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The public goods game is a broadly used paradigm for studying the evolution of cooperation in structured populations. According to the basic assumption, the interaction graph determines the connections of a player where the focal actor…

Physics and Society · Physics 2024-04-24 Ju Han , Xiaojie Chen , Attila Szolnoki

Understanding and resolving cooperation dilemmas are key challenges in evolutionary game theory, which have revealed several mechanisms to address them. This paper investigates the comprehensive influence of multiple reputation-related…

Physics and Society · Physics 2025-04-10 Kai Xie , Attila Szolnoki

Cooperative behavior among unrelated individuals in human and animal societies represents a most intriguing puzzle to scientists in various disciplines. Here we present a simple yet effective mechanism promoting cooperation under full…

Condensed Matter · Physics 2009-11-07 Gyorgy Szabo , Christoph Hauert

We study the evolution of cooperation in public goods games on the square lattice, focusing on the effects that are brought about by different sizes of groups where individuals collect their payoffs and search for potential strategy donors.…

Physics and Society · Physics 2011-12-14 Attila Szolnoki , Matjaz Perc

Cooperation and competition coexist and coevolve in natural and social systems. Cooperation generates resources, which in turn, drive non-cooperative competition to secure individual shares. How this complex interplay between cooperation…

Physics and Society · Physics 2025-09-03 Wenqiang Zhu , Xin Wang , Chaoqian Wang , Weijie Xing , Longzhao Liu , Hongwei Zheng , Jingwu Zhao , Shaoting Tang

The tragedy of the commons illustrates a fundamental social dilemma where individual rational actions lead to collectively undesired outcomes, threatening the sustainability of shared resources. Strategies to escape this dilemma, however,…

Computer Science and Game Theory · Computer Science 2026-03-26 Arend Hintze , Christoph Adami

The development of cooperative relations within and between firms plays an important role in the successful implementation of business strategy. How to produce such relations is less well understood. We build on work in relational contract…

Computer Science and Game Theory · Computer Science 2012-03-07 Dan Ladley , Ian Wilkinson , Louise Young

Cooperation arises in nature at every scale, from within cells to entire ecosystems. In the framework of evolutionary game theory, public goods games (PGGs) are used to analyse scenarios where individuals can cooperate or defect, and can…

The evolution of cooperation has remained an important problem in evolutionary theory and social sciences. In this regard, a curious question is why consistent cooperative and defective personalities exist and if they serve a role in the…

Populations and Evolution · Quantitative Biology 2022-01-14 Mohammad Salahshour

Cooperation is fundamental to human societies, and the interaction structure among individuals profoundly shapes its emergence and evolution. In real-world scenarios, cooperation prevails in multi-group (higher-order) populations, beyond…

Physics and Society · Physics 2025-01-28 Dini Wang , Peng Yi , Yiguang Hong , Jie Chen , Gang Yan

We model a dynamic public good contribution game, where players are (naturally) formed into groups. The groups are exogenously placed in a sequence, with limited information available to players about their groups' position in the sequence.…

Theoretical Economics · Economics 2022-10-18 Chowdhury Mohammad Sakib Anwar , Jorge Bruno , Sonali SenGupta

The public goods game is a model of a society investing some assets and regaining a profit, although can also model biological populations. In the classic public goods game only two strategies compete: either cooperate or defect; a third…

Adaptation and Self-Organizing Systems · Physics 2022-06-08 Gaspar Alfaro , Miguel A. F. Sanjuan

Indirect reciprocity unveils how social cooperation is founded upon moral systems. Within the frame of dyadic games based on individual reputations, the "leading-eight" strategies distinguish themselves in promoting and sustaining…

Physics and Society · Physics 2024-10-22 Ming Wei , Xin Wang , Longzhao Liu , Hongwei Zheng , Yishen Jiang , Yajing Hao , Zhiming Zheng , Feng Fu , Shaoting Tang

We live and cooperate in networks. However, links in networks only allow for pairwise interactions, thus making the framework suitable for dyadic games, but not for games that are played in groups of more than two players. Here, we study…

Punishment as a mechanism for promoting cooperation has been studied extensively for more than two decades, but its effectiveness remains a matter of dispute. Here, we examine how punishment's impact varies across cooperative settings…

General Economics · Economics 2025-08-26 Mohammed Alsobay , David G. Rand , Duncan J. Watts , Abdullah Almaatouq

The evolutionary mechanisms of cooperative behavior represent a fundamental topic in complex systems and evolutionary dynamics. Real-world collective interactions, particularly in multi-agent systems, are often characterized by…

Adaptation and Self-Organizing Systems · Physics 2026-02-23 Yishen Jiang , Xin Wang , Wenqiang Zhu , Ming Wei , Longzhao Liu , Shaoting Tang , Hongwei Zheng

This paper investigates the evolution of strategic play where players drawn from a finite well-mixed population are offered the opportunity to play in a public goods game. All players accept the offer. However, due to the possibility of…

Populations and Evolution · Quantitative Biology 2017-09-14 Alexander G. Ginsberg , Feng Fu

Synergies between evolutionary game theory and statistical physics have significantly improved our understanding of public cooperation in structured populations. Multiplex networks, in particular, provide the theoretical framework within…

Physics and Society · Physics 2017-07-13 Federico Battiston , Matjaz Perc , Vito Latora

The evolution of cooperation among unrelated individuals in human and animal societies remains a challenging issue across disciplines. It is an important subject also in the evolutionary game theory to understand how cooperation arises. The…

Physics and Society · Physics 2019-10-01 Norihito Toyota

Cooperation as a self-organized collective behavior plays a significant role in the evolution of ecosystems and human society. Reinforcement learning (RL) offers a new perspective, distinct from imitation learning in evolutionary games, for…

Physics and Society · Physics 2024-10-16 Bo-Ying Li , Zhen-Na Zhang , Guo-Zhong Zheng , Chao-Ran Cai , Ji-Qiang Zhang , Chen Li