29:113114. [PMID: 31779363 DOI: 10.1063/1.5093046] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/23/2019] [Accepted: 10/15/2019] [Indexed: 06/10/2023]
Abstract
Cooperation is an effective manner to enable different elements of complex networks to work well. In this work, we propose a coevolution mechanism of learning willingness in the network population: an agent will be more likely to imitate a given neighbor's strategy if her payoff is not less than the average performance of all her neighbors. Interestingly, increase of learning willingness will greatly promote cooperation even under the environment of extremely beneficial temptation to defectors. Through a microscopic analysis, it is unveiled that cooperators are protected due to the appearance of large-size clusters. Pair approximation theory also validates all these findings. Such an adaptive mechanism thus provides a feasible solution to relieve social dilemmas and will inspire further studies.
Collapse
Affiliation(s)
- Peican Zhu
- School of Computer Science and Engineering, Northwestern Polytechnical University (NWPU), Xi'an, Shaanxi 710072, China
| | - Zhao Song
- School of Mechanical Engineering, NWPU, Xi'an, Shaanxi 710072, China
| | - Hao Guo
- School of Mechanical Engineering, NWPU, Xi'an, Shaanxi 710072, China
| | - Zhen Wang
- School of Mechanical Engineering, NWPU, Xi'an, Shaanxi 710072, China
| | - Tianyun Zhao
- School of Automation, NWPU, Xi'an, Shaanxi 710072, China
| |
Collapse
|
13
|
Yamamoto H, Okada I, Taguchi T, Muto M. Effect of voluntary participation on an alternating and a simultaneous prisoner's dilemma. Phys Rev E 2019; 100:032304. [PMID: 31639975 DOI: 10.1103/physreve.100.032304] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/02/2019] [Indexed: 11/07/2022]
Abstract
We studied the evolution of cooperation in the framework of evolutionary game theory, implementing voluntary participation in the prisoner's dilemma. Although previous studies have tried to overcome the dilemma by introducing voluntary participation called a "loner," the question of which strategies among various strategies including voluntary participation are adaptive under competitive circumstances is still an unsolved puzzle. Here we have developed a model that consists of all possible strategies using a one-period memory of past actions. This model enables us to analyze a "melting pot" of strategies, wherein several strategies interact and compete with each other. Our results revealed that one strategy, in which one escapes if a partner defects or cooperates if a partner becomes a loner, dominates and maintains cooperation in an alternating prisoner's dilemma game. However, the so-called "win-stay, lose-shift" strategy dominates in a simultaneous prisoner's dilemma game. Our simulations clearly show that voluntary participation in the prisoner's dilemma game works in the alternating situation rather than the simultaneous one.
Collapse
Affiliation(s)
- H Yamamoto
- Faculty of Business Administration, Rissho University, Osaki 4-2-16, Shinagawa-ku, Tokyo 141-8602, Japan
| | - I Okada
- Faculty of Business Administration, Soka University, Tangi 1-236, Hachioji City, Tokyo 192-8577, Japan
| | - T Taguchi
- College of Systems Engineering and Science, Shibaura Institute of Technology, Fukasaku 307, Minuma-ku, Saitama City, Saitama, 337-8570, Japan
| | - M Muto
- College of Systems Engineering and Science, Shibaura Institute of Technology, Fukasaku 307, Minuma-ku, Saitama City, Saitama, 337-8570, Japan
| |
Collapse
|
14
|
Direct reciprocity and model-predictive rationality explain network reciprocity over social ties. Sci Rep 2019; 9:5367. [PMID: 30931975 PMCID: PMC6443768 DOI: 10.1038/s41598-019-41547-w] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/21/2018] [Accepted: 02/28/2019] [Indexed: 11/16/2022] Open
Abstract
Since M. A. Nowak & R. May’s (1992) influential paper, limiting each agent’s interactions to a few neighbors in a network of contacts has been proposed as the simplest mechanism to support the evolution of cooperation in biological and socio-economic systems. The network allows cooperative agents to self-assort into clusters, within which they reciprocate cooperation. This (induced) network reciprocity has been observed in several theoreticalmodels and shown to predict the fixation of cooperation under a simple rule: the benefit produced by an act of cooperation must outweigh the cost of cooperating with all neighbors. However, the experimental evidence among humans is controversial: though the rule seems to be confirmed, the underlying modeling assumptions are not. Specifically, models assume that agents update their strategies by imitating better performing neighbors, even though imitation lacks rationality when interactions are far from all-to-all. Indeed, imitation did not emerge in experiments. What did emerge is that humans are conditioned by their own mood and that, when in a cooperative mood, they reciprocate cooperation. To help resolve the controversy, we design a model in which we rationally confront the two main behaviors emerging from experiments—reciprocal cooperation and unconditional defection—in a networked prisoner’s dilemma. Rationality is introduced by means of a predictive rule for strategy update and is bounded by the assumed model society. We show that both reciprocity and a multi-step predictive horizon are necessary to stabilize cooperation, and sufficient for its fixation, provided the game benefit-to-cost ratio is larger than a measure of network connectivity. We hence rediscover the rule of network reciprocity, underpinned however by a different evolutionary mechanism.
Collapse
|
15
|
Indirect reciprocity with optional games and monitoring of interactions between defectors. Math Biosci 2018; 310:108-119. [PMID: 30529683 DOI: 10.1016/j.mbs.2018.12.005] [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: 08/09/2018] [Revised: 12/03/2018] [Accepted: 12/05/2018] [Indexed: 11/24/2022]
Abstract
We study evolution of cooperation by indirect reciprocity with optional interactions. There are repeated interactions between two types of players, cooperators and defectors, in a population of finite size. Previously, we considered the scenario where an encounter between a cooperator and a defector results in the defector's identity being revealed with some probability, while an encounter between two defectors does not reveal their identities. Here, we study a generalization of this model: an encounter between a cooperator and a defector results in the defector's identity being revealed with probability QC; an encounter between two defectors results in each of those defectors' identities being revealed independently with probability QD. We find that larger values of QD can significantly increase both the average payoffs for cooperators and, in a dynamical setting, the basin of attraction for cooperation. Moreover, if QC is sufficiently small and QD is sufficiently large, then we find a new behavior over the previous model in which cooperators and defectors can stably coexist. We also study hesitation to cooperate with unknown individuals and defectors refusing interactions with known defectors to preserve their own unknown status.
Collapse
|
16
|
Cardinot M, Griffith J, O'Riordan C, Perc M. Cooperation in the spatial prisoner's dilemma game with probabilistic abstention. Sci Rep 2018; 8:14531. [PMID: 30266934 PMCID: PMC6162230 DOI: 10.1038/s41598-018-32933-x] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/10/2018] [Accepted: 09/12/2018] [Indexed: 11/09/2022] Open
Abstract
Research has shown that the addition of abstention as an option transforms social dilemmas to rock-paper-scissor type games, where defectors dominate cooperators, cooperators dominate abstainers (loners), and abstainers (loners), in turn, dominate defectors. In this way, abstention can sustain cooperation even under adverse conditions, although defection also persists due to cyclic dominance. However, to abstain or to act as a loner has, to date, always been considered as an independent, third strategy to complement traditional cooperation and defection. Here we consider probabilistic abstention, where each player is assigned a probability to abstain in a particular instance of the game. In the two limiting cases, the studied game reverts to the prisoner's dilemma game without loners or to the optional prisoner's dilemma game. For intermediate probabilities, we have a new hybrid game, which turns out to be most favorable for the successful evolution of cooperation. We hope this novel hybrid game provides a more realistic view of the dilemma of optional/voluntary participation.
Collapse
Affiliation(s)
- Marcos Cardinot
- Discipline of Information Technology, National University of Ireland, Galway, Ireland.
| | - Josephine Griffith
- Discipline of Information Technology, National University of Ireland, Galway, Ireland
| | - Colm O'Riordan
- Discipline of Information Technology, National University of Ireland, Galway, Ireland
| | - Matjaž Perc
- Faculty of Natural Sciences and Mathematics, University of Maribor, Koroška cesta 160, SI-2000, Maribor, Slovenia
- School of Electronic and Information Engineering, Beihang University, Beijing, 100191, P.R. China
| |
Collapse
|
17
|
Shen C, Chu C, Geng Y, Jin J, Chen F, Shi L. Cooperation enhanced by the coevolution of teaching activity in evolutionary prisoner's dilemma games with voluntary participation. PLoS One 2018; 13:e0193151. [PMID: 29451899 PMCID: PMC5815606 DOI: 10.1371/journal.pone.0193151] [Citation(s) in RCA: 19] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/03/2017] [Accepted: 02/04/2018] [Indexed: 11/28/2022] Open
Abstract
Voluntary participation, as an additional strategy involved in repeated games, has been proved to be an efficient way to promote the evolution of cooperation theoretically and empirically. Besides, current studies show that the coevolution of teaching activity can promote cooperation. Thus, inspired by aforementioned above, we investigate the effect of coevolution of teaching activity on the evolution of cooperation for prisoner's dilemma game with voluntary participation: when the focal player successfully enforces its strategy on the opponent, his teaching ability will get an increase. Through numerical simulation, we have shown that voluntary participation could effectively promote the fraction of cooperation, which is also affected by the value of increment. Furthermore, we investigate the influence of the increment value on the density of different strategies and find that there exists an optimal increment value that plays an utmost role on the evolutionary dynamics. With regard to this observation, we unveil that an optimal value of increment can lead to strongest heterogeneity in agents' teaching ability, further promoting the evolution of cooperation.
Collapse
Affiliation(s)
- Chen Shen
- School of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming, Yunnan, PR China
| | - Chen Chu
- School of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming, Yunnan, PR China
| | - Yini Geng
- School of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming, Yunnan, PR China
| | - Jiahua Jin
- School of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming, Yunnan, PR China
- Library, Yunnan Normal University, Kunming, Yunnan, PR China
| | - Fei Chen
- School of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming, Yunnan, PR China
| | - Lei Shi
- School of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming, Yunnan, PR China
| |
Collapse
|
18
|
Shen C, Chu C, Guo H, Shi L, Duan J. Coevolution of Vertex Weights Resolves Social Dilemma in Spatial Networks. Sci Rep 2017; 7:15213. [PMID: 29123237 PMCID: PMC5680320 DOI: 10.1038/s41598-017-15603-2] [Citation(s) in RCA: 39] [Impact Index Per Article: 5.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/14/2017] [Accepted: 10/30/2017] [Indexed: 11/16/2022] Open
Abstract
In realistic social system, the role or influence of each individual varies and adaptively changes in time in the population. Inspired by this fact, we thus consider a new coevolution setup of game strategy and vertex weight on a square lattice. In detail, we model the structured population on a square lattice, on which the role or influence of each individual is depicted by vertex weight, and the prisoner’s dilemma game has been applied to describe the social dilemma of pairwise interactions of players. Through numerical simulation, we conclude that our coevolution setup can promote the evolution of cooperation effectively. Especially, there exists a moderate value of δ for each ε that can warrant an optimal resolution of social dilemma. For a further understanding of these results, we find that intermediate value of δ enables the strongest heterogeneous distribution of vertex weight. We hope our coevolution setup of vertex weight will provide new insight for the future research.
Collapse
Affiliation(s)
- Chen Shen
- School of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming, Yunnan, 650221, China
| | - Chen Chu
- School of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming, Yunnan, 650221, China
| | - Hao Guo
- School of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming, Yunnan, 650221, China
| | - Lei Shi
- School of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming, Yunnan, 650221, China. .,Shanghai Lixin University of Accounting and Finance, Shanghai, 201209, China.
| | - Jiangyan Duan
- School of Life Science, Shanxi Normal University, Linfen, Shanxi, 041004, China
| |
Collapse
|
19
|
Chu C, Liu J, Shen C, Jin J, Shi L. Win-stay-lose-learn promotes cooperation in the prisoner's dilemma game with voluntary participation. PLoS One 2017; 12:e0171680. [PMID: 28182707 PMCID: PMC5300200 DOI: 10.1371/journal.pone.0171680] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/01/2016] [Accepted: 01/24/2017] [Indexed: 11/19/2022] Open
Abstract
Voluntary participation, demonstrated to be a simple yet effective mechanism to promote persistent cooperative behavior, has been extensively studied. It has also been verified that the aspiration-based win-stay-lose-learn strategy updating rule promotes the evolution of cooperation. Inspired by this well-known fact, we combine the Win-Stay-Lose-Learn updating rule with voluntary participation: Players maintain their strategies when they are satisfied, or players attempt to imitate the strategy of one randomly chosen neighbor. We find that this mechanism maintains persistent cooperative behavior, even further promotes the evolution of cooperation under certain conditions.
Collapse
Affiliation(s)
- Chen Chu
- School of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming, Yunnan, China
| | - Jinzhuo Liu
- School of Software, Yunnan University, Kunming, Yunnan, China
| | - Chen Shen
- School of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming, Yunnan, China
| | - Jiahua Jin
- School of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming, Yunnan, China
- Library of Yunnan Normal University, Kunming, Yunnan, China
| | - Lei Shi
- School of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming, Yunnan, China
- * E-mail:
| |
Collapse
|
20
|
Szabó G, Bodó KS, Samani KA. Separation of cyclic and starlike hierarchical dominance in evolutionary matrix games. Phys Rev E 2017; 95:012320. [PMID: 28208502 DOI: 10.1103/physreve.95.012320] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/10/2016] [Indexed: 06/06/2023]
Abstract
We study antisymmetric components of matrices characterizing pair interactions in multistrategy evolutionary games. Based on the dyadic decomposition of matrices we distinguish cyclic and starlike hierarchical dominance in the appropriate components. In the symmetric matrix games the strengths of these elementary components are determined. The general features and intrinsic symmetries of these interactions are represented by directed graphs. It is found that the variation of a single matrix component modifies simultaneously the strengths of two starlike hierarchical basis games and many other independent rock-paper-scissors type cyclic basis games. The application of the related concepts is illustrated by discussing the three-strategy voluntary prisoner's dilemma.
Collapse
Affiliation(s)
- György Szabó
- Institute of Technical Physics and Materials Science, Centre for Energy Research, Hungarian Academy of Sciences, P.O. Box 49, H-1525 Budapest, Hungary
| | - Kinga S Bodó
- Budapest University of Technology and Economics, Budafoki út 8, H-1111 Budapest, Hungary
| | | |
Collapse
|
21
|
Kim J, Yook SH, Kim Y. Reciprocity in spatial evolutionary public goods game on double-layered network. Sci Rep 2016; 6:31299. [PMID: 27503801 PMCID: PMC4977568 DOI: 10.1038/srep31299] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/18/2016] [Accepted: 07/15/2016] [Indexed: 11/25/2022] Open
Abstract
Spatial evolutionary games have mainly been studied on a single, isolated network. However, in real world systems, many interaction topologies are not isolated but many different types of networks are inter-connected to each other. In this study, we investigate the spatial evolutionary public goods game (SEPGG) on double-layered random networks (DRN). Based on the mean-field type arguments and numerical simulations, we find that SEPGG on DRN shows very rich interesting phenomena, especially, depending on the size of each layer, intra-connectivity, and inter-connected couplings, the network reciprocity of SEPGG on DRN can be drastically enhanced through the inter-connected coupling. Furthermore, SEPGG on DRN can provide a more general framework which includes the evolutionary dynamics on multiplex networks and inter-connected networks at the same time.
Collapse
Affiliation(s)
- Jinho Kim
- Department of Social Network Science, Kyung Hee University, Seoul 130-701, Korea
| | - Soon-Hyung Yook
- Department of Social Network Science, Kyung Hee University, Seoul 130-701, Korea
- Department of Physics and Research Institute for Basic Sciences, Kyung Hee University, Seoul 130-701, Korea
| | - Yup Kim
- Department of Physics and Research Institute for Basic Sciences, Kyung Hee University, Seoul 130-701, Korea
| |
Collapse
|
22
|
Liu X, He M, Kang Y, Pan Q. Aspiration promotes cooperation in the prisoner's dilemma game with the imitation rule. Phys Rev E 2016; 94:012124. [PMID: 27575094 DOI: 10.1103/physreve.94.012124] [Citation(s) in RCA: 41] [Impact Index Per Article: 5.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/22/2015] [Indexed: 11/07/2022]
Abstract
A model of stochastic evolutionary game dynamics with finite population of size N+M was built. Among these individuals, N individuals update strategies with aspiration updating, while the other M individuals update strategies with imitation updating. In the proposed model, we obtain the expression of the mean fraction of cooperators and analyze some concrete cases. Compared with the standard imitation dynamics, there is always a positive probability to support the formation of cooperation in the system with the aspiration and imitation rules. Moreover, the numerical results indicate that more aspiration-driven individuals lead to a higher mean fraction of imitation-driven cooperators, which means the invasion of the aspiration-driven individuals is conducive to promoting the cooperation of the imitation-driven individuals.
Collapse
Affiliation(s)
- Xuesong Liu
- School of Mathematical Science, Dalian University of Technology, Dalian 116024, China
| | - Mingfeng He
- School of Mathematical Science, Dalian University of Technology, Dalian 116024, China
| | - Yibin Kang
- School of Mathematical Science, 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
| |
Collapse
|
23
|
Szabó G, Király B. Extension of a spatial evolutionary coordination game with neutral options. Phys Rev E 2016; 93:052108. [PMID: 27300831 DOI: 10.1103/physreve.93.052108] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/05/2016] [Indexed: 11/07/2022]
Abstract
The multiagent evolutionary games on a lattice are equivalent to a kinetic Ising model if the uniform pair interactions are defined by a two-strategy coordination game and the logit rule controls the strategy updates. Now we extend this model by allowing the players to use additional neutral strategies that provide zero payoffs for both players if one of them selects one of the neutral strategies. In the resulting n-strategy evolutionary games the analytical methods and numerical simulations indicate continuous order-disorder phase transitions when increasing the noise level if n does not exceed a threshold value. For larger n the system exhibits a first order phase transition at a critical noise level decreasing asymptotically as 2/ln(n).
Collapse
Affiliation(s)
- György Szabó
- Institute of Technical Physics and Materials Science, Centre for Energy Research, Hungarian Academy of Sciences, P.O. Box 49, H-1525 Budapest, Hungary
| | - Balázs Király
- Budapest University of Technology and Economics, Budafoki út 8, H-1111 Budapest, Hungary
| |
Collapse
|
24
|
Zhang J, Chen Z, Liu Z. Fostering cooperation of selfish agents through public goods in relation to the loners. Phys Rev E 2016; 93:032320. [PMID: 27078379 DOI: 10.1103/physreve.93.032320] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/07/2015] [Indexed: 11/07/2022]
Abstract
Altruistic behaviors in multiplayer groups have obtained great attention in the context of the public goods game, which poses a riddle from the evolutionary viewpoint. Here we focus on a particular type of public goods game model in which the benefits of cooperation are either discounted or synergistically enhanced at the appearance of multiple cooperators in a group. Moreover, we focus on the three-strategies profile by adding the role of loners, besides the often-used cooperation and defection. Using the replicator dynamic equations, we investigate a range of dynamical portraits that characterizes the properties of the steady state. Analysis results indicate that loners and cooperators both have chances to be the stable equilibrium points in the presence of perturbations, while defectors fail to do so in this three-strategy competition. Moreover, the coexistence state, in which all three strategies exist in equilibrium, can be led by suitable parameters and stabilized for perturbations. These results elucidate the interplay between the characteristics of the public goods game and evolutionary dynamics in well-mixed systems.
Collapse
Affiliation(s)
- Jianlei Zhang
- Department of Automation, College of Computer and Control Engineering, Nankai University, Tianjin 300071, People's Republic of China and Tianjin Key Laboratory of Intelligent Robotics, Computer and Control Engineering, Nankai University, Tianjin 300071, People's Republic of China
| | - Zengqiang Chen
- Department of Automation, College of Computer and Control Engineering, Nankai University, Tianjin 300071, People's Republic of China and Tianjin Key Laboratory of Intelligent Robotics, Computer and Control Engineering, Nankai University, Tianjin 300071, People's Republic of China
| | - Zhongxin Liu
- Department of Automation, College of Computer and Control Engineering, Nankai University, Tianjin 300071, People's Republic of China and Tianjin Key Laboratory of Intelligent Robotics, Computer and Control Engineering, Nankai University, Tianjin 300071, People's Republic of China
| |
Collapse
|
25
|
Deng X, Zhang Q, Deng Y, Wang Z. A novel framework of classical and quantum prisoner's dilemma games on coupled networks. Sci Rep 2016; 6:23024. [PMID: 26975447 PMCID: PMC4792163 DOI: 10.1038/srep23024] [Citation(s) in RCA: 22] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/30/2015] [Accepted: 02/22/2016] [Indexed: 11/16/2022] Open
Abstract
Evolutionary games on multilayer networks are attracting growing interest. While among previous studies, the role of quantum games in such a infrastructure is still virgin and may become a fascinating issue across a myriad of research realms. To mimick two kinds of different interactive environments and mechanisms, in this paper a new framework of classical and quantum prisoner's dilemma games on two-layer coupled networks is considered. Within the proposed model, the impact of coupling factor of networks and entanglement degree in quantum games on the evolutionary process has been studied. Simulation results show that the entanglement has no impact on the evolution of the classical prisoner's dilemma, while the rise of the coupling factor obviously impedes cooperation in this game, and the evolution of quantum prisoner's dilemma is greatly impacted by the combined effect of entanglement and coupling.
Collapse
Affiliation(s)
- Xinyang Deng
- School of Computer and Information Science, Southwest University, Chongqing, 400715, China
- Center for Quantitative Sciences, Vanderbilt University School of Medicine, Nashville, TN, 37232, USA
| | - Qi Zhang
- School of Computer and Information Science, Southwest University, Chongqing, 400715, China
| | - Yong Deng
- School of Computer and Information Science, Southwest University, Chongqing, 400715, China
- Big Data Decision Institute, Jinan University, Tianhe, Guangzhou, 510632, China
| | - Zhen Wang
- School of Automation, Northwestern Polytechnical University, Xi’an, 710072, China
| |
Collapse
|
26
|
Gianetto DA, Heydari B. Sparse cliques trump scale-free networks in coordination and competition. Sci Rep 2016; 6:21870. [PMID: 26899456 PMCID: PMC4761901 DOI: 10.1038/srep21870] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/15/2015] [Accepted: 02/02/2016] [Indexed: 11/09/2022] Open
Abstract
Cooperative behavior, a natural, pervasive and yet puzzling phenomenon, can be significantly enhanced by networks. Many studies have shown how global network characteristics affect cooperation; however, it is difficult to understand how this occurs based on global factors alone, low-level network building blocks, or motifs are necessary. In this work, we systematically alter the structure of scale-free and clique networks and show, through a stochastic evolutionary game theory model, that cooperation on cliques increases linearly with community motif count. We further show that, for reactive stochastic strategies, network modularity improves cooperation in the anti-coordination Snowdrift game and the Prisoner's Dilemma game but not in the Stag Hunt coordination game. We also confirm the negative effect of the scale-free graph on cooperation when effective payoffs are used. On the flip side, clique graphs are highly cooperative across social environments. Adding cycles to the acyclic scale-free graph increases cooperation when multiple games are considered; however, cycles have the opposite effect on how forgiving agents are when playing the Prisoner's Dilemma game.
Collapse
Affiliation(s)
- David A Gianetto
- School of Systems and Enterprises, Stevens Institute of Technology, Hoboken NJ, USA.,Raytheon Space and Airborne Systems, El Segundo CA, USA
| | - Babak Heydari
- School of Systems and Enterprises, Stevens Institute of Technology, Hoboken NJ, USA
| |
Collapse
|
27
|
Wang Z, Kokubo S, Jusup M, Tanimoto J. Dilemma strength as a framework for advancing evolutionary game theory: Reply to comments on "Universal scaling for the dilemma strength in evolutionary games". Phys Life Rev 2015; 14:56-8. [PMID: 26298212 DOI: 10.1016/j.plrev.2015.07.012] [Citation(s) in RCA: 25] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/13/2015] [Accepted: 07/15/2015] [Indexed: 11/26/2022]
Affiliation(s)
- Zhen Wang
- School of Automation, Northwestern Polytechnical University, Xi'an 710072, China; Interdisciplinary Graduate School of Engineering Sciences, Kyushu University, Fukuoka, 816-8580, Japan.
| | - Satoshi Kokubo
- Interdisciplinary Graduate School of Engineering Sciences, Kyushu University, Fukuoka, 816-8580, Japan
| | - Marko Jusup
- Faculty of Sciences, Kyushu University, Fukuoka 812-8581, Japan.
| | - Jun Tanimoto
- Interdisciplinary Graduate School of Engineering Sciences, Kyushu University, Fukuoka, 816-8580, Japan.
| |
Collapse
|
28
|
Universal scaling for the dilemma strength in evolutionary games. Phys Life Rev 2015; 14:1-30. [PMID: 25979121 DOI: 10.1016/j.plrev.2015.04.033] [Citation(s) in RCA: 345] [Impact Index Per Article: 38.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/11/2015] [Revised: 04/20/2015] [Accepted: 04/20/2015] [Indexed: 11/24/2022]
Abstract
Why would natural selection favor the prevalence of cooperation within the groups of selfish individuals? A fruitful framework to address this question is evolutionary game theory, the essence of which is captured in the so-called social dilemmas. Such dilemmas have sparked the development of a variety of mathematical approaches to assess the conditions under which cooperation evolves. Furthermore, borrowing from statistical physics and network science, the research of the evolutionary game dynamics has been enriched with phenomena such as pattern formation, equilibrium selection, and self-organization. Numerous advances in understanding the evolution of cooperative behavior over the last few decades have recently been distilled into five reciprocity mechanisms: direct reciprocity, indirect reciprocity, kin selection, group selection, and network reciprocity. However, when social viscosity is introduced into a population via any of the reciprocity mechanisms, the existing scaling parameters for the dilemma strength do not yield a unique answer as to how the evolutionary dynamics should unfold. Motivated by this problem, we review the developments that led to the present state of affairs, highlight the accompanying pitfalls, and propose new universal scaling parameters for the dilemma strength. We prove universality by showing that the conditions for an ESS and the expressions for the internal equilibriums in an infinite, well-mixed population subjected to any of the five reciprocity mechanisms depend only on the new scaling parameters. A similar result is shown to hold for the fixation probability of the different strategies in a finite, well-mixed population. Furthermore, by means of numerical simulations, the same scaling parameters are shown to be effective even if the evolution of cooperation is considered on the spatial networks (with the exception of highly heterogeneous setups). We close the discussion by suggesting promising directions for future research including (i) how to handle the dilemma strength in the context of co-evolution and (ii) where to seek opportunities for applying the game theoretical approach with meaningful impact.
Collapse
|
29
|
Intoy B, Pleimling M. Synchronization and extinction in cyclic games with mixed strategies. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 91:052135. [PMID: 26066147 DOI: 10.1103/physreve.91.052135] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/22/2015] [Indexed: 06/04/2023]
Abstract
We consider cyclic Lotka-Volterra models with three and four strategies where at every interaction agents play a strategy using a time-dependent probability distribution. Agents learn from a loss by reducing the probability to play a losing strategy at the next interaction. For that, an agent is described as an urn containing β balls of three and four types, respectively, where after a loss one of the balls corresponding to the losing strategy is replaced by a ball representing the winning strategy. Using both mean-field rate equations and numerical simulations, we investigate a range of quantities that allows us to characterize the properties of these cyclic models with time-dependent probability distributions. For the three-strategy case in a spatial setting we observe a transition from neutrally stable to stable when changing the level of discretization of the probability distribution. For large values of β, yielding a good approximation to a continuous distribution, spatially synchronized temporal oscillations dominate the system. For the four-strategy game the system is always neutrally stable, but different regimes emerge, depending on the size of the system and the level of discretization.
Collapse
Affiliation(s)
- Ben Intoy
- Department of Physics, Virginia Tech, Blacksburg, Virginia 24061-0435, USA
| | - Michel Pleimling
- Department of Physics, Virginia Tech, Blacksburg, Virginia 24061-0435, USA
| |
Collapse
|
30
|
Fixation in large populations: a continuous view of a discrete problem. J Math Biol 2015; 72:283-330. [DOI: 10.1007/s00285-015-0889-9] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/23/2014] [Revised: 03/30/2015] [Indexed: 10/23/2022]
|
31
|
Qian X, Xu F, Yang J, Kurths J. The expansion of neighborhood and pattern formation on spatial prisoner's dilemma. CHAOS (WOODBURY, N.Y.) 2015; 25:043115. [PMID: 25933663 DOI: 10.1063/1.4919080] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
The prisoner's dilemma (PD), in which players can either cooperate or defect, is considered a paradigm for studying the evolution of cooperation in spatially structured populations. There the compact cooperator cluster is identified as a characteristic pattern and the probability of forming such pattern in turn depends on the features of the networks. In this paper, we investigate the influence of expansion of neighborhood on pattern formation by taking a weak PD game with one free parameter T, the temptation to defect. Two different expansion methods of neighborhood are considered. One is based on a square lattice and expanses along four directions generating networks with degree increasing with K=4m. The other is based on a lattice with Moore neighborhood and expanses along eight directions, generating networks with degree of K=8m. Individuals are placed on the nodes of the networks, interact with their neighbors and learn from the better one. We find that cooperator can survive for a broad degree 4≤K≤70 by taking a loose type of cooperator clusters. The former simple corresponding relationship between macroscopic patterns and the microscopic PD interactions is broken. Under a condition that is unfavorable for cooperators such as large T and K, systems prefer to evolve to a loose type of cooperator clusters to support cooperation. However, compared to the well-known compact pattern, it is a suboptimal strategy because it cannot help cooperators dominating the population and always corresponding to a low cooperation level.
Collapse
Affiliation(s)
- Xiaolan Qian
- School of Electronics and Information, Zhejiang University of Media and Communications, Hangzhou 310018, China
| | - Fangqian Xu
- School of Electronics and Information, Zhejiang University of Media and Communications, Hangzhou 310018, China
| | - Junzhong Yang
- School of Science, Beijing University of Posts and Telecommunications, Beijing 100876, China
| | - Jürgen Kurths
- Institute of Physics, Humboldt University Berlin, Berlin D-12489, Germany
| |
Collapse
|
32
|
Evolutionary Voluntary Prisoner’s Dilemma Game under Deterministic and Stochastic Dynamics. ENTROPY 2015. [DOI: 10.3390/e17041660] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
|
33
|
Kim J, Chae H, Yook SH, Kim Y. Spatial evolutionary public goods game on complete graph and dense complex networks. Sci Rep 2015; 5:9381. [PMID: 25796988 PMCID: PMC4369736 DOI: 10.1038/srep09381] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/03/2014] [Accepted: 03/02/2015] [Indexed: 11/09/2022] Open
Abstract
We study the spatial evolutionary public goods game (SEPGG) with voluntary or optional participation on a complete graph (CG) and on dense networks. Based on analyses of the SEPGG rate equation on finite CG, we find that SEPGG has two stable states depending on the value of multiplication factor r, illustrating how the "tragedy of the commons" and "an anomalous state without any active participants" occurs in real-life situations. When r is low (<<), the state with only loners is stable, and the state with only defectors is stable when r is high (>>). We also derive the exact scaling relation for r*. All of the results are confirmed by numerical simulation. Furthermore, we find that a cooperator-dominant state emerges when the number of participants or the mean degree, 〈k〉, decreases. We also investigate the scaling dependence of the emergence of cooperation on r and 〈k〉. These results show how "tragedy of the commons" disappears when cooperation between egoistic individuals without any additional socioeconomic punishment increases.
Collapse
Affiliation(s)
- Jinho Kim
- Department of Physics and Research Institute for Basic Sciences, Kyung Hee University, Seoul 130-701, Korea
| | - Huiseung Chae
- Department of Physics and Research Institute for Basic Sciences, Kyung Hee University, Seoul 130-701, Korea
| | - Soon-Hyung Yook
- Department of Physics and Research Institute for Basic Sciences, Kyung Hee University, Seoul 130-701, Korea
| | - Yup Kim
- Department of Physics and Research Institute for Basic Sciences, Kyung Hee University, Seoul 130-701, Korea
| |
Collapse
|
34
|
Wang X, Nie S, Wang B. Dependency links can hinder the evolution of cooperation in the prisoner's dilemma game on lattices and networks. PLoS One 2015; 10:e0121508. [PMID: 25798579 PMCID: PMC4370660 DOI: 10.1371/journal.pone.0121508] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/12/2015] [Accepted: 02/03/2015] [Indexed: 11/23/2022] Open
Abstract
Networks with dependency links are more vulnerable when facing the attacks. Recent research also has demonstrated that the interdependent groups support the spreading of cooperation. We study the prisoner's dilemma games on spatial networks with dependency links, in which a fraction of individual pairs is selected to depend on each other. The dependency individuals can gain an extra payoff whose value is between the payoff of mutual cooperation and the value of temptation to defect. Thus, this mechanism reflects that the dependency relation is stronger than the relation of ordinary mutual cooperation, but it is not large enough to cause the defection of the dependency pair. We show that the dependence of individuals hinders, promotes and never affects the cooperation on regular ring networks, square lattice, random and scale-free networks, respectively. The results for the square lattice and regular ring networks are demonstrated by the pair approximation.
Collapse
Affiliation(s)
- Xuwen Wang
- Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui, 230026, P. R. China
| | - Sen Nie
- Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui, 230026, P. R. China
| | - Binghong Wang
- Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui, 230026, P. R. China
- College of Physics and Electronic Information Engineering, Wenzhou University, Wenzhou, Zhejiang, 325035, P. R. China
- School of Science, Southwest University of Science and Technology, Mianyang, Sichuan, 621010, P. R. China
| |
Collapse
|
35
|
Szabó G, Bodó KS, Allen B, Nowak MA. Fourier decomposition of payoff matrix for symmetric three-strategy games. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:042811. [PMID: 25375553 DOI: 10.1103/physreve.90.042811] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/30/2014] [Indexed: 06/04/2023]
Abstract
In spatial evolutionary games the payoff matrices are used to describe pair interactions among neighboring players located on a lattice. Now we introduce a way how the payoff matrices can be built up as a sum of payoff components reflecting basic symmetries. For the two-strategy games this decomposition reproduces interactions characteristic to the Ising model. For the three-strategy symmetric games the Fourier components can be classified into four types representing games with self-dependent and cross-dependent payoffs, variants of three-strategy coordinations, and the rock-scissors-paper (RSP) game. In the absence of the RSP component the game is a potential game. The resultant potential matrix has been evaluated. The general features of these systems are analyzed when the game is expressed by the linear combinations of these components.
Collapse
Affiliation(s)
- György Szabó
- Institute of Technical Physics and Materials Science, Research Centre for Natural Sciences, Hungarian Academy of Sciences, P.O. Box 49, H-1525 Budapest, Hungary and Regional Knowledge Centre, Eötvös University, Irányi Dániel u. 4, H-8000 Székesfehérvár, Hungary
| | - Kinga S Bodó
- Roland Eötvös University, Institute of Physics, Pázmány P. sétány 1/A, H-1117 Budapest, Hungary
| | - Benjamin Allen
- Program for Evolutionary Dynamics, Harvard University, One Brattle Square, Cambridge, Massachusetts 02138, USA
| | - Martin A Nowak
- Program for Evolutionary Dynamics, Harvard University, One Brattle Square, Cambridge, Massachusetts 02138, USA and Department of Mathematics, Department of Organismic and Evolutionary Biology, Harvard University, Cambridge, Massachusetts 02138, USA
| |
Collapse
|
36
|
Buesser P, Tomassini M. The role of opportunistic migration in cyclic games. PLoS One 2014; 9:e98190. [PMID: 24892660 PMCID: PMC4043639 DOI: 10.1371/journal.pone.0098190] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/05/2014] [Accepted: 04/25/2014] [Indexed: 11/18/2022] Open
Abstract
We study cyclic evolutionary games in a spatial diluted grid environment in which agents strategically interact locally but can also opportunistically move to other positions within a given migration radius. We find that opportunistic migration can inverse the cyclic prevalence between the strategies when the frequency of random imitation is large enough compared to the payoff-driven imitation. At the transition the average size of the patterns diverges and this threatens diversity of strategies.
Collapse
Affiliation(s)
- Pierre Buesser
- Faculty of Business and Economics, University of Lausanne, Lausanne, Switzerland
- * E-mail:
| | - Marco Tomassini
- Faculty of Business and Economics, University of Lausanne, Lausanne, Switzerland
| |
Collapse
|
37
|
Kun Á, Dieckmann U. Resource heterogeneity can facilitate cooperation. Nat Commun 2014; 4:2453. [PMID: 24088665 PMCID: PMC3806347 DOI: 10.1038/ncomms3453] [Citation(s) in RCA: 35] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/14/2012] [Accepted: 08/16/2013] [Indexed: 11/19/2022] Open
Abstract
Although social structure is known to promote cooperation, by locally exposing selfish agents to their own deeds, studies to date assumed that all agents have access to the same level of resources. This is clearly unrealistic. Here we find that cooperation can be maintained when some agents have access to more resources than others. Cooperation can then emerge even in populations in which the temptation to defect is so strong that players would act fully selfishly if their resources were distributed uniformly. Resource heterogeneity can thus be crucial for the emergence and maintenance of cooperation. We also show that resource heterogeneity can hinder cooperation once the temptation to defect is significantly lowered. In all cases, the level of cooperation can be maximized by managing resource heterogeneity. Differences in resource availability or inequality of wealth are common both in nature and in human societies. Here the authors find that such inequality facilitates cooperation when the generation of public goods is inefficient, but hinders cooperation when the efficiency of joint actions is high.
Collapse
Affiliation(s)
- Ádám Kun
- 1] Evolution and Ecology Program, International Institute for Advanced System Analysis, Schlossplatz 1, A-2361 Laxenburg, Austria [2] Parmenides Center for the Conceptual Foundations of Science, Kirchplatz 1, D-82049 Munich/Pullach, Germany [3] Department of Plant Systematics, Ecology and Theoretical Biology, Institute of Biology, Eötvös University, Pázmány Péter sétány 1/C, 1117 Budapest, Hungary [4] Research Group of Theoretical Biology and Evolutionary Ecology, Eötvös University and The Hungarian Academy of Sciences, Pázmány P. sétány 1/C, H-1117 Budapest, Hungary
| | | |
Collapse
|
38
|
Jeong HC, Oh SY, Allen B, Nowak MA. Optional games on cycles and complete graphs. J Theor Biol 2014; 356:98-112. [PMID: 24780293 DOI: 10.1016/j.jtbi.2014.04.025] [Citation(s) in RCA: 24] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/18/2014] [Revised: 04/16/2014] [Accepted: 04/17/2014] [Indexed: 11/16/2022]
Abstract
We study stochastic evolution of optional games on simple graphs. There are two strategies, A and B, whose interaction is described by a general payoff matrix. In addition, there are one or several possibilities to opt out from the game by adopting loner strategies. Optional games lead to relaxed social dilemmas. Here we explore the interaction between spatial structure and optional games. We find that increasing the number of loner strategies (or equivalently increasing mutational bias toward loner strategies) facilitates evolution of cooperation both in well-mixed and in structured populations. We derive various limits for weak selection and large population size. For some cases we derive analytic results for strong selection. We also analyze strategy selection numerically for finite selection intensity and discuss combined effects of optionality and spatial structure.
Collapse
Affiliation(s)
- Hyeong-Chai Jeong
- Department of Physics, Sejong University, Gangjingu, Seoul 143-747, Republic of Korea; Program for Evolutionary Dynamics, Harvard University, Cambridge, MA 20138, USA
| | - Seung-Yoon Oh
- Department of Physics, Sejong University, Gangjingu, Seoul 143-747, Republic of Korea
| | - Benjamin Allen
- Program for Evolutionary Dynamics, Harvard University, Cambridge, MA 20138, USA; Department of Mathematics, Emmanuel College, Boston, MA 02115, USA
| | - Martin A Nowak
- Program for Evolutionary Dynamics, Harvard University, Cambridge, MA 20138, USA; Department of Mathematics, Harvard University, Cambridge, MA 20138, USA; Department of Organismic and Evolutionary Biology, Harvard University, Cambridge, MA 20138, USA
| |
Collapse
|
39
|
Hashimoto K. Multigame effect in finite populations induces strategy linkage between two games. J Theor Biol 2014; 345:70-7. [PMID: 24361329 DOI: 10.1016/j.jtbi.2013.12.007] [Citation(s) in RCA: 25] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/31/2013] [Revised: 11/05/2013] [Accepted: 12/05/2013] [Indexed: 11/18/2022]
Abstract
Evolutionary game dynamics with two 2-strategy games in a finite population has been investigated in this study. Traditionally, frequency-dependent evolutionary dynamics are modeled by deterministic replicator dynamics under the assumption that the population size is infinite. However, in reality, population sizes are finite. Recently, stochastic processes in finite populations have been introduced into evolutionary games in order to study finite size effects in evolutionary game dynamics. However, most of these studies focus on populations playing only single games. In this study, we investigate a finite population with two games and show that a finite population playing two games tends to evolve toward a specific direction to form particular linkages between the strategies of the two games.
Collapse
Affiliation(s)
- Koh Hashimoto
- Graduate School of Arts and Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo 153-8902, Japan.
| |
Collapse
|
40
|
Effect of initial fraction of cooperators on cooperative behavior in evolutionary prisoner's dilemma game. PLoS One 2013; 8:e76942. [PMID: 24244270 PMCID: PMC3820665 DOI: 10.1371/journal.pone.0076942] [Citation(s) in RCA: 46] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/25/2013] [Accepted: 09/02/2013] [Indexed: 11/19/2022] Open
Abstract
We investigate the influence of initial fraction of cooperators on the evolution of cooperation in spatial prisoner's dilemma games. Compared with the results of heterogeneous networks, we find that there is a relatively low initial fraction of cooperators to guarantee higher equilibrium cooperative level. While this interesting phenomenon is contrary to the commonly shared knowledge that higher initial fraction of cooperators can provide better environment for the evolution of cooperation. To support our outcome, we explore the time courses of cooperation and find that the whole course can be divided into two sequent stages: enduring (END) and expanding (EXP) periods. At the end of END period, thought there is a limited number of cooperator clusters left for the case of low initial setup, these clusters can smoothly expand to hold the whole system in the EXP period. However, for high initial fraction of cooperators, superfluous cooperator clusters hinder their effective expansion, which induces many remaining defectors surrounding the cooperator clusters. Moreover, through intensive analysis, we also demonstrate that when the tendency of three cooperation cluster characteristics (cluster size, cluster number and cluster shape) are consistent within END and EXP periods, the state that maximizes cooperation can be favored.
Collapse
|
41
|
Wang Z, Kokubo S, Tanimoto J, Fukuda E, Shigaki K. Insight into the so-called spatial reciprocity. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 88:042145. [PMID: 24229153 DOI: 10.1103/physreve.88.042145] [Citation(s) in RCA: 37] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/23/2013] [Indexed: 06/02/2023]
Abstract
Up to now, there have been a great number of studies that demonstrate the effect of spatial topology on the promotion of cooperation dynamics (namely, the so-called "spatial reciprocity"). However, most researchers probably attribute it to the positive assortment of strategies supported by spatial arrangement. In this paper, we analyze the time course of cooperation evolution under different evolution rules. Interestingly, a typical evolution process can be divided into two evident periods: the enduring (END) period and the expanding (EXP) period where the former features that cooperators try to endure defectors' invasion and the latter shows that perfect C clusters fast expand their area. We find that the final cooperation level relies on two key factors: the formation of the perfect C cluster at the end of the END period and the expanding fashion of the perfect C cluster during the EXP period. For deterministic rule, the smooth expansion of C cluster boundaries enables cooperators to reach a dominant state, whereas, the rough boundaries for stochastic rule cannot provide a sufficient beneficial environment for the evolution of cooperation. Moreover, we show that expansion of the perfect C cluster is closely related to the cluster coefficient of interaction topology. To some extent, we present a viable method for understanding the spatial reciprocity mechanism in nature and hope that it will inspire further studies to resolve social dilemmas.
Collapse
Affiliation(s)
- Zhen Wang
- Department of Physics, Hong Kong Baptist University, Kowloon Tong, Hong Kong and Center for Nonlinear Studies, the Beijing-Hong Kong-Singapore Joint Center for Nonlinear and Complex Systems (Hong Kong), Hong Kong Baptist University, Kowloon Tong, Hong Kong
| | | | | | | | | |
Collapse
|
42
|
Abstract
In this paper, I investigate the co-evolution of fast and slow strategy spread and game strategies in populations of spatially distributed agents engaged in a one off evolutionary dilemma game. Agents are characterized by a pair of traits, a game strategy (cooperate or defect) and a binary ‘advertising’ strategy (advertise or don’t advertise). Advertising, which comes at a cost , allows investment into faster propagation of the agents’ traits to adjacent individuals. Importantly, game strategy and advertising strategy are subject to the same evolutionary mechanism. Via analytical reasoning and numerical simulations I demonstrate that a range of advertising costs exists, such that the prevalence of cooperation is significantly enhanced through co-evolution. Linking costly replication to the success of cooperators exposes a novel co-evolutionary mechanism that might contribute towards a better understanding of the origins of cooperation-supporting heterogeneity in agent populations.
Collapse
Affiliation(s)
- Markus Brede
- Department of Electronics and Computer Science, University of Southampton, Southampton, Hampshire, United Kingdom.
| |
Collapse
|
43
|
Szabó G, Szolnoki A, Czakó L. Coexistence of fraternity and egoism for spatial social dilemmas. J Theor Biol 2013; 317:126-32. [PMID: 23079284 DOI: 10.1016/j.jtbi.2012.10.014] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/17/2012] [Revised: 10/06/2012] [Accepted: 10/08/2012] [Indexed: 11/19/2022]
Abstract
We have studied an evolutionary game with spatially arranged players who can choose one of the two strategies (named cooperation and defection for social dilemmas) when playing with their neighbors. In addition to the application of the usual strategies in the present model the players are also characterized by one of the two extreme personal features representing the egoist or fraternal behavior. During the evolution each player can modify both her own strategy and/or personal feature via a myopic update process in order to improve her utility. The results of numerical simulations and stability analysis are summarized in phase diagrams representing a wide scale of spatially ordered distribution of strategies and personal features when varying the payoff parameters. In most of the cases only two of the four possible options prevail and may form sublattice ordered spatial structure. The evolutionary advantage of the fraternal attitude is demonstrated within a large range of payoff parameters including the region of prisoner's dilemma where egoist defectors and fraternal cooperators form a role-separating chessboard like pattern.
Collapse
Affiliation(s)
- György Szabó
- Institute of Technical Physics and Materials Science, Research Centre for Natural Sciences, Hungarian Academy of Sciences, P.O. Box 49, H-1525 Budapest, Hungary.
| | | | | |
Collapse
|
44
|
Traulsen A, Claussen JC, Hauert C. Stochastic differential equations for evolutionary dynamics with demographic noise and mutations. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 85:041901. [PMID: 22680492 DOI: 10.1103/physreve.85.041901] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/03/2011] [Revised: 03/09/2012] [Indexed: 06/01/2023]
Abstract
We present a general framework to describe the evolutionary dynamics of an arbitrary number of types in finite populations based on stochastic differential equations (SDEs). For large, but finite populations this allows us to include demographic noise without requiring explicit simulations. Instead, the population size only rescales the amplitude of the noise. Moreover, this framework admits the inclusion of mutations between different types, provided that mutation rates μ are not too small compared to the inverse population size 1/N. This ensures that all types are almost always represented in the population and that the occasional extinction of one type does not result in an extended absence of that type. For μN≪1 this limits the use of SDEs, but in this case there are well established alternative approximations based on time scale separation. We illustrate our approach by a rock-scissors-paper game with mutations, where we demonstrate excellent agreement with simulation based results for sufficiently large populations. In the absence of mutations the excellent agreement extends to small population sizes.
Collapse
Affiliation(s)
- Arne Traulsen
- Evolutionary Theory Group, Max-Planck-Institute for Evolutionary Biology, August-Thienemann-Strasse 2, 24306 Plön, Germany
| | | | | |
Collapse
|
45
|
Szolnoki A, Szabó G, Czakó L. Competition of individual and institutional punishments in spatial public goods games. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 84:046106. [PMID: 22181226 DOI: 10.1103/physreve.84.046106] [Citation(s) in RCA: 43] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/26/2011] [Indexed: 05/31/2023]
Abstract
We have studied the evolution of strategies in spatial public goods games where both individual (peer) and institutional (pool) punishments are present in addition to unconditional defector and cooperator strategies. The evolution of strategy distribution is governed by imitation based on the random sequential comparison of neighbors' payoff for a fixed level of noise. Using numerical simulations, we evaluate the strategy frequencies and phase diagrams when varying the synergy factor, punishment cost, and fine. Our attention is focused on two extreme cases describing all the relevant behaviors in such a complex system. According to our numerical data peer punishers prevail and control the system behavior in a large segments of parameters while pool punishers can only survive in the limit of weak peer punishment when a rich variety of solutions is observed. Paradoxically, the two types of punishment may extinguish each other's impact, resulting in the triumph of defectors. The technical difficulties and suggested methods are briefly discussed.
Collapse
Affiliation(s)
- Attila Szolnoki
- Research Institute for Technical Physics and Materials Science, P.O. Box 49, H-1525 Budapest, Hungary
| | | | | |
Collapse
|
46
|
Aktipis CA. Is cooperation viable in mobile organisms? Simple Walk Away rule favors the evolution of cooperation in groups. EVOL HUM BEHAV 2011; 32:263-276. [PMID: 21666771 DOI: 10.1016/j.evolhumbehav.2011.01.002] [Citation(s) in RCA: 56] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/20/2022]
Abstract
The evolution of cooperation through partner choice mechanisms is often thought to involve relatively complex cognitive abilities. Using agent-based simulations I model a simple partner choice rule, the 'Walk Away' rule, where individuals stay in groups that provide higher returns (by virtue of having more cooperators), and 'Walk Away' from groups providing low returns. Implementing this conditional movement rule in a public goods game leads to a number of interesting findings: 1) cooperators have a selective advantage when thresholds are high, corresponding to low tolerance for defectors, 2) high thresholds lead to high initial rates of movement and low final rates of movement (after selection), and 3) as cooperation is selected, the population undergoes a spatial transition from high migration (and a many small and ephemeral groups) to low migration (and large and stable groups). These results suggest that the very simple 'Walk Away' rule of leaving uncooperative groups can favor the evolution of cooperation, and that cooperation can evolve in populations in which individuals are able to move in response to local social conditions. A diverse array of organisms are able to leave degraded physical or social environments. The ubiquitous nature of conditional movement suggests that 'Walk Away' dynamics may play an important role in the evolution of social behavior in both cognitively complex and cognitively simple organisms.
Collapse
Affiliation(s)
- C Athena Aktipis
- Department of Ecology and Evolutionary Biology, University of Arizona, P.O. Box 210088, Tucson, AZ 85721, , phone: 215 221 4493
| |
Collapse
|
47
|
Dai Q, Cheng H, Li H, Li Y, Zhang M, Yang J. Crossover between structured and well-mixed networks in an evolutionary prisoner's dilemma game. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 84:011103. [PMID: 21867109 DOI: 10.1103/physreve.84.011103] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/17/2011] [Indexed: 05/31/2023]
Abstract
In a spatial evolutionary prisoner's dilemma game (PDG), individuals interact with their neighbors and update their strategies according to some rules. As is well known, cooperators are destined to become extinct in a well-mixed population, whereas they could emerge and be sustained on a structured network. In this work, we introduce a simple model to investigate the crossover between a structured network and a well-mixed one in an evolutionary PDG. In the model, each link j is designated a rewiring parameter τ(j), which defines the time interval between two successive rewiring events for link j. By adjusting the rewiring parameter τ (the mean time interval for any link in the network), we could change a structured network into a well-mixed one. For the link rewiring events, three situations are considered: one synchronous situation and two asynchronous situations. Simulation results show that there are three regimes of τ: large τ where the density of cooperators ρ(c) rises to ρ(c,∞) (the value of ρ(c) for the case without link rewiring), small τ where the mean-field description for a well-mixed network is applicable, and moderate τ where the crossover between a structured network and a well-mixed one happens.
Collapse
Affiliation(s)
- Qionglin Dai
- School of Science, Beijing University of Posts and Telecommunications, Beijing 100876, China
| | | | | | | | | | | |
Collapse
|
48
|
Szolnoki A, Szabó G, Perc M. Phase diagrams for the spatial public goods game with pool punishment. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 83:036101. [PMID: 21517552 DOI: 10.1103/physreve.83.036101] [Citation(s) in RCA: 72] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/20/2010] [Indexed: 05/30/2023]
Abstract
The efficiency of institutionalized punishment is studied by evaluating the stationary states in the spatial public goods game comprising unconditional defectors, cooperators, and cooperating pool punishers as the three competing strategies. Fines and costs of pool punishment are considered as the two main parameters determining the stationary distributions of strategies on the square lattice. Each player collects a payoff from five five-person public goods games, and the evolution of strategies is subsequently governed by imitation based on pairwise comparisons at a low level of noise. The impact of pool punishment on the evolution of cooperation in structured populations is significantly different from that reported previously for peer punishment. Representative phase diagrams reveal remarkably rich behavior, depending also on the value of the synergy factor that characterizes the efficiency of investments payed into the common pool. Besides traditional single- and two-strategy stationary states, a rock-paper-scissors type of cyclic dominance can emerge in strikingly different ways.
Collapse
Affiliation(s)
- Attila Szolnoki
- Research Institute for Technical Physics and Materials Science, Post Office Box 49, H-1525 Budapest, Hungary
| | | | | |
Collapse
|
49
|
Wang Z, Murks A, Du WB, Rong ZH, Perc M. Coveting thy neighbors fitness as a means to resolve social dilemmas. J Theor Biol 2011; 277:19-26. [PMID: 21354430 DOI: 10.1016/j.jtbi.2011.02.016] [Citation(s) in RCA: 75] [Impact Index Per Article: 5.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/16/2010] [Revised: 01/18/2011] [Accepted: 02/19/2011] [Indexed: 11/29/2022]
Abstract
In spatial evolutionary games the fitness of each individual is traditionally determined by the payoffs it obtains upon playing the game with its neighbors. Since defection yields the highest individual benefits, the outlook for cooperators is gloomy. While network reciprocity promotes collaborative efforts, chances of averting the impending social decline are slim if the temptation to defect is strong. It is, therefore, of interest to identify viable mechanisms that provide additional support for the evolution of cooperation. Inspired by the fact that the environment may be just as important as inheritance for individual development, we introduce a simple switch that allows a player to either keep its original payoff or use the average payoff of all its neighbors. Depending on which payoff is higher, the influence of either option can be tuned by means of a single parameter. We show that, in general, taking into account the environment promotes cooperation. Yet coveting the fitness of one's neighbors too strongly is not optimal. In fact, cooperation thrives best only if the influence of payoffs obtained in the traditional way is equal to that of the average payoff of the neighborhood. We present results for the prisoner's dilemma and the snowdrift game, for different levels of uncertainty governing the strategy adoption process, and for different neighborhood sizes. Our approach outlines a viable route to increased levels of cooperative behavior in structured populations, but one that requires a thoughtful implementation.
Collapse
Affiliation(s)
- Zhen Wang
- School of Physics, Nankai University, Tianjin 300071, China
| | | | | | | | | |
Collapse
|
50
|
Izquierdo SS, Izquierdo LR, Vega-Redondo F. The option to leave: Conditional dissociation in the evolution of cooperation. J Theor Biol 2010; 267:76-84. [PMID: 20688083 DOI: 10.1016/j.jtbi.2010.07.039] [Citation(s) in RCA: 49] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/18/2010] [Revised: 07/01/2010] [Accepted: 07/28/2010] [Indexed: 10/19/2022]
|