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Strong reciprocity is a fundamental human characteristic associated with our extraordinary sociality and cooperation. Laboratory experiments on social dilemma games and many field studies have quantified well-defined levels of cooperation…

Physics and Society · Physics 2007-11-21 D. Darcet , D. Sornette

The evolution of cooperation is a central enigma in evolutionary game theory. Traditionally, the combination of pairwise networks and repeated Public Goods Games with a single state fails to adequately describe realistic group interaction…

Physics and Society · Physics 2026-03-25 Nankun Wei , Xiaojin Xiong , Qin Li , Minyu Feng , Attila Szolnoki

This study investigates the effect of behavioral mistakes on the evolutionary stability of the cooperative equilibrium in a repeated public goods game. Many studies show that behavioral mistakes have detrimental effects on cooperation…

Theoretical Economics · Economics 2021-07-01 Jung-Kyoo Choi , Jun Sok Huhh

We study the evolution of cooperation under the assumption that the collective benefits of group membership can only be harvested if the fraction of cooperators within the group, i.e. their critical mass, exceeds a threshold value.…

Physics and Society · Physics 2010-05-05 Attila Szolnoki , Matjaz Perc

The emergence and prevalence of cooperative behavior within a group of selfish individuals remains a puzzle for \text{evolutionary game theory} precisely because it conflicts directly with the central idea of natural selection. Accordingly,…

Physics and Society · Physics 2019-08-29 Paulo Victor Santos Souza , Rafael Silva , Chris T. Bauch , Daniel Girardi

Societies consisting of cooperative individuals seem to require for their continuing success that defectors be policed. The precise connection between punishers and benefits, population structure, and division of labour, however, remains…

Populations and Evolution · Quantitative Biology 2015-12-11 Gereon A. Kaiping , Timothy J. Sluckin , Simon J. Cox

Continuously changing environments have a paramount role in the evolution of cooperative behavior. Previous works have shown that the transitions among different games, as the feedback between behaviors and environments, can promote…

Physics and Society · Physics 2026-03-25 Yuji Zhang , Minyu Feng , Qin Li , Matjaz Perc , Attila Szolnoki

Understanding the emergence of cooperation in social networks has advanced through pairwise interactions, but the corresponding theory for group-based public goods games (PGGs) remains less explored. Here, we provide theoretical conditions…

Computer Science and Game Theory · Computer Science 2026-02-11 Chaoqian Wang , Qi Su

Commonly, the strategy revision phase in evolutionary games relies on payoff comparison. Namely, agents compare their payoff with the opponent, assessing whether changing strategy can be potentially convenient. Even tiny payoff differences…

Physics and Society · Physics 2023-10-24 Marco Alberto Javarone , Shaurya Pratap Singh

We study the evolution of cooperation in the evolutionary spatial prisoner's dilemma game (PDG) and snowdrift game (SG), within which a fraction $\alpha$ of the payoffs of each player gained from direct game interactions is shared equally…

Physics and Society · Physics 2014-01-13 Zhi-Xi Wu , Han-Xin Yang

We study the evolution of cooperation in public goods games on different regular graphs as a function of the noise level underlying strategy adoptions. We focus on the effects that are brought about by different group sizes of public goods…

Physics and Society · Physics 2009-11-19 Attila Szolnoki , Matjaz Perc , Gyorgy Szabo

Facing a heavy task, any single person can only make a limited contribution and team cooperation is needed. As one enjoys the benefit of the public goods, the potential benefits of the project are not always maximized and may be partly…

Physics and Society · Physics 2017-06-28 Li-Xin Zhong , Wen-Juan Xu , Yun-Xin He , Chen-Yang Zhong , Rong-Da Chen , Tian Qiu , Yong-Dong Shi , Fei Ren

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…

Populations and Evolution · Quantitative Biology 2011-04-04 Zhen Wang , Aleksandra Murks , Wen-Bo Du , Zhi-Hai Rong , Matjaz Perc

The emergence and maintenance of cooperative behavior is a fascinating topic in evolutionary biology and social science. The public goods game (PGG) is a paradigm for exploring cooperative behavior. In PGG, the total resulting payoff is…

Populations and Evolution · Quantitative Biology 2019-07-15 Yan Li , Xinsheng Liu , Jens Christian Claussen , Wanlin Guo

The mitigation of the effects of climate change on humankind is one of the most pressing and important collective governance problems nowadays$^{1-4}$. To explore different solutions and scenarios, previous works have framed this problem…

Physics and Society · Physics 2016-04-19 Luo-Luo Jiang , Zhen Wang , Chang-Song Zhou , Jurgen Kurths , Yamir Moreno

How cooperation can evolve between players is an unsolved problem of biology. Here we use Hamiltonian dynamics of models of the Ising type to describe populations of cooperating and defecting players to show that the equilibrium fraction of…

Populations and Evolution · Quantitative Biology 2018-06-27 Christoph Adami , Arend Hintze

The emergence of cooperation figures among the main goal of game theory in competitive-cooperative environments. Potential games have long been hinted as viable alternatives to study realistic player behavior. Here, we expand the potential…

Computer Science and Game Theory · Computer Science 2018-10-12 G. M. Nakamura , G. S. Contesini , A. S. Martinez

Monitoring with implicated punishment is common in human societies to avert freeriding on common goods. But is it effective in promoting public cooperation? We show that the introduction of monitoring and implicated punishment is indeed…

Populations and Evolution · Quantitative Biology 2015-11-20 Xiaojie Chen , Tatsuya Sasaki , Matjaz Perc

The view that altruistic punishment plays an important role in supporting public cooperation among human beings and other species has been widely accepted by the public. However, the positive role of altruistic punishment in enhancing…

Dynamical Systems · Mathematics 2022-03-08 Linjie Liu , Xiaojie Chen

An open problem in evolutionary game dynamics is to understand the effect of peer pressure on cooperation in a quantitative manner. Peer pressure can be modeled by punishment, which has been proved to be an effective mechanism to sustain…

Physics and Society · Physics 2015-09-23 Han-Xin Yang , Zhi-Xi Wu , Zhihai Rong , Ying-Cheng Lai