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A stochastic model for behavioral changes by imitative pair interactions of individuals is developed. `Microscopic' assumptions on the specific form of the imitative processes lead to a stochastic version of the game dynamical equations.…

Statistical Mechanics · Physics 2007-05-23 Dirk Helbing

Recent developments of eco-evolutionary models have shown that evolving feedbacks between behavioral strategies and the environment of game interactions, leading to changes in the underlying payoff matrix, can impact the underlying…

Physics and Society · Physics 2024-06-10 Katherine Betz , Feng Fu , Naoki Masuda

Networks determine our social circles and the way we cooperate with others. We know that topological features like hubs and degree assortativity affect cooperation, and we know that cooperation is favoured if the benefit of the altruistic…

Physics and Society · Physics 2021-10-04 A. Zhuk , I. Sendiña-Nadal , I. Leyva , D. Musatov , A. M. Raigorodskii , M. Perc , S. Boccaletti

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

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…

Adaptation and Self-Organizing Systems · Physics 2024-03-12 Hao Guo , Chen Shen , Rongcheng Zou , Pin Tao , Yuanchun Shi , Zhen Wang , Junliang Xing

In a static environment, optional participation and a local agglomeration of cooperators are found to be beneficial for the occurrence and maintenance of cooperation. In the optional public goods game, the rock-scissors-paper cycles of…

Physics and Society · Physics 2015-06-05 Li-Xin Zhong , Wen-Juan Xu , Yong-Dong Shi , Tian Qiu

We study a coevolutionary public goods game on a dynamic hypergraph, where an individual's payoff directly determines the number of hyperedges it can join. In the proposed mechanism, nodes adjust their participation according to the group…

Physics and Society · Physics 2026-05-27 Yichao Yao , Yuji Zhang , Juan Wu , Minyu Feng , Attila Szolnoki

Elucidating the mechanisms that lead to cooperation is still one of the main scientific challenges of current times, as many common cooperative scenarios remain elusive and at odds with Darwin's natural selection theory. Here, we study…

Physics and Society · Physics 2021-07-14 H. Guo , D. Jia , I. Sendiña-Nadal , M. Zhang , Z. Wang , X. Li , K. Alfaro-Bittner , Y. Moreno , S. Boccaletti

Studying social dilemmas prompts the question of how cooperation can emerge in situations where individuals are expected to act selfishly. Here, in the framework of the one-shot Public Goods Game (PGG), we introduce the concept that…

Physics and Society · Physics 2024-02-09 Lucas S. Flores , The Anh Han

We consider a broad class of stochastic imitation dynamics over networks, encompassing several well known learning models such as the replicator dynamics. In the considered models, players have no global information about the game…

Systems and Control · Computer Science 2021-03-02 Lorenzo Zino , Giacomo Como , Fabio Fagnani

Exploiting others is beneficial individually but it could also be detrimental globally. The reverse is also true: a higher cooperation level may change the environment in a way that is beneficial for all competitors. To explore the possible…

Physics and Society · Physics 2018-02-23 Attila Szolnoki , Xiaojie Chen

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 emergence and maintenance of cooperation within sizable groups of unrelated humans offer many challenges for our understanding. We propose that the humans' capacity of communication, such as how many and how far away the fellows can…

Physics and Society · Physics 2009-09-29 Zi-Gang Huang , Sheng-Jun Wang , Xin-Jian Xu , Ying-Hai Wang

Cooperation in heterogeneous groups, where individuals differ in resources, productivity, and behavioural responsiveness, underpins collective action across many social and biological systems. Introspection dynamics, in which each player…

Computer Science and Game Theory · Computer Science 2026-05-25 Harry Foster , Vincent A. Knight , Sebastian Krapohl

Many mathematical frameworks of evolutionary game dynamics assume that the total population size is constant and that selection affects only the relative frequency of strategies. Here, we consider evolutionary game dynamics in an extended…

Populations and Evolution · Quantitative Biology 2018-02-16 Alex McAvoy , Nicolas Fraiman , Christoph Hauert , John Wakeley , Martin A. Nowak

Cooperation among unrelated individuals is frequently observed in social groups when their members combine efforts and resources to obtain a shared benefit that is unachievable by an individual alone. However, understanding why cooperation…

Spatial reciprocity is a well known tour de force of cooperation promotion. A thorough understanding of the effects of different population densities is therefore crucial. Here we study the evolution of cooperation in social dilemmas on…

Physics and Society · Physics 2012-05-14 Zhen Wang , Attila Szolnoki , Matjaz Perc

To investigate the origin of cooperative behaviors, we developed an evolutionary model of sequential strategies and tested our model with computer simulations. The sequential strategies represented by stochastic machines were evaluated…

Computer Science and Game Theory · Computer Science 2021-01-12 Jin Hong Kuan , Aadesh Salecha

Evolutionary dynamics can be studied in well-mixed or structured populations. Population structure typically arises from the heterogeneous distribution of individuals in physical space or on social networks. Here we introduce a new type of…

Populations and Evolution · Quantitative Biology 2009-06-04 Tibor Antal , Hisashi Ohtsuki , John Wakeley , Peter D. Taylor , Martin A. Nowak

Rewards and penalties are common practical tools that can be used to promote cooperation in social institutions. The evolution of cooperation under reward and punishment incentives in joint enterprises has been formalized and investigated,…

Physics and Society · Physics 2013-08-20 Tatsuya Sasaki