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Guo H, Shen C, Zou R, Tao P, Shi Y, Wang Z, Xing J. Complex pathways to cooperation emergent from asymmetry in heterogeneous populations. CHAOS (WOODBURY, N.Y.) 2024; 34:023139. [PMID: 38416672 DOI: 10.1063/5.0188177] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/20/2023] [Accepted: 02/02/2024] [Indexed: 03/01/2024]
Abstract
Cooperation within asymmetric populations has garnered significant attention in evolutionary games. This paper explores cooperation evolution in populations with weak and strong players, using a game model where players choose between cooperation and defection. Asymmetry stems from different benefits for strong and weak cooperators, with their benefit ratio indicating the degree of asymmetry. Varied rankings of parameters including the asymmetry degree, cooperation costs, and benefits brought by weak players give rise to scenarios including the prisoner's dilemma (PDG) for both player types, the snowdrift game (SDG), and mixed PDG-SDG interactions. Our results indicate that in an infinite well-mixed population, defection remains the dominant strategy when strong players engage in the prisoner's dilemma game. However, if strong players play snowdrift games, global cooperation increases with the proportion of strong players. In this scenario, strong cooperators can prevail over strong defectors when the proportion of strong players is low, but the prevalence of cooperation among strong players decreases as their proportion increases. In contrast, within a square lattice, the optimum global cooperation emerges at intermediate proportions of strong players with moderate degrees of asymmetry. Additionally, weak players protect cooperative clusters from exploitation by strong defectors. This study highlights the complex dynamics of cooperation in asymmetric interactions, contributing to the theory of cooperation in asymmetric games.
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Affiliation(s)
- Hao Guo
- Department of Computer Science and Technology, Tsinghua University, Beijing 100084, China
| | - Chen Shen
- Faculty of Engineering Sciences, Kyushu University, Fukuoka 816-8580, Japan
| | - Rongcheng Zou
- School of Automation, Northwestern Polytechnical University, Xi'an 710072, China
| | - Pin Tao
- Department of Computer Science and Technology, Tsinghua University, Beijing 100084, China
| | - Yuanchun Shi
- Department of Computer Science and Technology, Tsinghua University, Beijing 100084, China
| | - Zhen Wang
- School of Artificial Intelligence, Optics and Electronics (iOPEN), Northwestern Polytechnical University, Xi'an 710072, China
| | - Junliang Xing
- Department of Computer Science and Technology, Tsinghua University, Beijing 100084, China
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2
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Guo H, Shen C, Hu S, Xing J, Tao P, Shi Y, Wang Z. Facilitating cooperation in human-agent hybrid populations through autonomous agents. iScience 2023; 26:108179. [PMID: 37920671 PMCID: PMC10618689 DOI: 10.1016/j.isci.2023.108179] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/19/2023] [Revised: 07/10/2023] [Accepted: 10/09/2023] [Indexed: 11/04/2023] Open
Abstract
Cooperative AI has shown its effectiveness in solving the conundrum of cooperation. Understanding how cooperation emerges in human-agent hybrid populations is a topic of significant interest, particularly in the realm of evolutionary game theory. In this article, we scrutinize how cooperative and defective Autonomous Agents (AAs) influence human cooperation in social dilemma games with a one-shot setting. Focusing on well-mixed populations, we find that cooperative AAs have a limited impact in the prisoner's dilemma games but facilitate cooperation in the stag hunt games. Surprisingly, defective AAs can promote complete dominance of cooperation in the snowdrift games. As the proportion of AAs increases, both cooperative and defective AAs have the potential to cause human cooperation to disappear. We then extend our investigation to consider the pairwise comparison rule and complex networks, elucidating that imitation strength and population structure are critical for the emergence of human cooperation in human-agent hybrid populations.
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Affiliation(s)
- Hao Guo
- School of Artificial Intelligence, Optics and Electronics (iOPEN), Northwestern Polytechnical University, Xi’an 710072, China
- Department of Computer Science and Technology, Tsinghua University, Beijing 100084, China
| | - Chen Shen
- Faculty of Engineering Sciences, Kyushu University, Kasuga-koen, Kasuga-shi, Fukuoka 816-8580, Japan
| | - Shuyue Hu
- Shanghai Artificial Intelligence Laboratory, Shanghai, China
| | - Junliang Xing
- Department of Computer Science and Technology, Tsinghua University, Beijing 100084, China
| | - Pin Tao
- Department of Computer Science and Technology, Tsinghua University, Beijing 100084, China
| | - Yuanchun Shi
- Department of Computer Science and Technology, Tsinghua University, Beijing 100084, China
| | - Zhen Wang
- School of Artificial Intelligence, Optics and Electronics (iOPEN), Northwestern Polytechnical University, Xi’an 710072, China
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3
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Wang SY, Yao X, Yang YM, Chen D, Wang RW, Xie FJ. Super-rational aspiration promotes cooperation in the asymmetric game with peer exit punishment and reward. Heliyon 2023; 9:e16729. [PMID: 37346327 PMCID: PMC10279827 DOI: 10.1016/j.heliyon.2023.e16729] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/31/2022] [Revised: 05/19/2023] [Accepted: 05/25/2023] [Indexed: 06/23/2023] Open
Abstract
Super-rational aspiration induced strategy updating with exit rights has been considered in some previous studies, in which the players adjust strategies in line with their payoffs and aspirations, and they have access to exit the game. However, exit payoffs for exiting players are automatically allocated, which is clearly contrary to reality. In this study, evolutionary cooperation dynamics with super-rational aspiration and asymmetry in the Prisoner's Dilemma game is investigated, where exit payoffs are implemented by local peers. The results show that for different population structures, the asymmetry of the system is always contributive to the participation of the players. Furthermore, we show that under different exit payoffs, super-rationality and asymmetry are conductive to the evolution of cooperation.
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Affiliation(s)
- Si-Yi Wang
- School of Modern Posts, Xi’an University of Posts & Telecommunications, Xi’an, Shaanxi, 710061, China
| | - Xin Yao
- School of Modern Posts, Xi’an University of Posts & Telecommunications, Xi’an, Shaanxi, 710061, China
| | - Yi-Mei Yang
- Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an, 710129, China
| | - Daniel Chen
- The High School Affiliated to Renmin University of China, Beijing, 100097, China
| | - Rui-Wu Wang
- School of Ecology and Environment, Northwestern Polytechnical University, Xi'an, 710129, China
| | - Feng-Jie Xie
- School of Modern Posts, Xi’an University of Posts & Telecommunications, Xi’an, Shaanxi, 710061, China
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4
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Impact of social reward on the evolution of cooperation in voluntary prisoner's dilemma. Biosystems 2023; 223:104821. [PMID: 36464161 DOI: 10.1016/j.biosystems.2022.104821] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/26/2022] [Revised: 11/26/2022] [Accepted: 11/28/2022] [Indexed: 12/02/2022]
Abstract
The existence and sustainability of cooperation is a critical issue in nature and social systems. Reward is an essential mechanism to enhance cooperation. Meanwhile, some individuals loathe competition and then choose to escape and become a loner in competition. In this scenario, we propose a four-strategy networked evolutionary game model involving rewarders, loners, cooperators, and defectors. The classical square lattice and the Erdös-Rényi random network are adopted to describe the interaction between individuals. The four-strategy model is an extension of the classic prisoner's dilemma game model. The simulation results show that the introduction of new strategic choices can significantly improve cooperation in the population. The promotion level of cooperation is directly correlated with reward intensity and negatively correlated with reward cost. With regard to the evolution of altruistic behaviors, the fixed income from interactions with loners has an impact that is connected to the temptation to defect. Furthermore, by analyzing characteristic snapshots of four strategies, we further dissect the essence of the evolution of cooperation. As the temptation value increases, cooperators and rewarders first form compact clusters, then more and more loners join to resist the intrusion of defectors. Eventually, the three strategies coexist stably in a spatially structured population. Our research may shed some light on exploring the nature of cooperation and solving social dilemmas in the future.
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Fan L, Song Z, Wang L, Liu Y, Wang Z. Incorporating social payoff into reinforcement learning promotes cooperation. CHAOS (WOODBURY, N.Y.) 2022; 32:123140. [PMID: 36587319 DOI: 10.1063/5.0093996] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/31/2022] [Accepted: 12/01/2022] [Indexed: 06/17/2023]
Abstract
Reinforcement learning has been demonstrated to be an effective approach to investigate the dynamic of strategy updating and the learning process of agents in game theory. Most studies have shown that Q-learning failed to resolve the problem of cooperation in well-mixed populations or homogeneous networks. To this aim, we investigate the self-regarding Q-learning's effect on cooperation in spatial prisoner's dilemma games by incorporating the social payoff. Here, we redefine the reward term of self-regarding Q-learning by involving the social payoff; that is, the reward is defined as a monotonic function of the individual payoff and the social payoff represented by its neighbors' payoff. Numerical simulations reveal that such a framework can facilitate cooperation remarkably because the social payoff ensures agents learn to cooperate toward socially optimal outcomes. Moreover, we find that self-regarding Q-learning is an innovative rule that ensures cooperators coexist with defectors even at high temptations to defection. The investigation of the emergence and stability of the sublattice-ordered structure shows that such a mechanism tends to generate a checkerboard pattern to increase agents' payoff. Finally, the effects of Q-learning parameters are also analyzed, and the robustness of this mechanism is verified on different networks.
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Affiliation(s)
- Litong Fan
- School of Mechanical Engineering, Northwestern Polytechnical University, Xi'an, Shaanxi 710072, China
| | - Zhao Song
- School of Mechanical Engineering, Northwestern Polytechnical University, Xi'an, Shaanxi 710072, China
| | - Lu Wang
- School of Mechanical Engineering, Northwestern Polytechnical University, Xi'an, Shaanxi 710072, China
| | - Yang Liu
- School of Artificial Intelligence, Optics and Electronics (iOPEN), Northwestern Polytechnical University, Xi'an, Shaanxi 710072, China
| | - Zhen Wang
- School of Mechanical Engineering, Northwestern Polytechnical University, Xi'an, Shaanxi 710072, China
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Song Z, Guo H, Jia D, Perc M, Li X, Wang Z. Reinforcement learning facilitates an optimal interaction intensity for cooperation. Neurocomputing 2022. [DOI: 10.1016/j.neucom.2022.09.109] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
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Guo H, Wang Z, Song Z, Yuan Y, Deng X, Li X. Effect of state transition triggered by reinforcement learning in evolutionary prisoner’s dilemma game. Neurocomputing 2022. [DOI: 10.1016/j.neucom.2022.08.023] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/14/2022]
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8
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Lu Y, Wang X, Wu M, Shi L, Park J. Effects of species vigilance on coexistence in evolutionary dynamics of spatial rock-paper-scissors game. CHAOS (WOODBURY, N.Y.) 2022; 32:093116. [PMID: 36182385 DOI: 10.1063/5.0103247] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/15/2022] [Accepted: 08/15/2022] [Indexed: 06/16/2023]
Abstract
Recognizing surrounding situations, such as enemy attacks, which can be realized by predator-prey relationships, is one of the common behaviors of the population in ecosystems. In this paper, we explore the relationship between such species' behavior and biodiversity in the spatial rock-paper-scissors game by employing the ecological concept "vigilance." In order to describe the vigilance process, we adopt a multiplex structure where two distinct layers describe virtual and physical interactions. By investigating the process of evolution in species, we also found that species with different vigilance go together. In addition, by utilizing the dynamic time warping method, we found that species with the same vigilance have consistent behavior, but species with different vigilance have diverse behavior. Our findings may lead to broader interpretations of mechanisms promoting biodiversity via vigilance in species ecosystems.
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Affiliation(s)
- Yikang Lu
- School of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming, Yunnan 650221, China
| | - Xiaoyue Wang
- School of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming, Yunnan 650221, China
| | - Mengjie Wu
- 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
| | - Junpyo Park
- Department of Applied Mathematics, Kyung Hee University, Yongin 17104, Republic of Korea
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Islam S, Mondal A, Mobilia M, Bhattacharyya S, Hens C. Effect of mobility in the rock-paper-scissor dynamics with high mortality. Phys Rev E 2022; 105:014215. [PMID: 35193192 DOI: 10.1103/physreve.105.014215] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/27/2021] [Accepted: 01/11/2022] [Indexed: 06/14/2023]
Abstract
In the evolutionary dynamics of a rock-paper-scissor model, the effect of natural death plays a major role in determining the fate of the system. Coexistence, being an unstable fixed point of the model, becomes very sensitive toward this parameter. In order to study the effect of mobility in such a system which has explicit dependence on mortality, we perform Monte Carlo simulation on a two-dimensional lattice having three cyclically competing species. The spatiotemporal dynamics has been studied along with the two-site correlation function. Spatial distribution exhibits emergence of spiral patterns in the presence of mobility. It reveals that the joint effect of death rate and mobility (diffusion) leads to new coexistence and extinction scenarios.
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Affiliation(s)
- Sahil Islam
- Department of Physics, Jadavpur University, Jadavpur, Kolkata 700032, India
| | - Argha Mondal
- Department of Mathematics, Sidho-Kanho-Birsha University, Purulia 723104, WB, India
- Department of Mathematical Sciences, University of Essex, Wivenhoe Park, Colchester CO4 3SQ, United Kingdom
| | - Mauro Mobilia
- Department of Applied Mathematics, School of Mathematics, University of Leeds, Leeds LS2 9JT, United Kingdom
| | | | - Chittaranjan Hens
- Physics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata 700108, India
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Gupta S, Patteson AE, Schwarz JM. The role of vimentin-nuclear interactions in persistent cell motility through confined spaces. NEW JOURNAL OF PHYSICS 2021; 23:093042. [PMID: 35530563 PMCID: PMC9075336 DOI: 10.1088/1367-2630/ac2550] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/17/2023]
Abstract
The ability of cells to move through small spaces depends on the mechanical properties of the cellular cytoskeleton and on nuclear deformability. In mammalian cells, the cytoskeleton is composed of three interacting, semi-flexible polymer networks: actin, microtubules, and intermediate filaments (IF). Recent experiments of mouse embryonic fibroblasts with and without vimentin have shown that the IF vimentin plays a role in confined cell motility. Here, we develop a minimal model of a cell moving through a microchannel that incorporates explicit effects of actin and vimentin and implicit effects of microtubules. Specifically, the model consists of a cell with an actomyosin cortex and a deformable cell nucleus and mechanical linkages between the two. By decreasing the amount of vimentin, we find that the cell speed increases for vimentin-null cells compared to cells with vimentin. The loss of vimentin increases nuclear deformation and alters nuclear positioning in the cell. Assuming nuclear positioning is a read-out for cell polarity, we propose a new polarity mechanism which couples cell directional motion with cytoskeletal strength and nuclear positioning and captures the abnormally persistent motion of vimentin-null cells, as observed in experiments. The enhanced persistence indicates that the vimentin-null cells are more controlled by the confinement and so less autonomous, relying more heavily on external cues than their wild-type counterparts. Our modeling results present a quantitative interpretation for recent experiments and have implications for understanding the role of vimentin in the epithelial-mesenchymal transition.
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Affiliation(s)
- Sarthak Gupta
- Physics Department and BioInspired Institute, Syracuse University, Syracuse, NY USA
| | - Alison E Patteson
- Physics Department and BioInspired Institute, Syracuse University, Syracuse, NY USA
| | - J M Schwarz
- Physics Department and BioInspired Institute, Syracuse University, Syracuse, NY USA
- Indian Creek Farm, Ithaca, NY USA
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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.
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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.
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12
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Kleshnina M, Streipert SS, Filar JA, Chatterjee K. Mistakes can stabilise the dynamics of rock-paper-scissors games. PLoS Comput Biol 2021; 17:e1008523. [PMID: 33844680 PMCID: PMC8062094 DOI: 10.1371/journal.pcbi.1008523] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/17/2020] [Revised: 04/22/2021] [Accepted: 03/18/2021] [Indexed: 11/19/2022] Open
Abstract
A game of rock-paper-scissors is an interesting example of an interaction where none of the pure strategies strictly dominates all others, leading to a cyclic pattern. In this work, we consider an unstable version of rock-paper-scissors dynamics and allow individuals to make behavioural mistakes during the strategy execution. We show that such an assumption can break a cyclic relationship leading to a stable equilibrium emerging with only one strategy surviving. We consider two cases: completely random mistakes when individuals have no bias towards any strategy and a general form of mistakes. Then, we determine conditions for a strategy to dominate all other strategies. However, given that individuals who adopt a dominating strategy are still prone to behavioural mistakes in the observed behaviour, we may still observe extinct strategies. That is, behavioural mistakes in strategy execution stabilise evolutionary dynamics leading to an evolutionary stable and, potentially, mixed co-existence equilibrium.
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Affiliation(s)
- Maria Kleshnina
- Institute of Science and Technology Austria (IST Austria), Klosterneuburg, Austria
| | | | - Jerzy A. Filar
- School of Mathematics and Physics, University of Queensland, Brisbane, Australia
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13
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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.
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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
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