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This tutorial article puts forth a framework to analyze the noncooperative strategic interactions among the members of a large population of bounded rationality agents. Our approach hinges on, unifies and generalizes existing methods and…

Optimization and Control · Mathematics 2020-07-15 Shinkyu Park , Nuno C. Martins , Jeff S. Shamma

Communication is fundamental to sustaining reciprocity and cooperation in strategic interactions. We identify and formulate the influence attribution problem as the central optimization difficulty inherent in such dynamics for a learning…

Machine Learning · Computer Science 2026-05-12 Yue Lin , Pascal Poupart , Shuhui Zhu , Dan Qiao , Wenhao Li , Yuan Liu , Hongyuan Zha , Baoxiang Wang

We present a novel approach allowing the study of rare events like fixation under fluctuating environments, modeled as extrinsic noise, in evolutionary processes characterized by the dominance of one species. Our treatment consists of…

Populations and Evolution · Quantitative Biology 2013-12-16 Michael Assaf , Mauro Mobilia , Elijah Roberts

Besides the structure of interactions within networks, also the interactions between networks are of the outmost importance. We therefore study the outcome of the public goods game on two interdependent networks that are connected by means…

Physics and Society · Physics 2013-08-13 Zhen Wang , Attila Szolnoki , Matjaz Perc

In this paper we extend the investigation of cooperation in some classical evolutionary games on populations were the network of interactions among individuals is of the scale-free type. We show that the update rule, the payoff computation…

Physics and Society · Physics 2009-11-13 M. Tomassini , L. Luthi , E. Pestelacci

If two species exhibit different nonlinear responses to a single shared resource, and if each species modifies the resource dynamics such that this favors its competitor, they may stably coexist. This coexistence mechanism, known as…

Populations and Evolution · Quantitative Biology 2015-06-16 Florian Hartig , Tamara Münkemüller , Karin Johst , Ulf Dieckmann

Human sociality depends upon the benefits of mutual aid and extensive communication. However mutual aid is made difficult by the problems of coordinating diverse norms and preferences, and communication is harried by substantial ambiguity…

Physics and Society · Physics 2015-11-17 Paul E. Smaldino , Thomas J. Flamson , Richard McElreath

Many organisms live in populations structured by space and by class, exhibit plastic responses to their social partners, and are subject to non-additive ecological and fitness effects. Social evolution theory has long recognized that all of…

Populations and Evolution · Quantitative Biology 2014-04-24 Jeremy Van Cleve , Erol Akçay

Our wellbeing depends as much on our personal success, as it does on the success of our society. The realization of this fact makes cooperation a very much needed trait. Experiments have shown that rewards can elevate our readiness to…

Physics and Society · Physics 2012-09-12 Attila Szolnoki , Matjaz Perc

Experimental evidence suggests that human decisions involve a mixture of self-interest and internalized social norms which cannot be accounted for by the Nash equilibrium behavior of Homo Oeconomicus. This led to the notion of strong…

Adaptation and Self-Organizing Systems · Physics 2007-05-23 R. Vilela Mendes

The network reciprocity is an important dynamic rule fostering the emergence of cooperation among selfish individuals. This was reported firstly in the seminal work of Nowak and May, where individuals were arranged on the regular lattice…

Adaptation and Self-Organizing Systems · Physics 2015-06-15 Gui-Qing Zhang , Qi-Bo Sun , Lin Wang

Reputation plays a major role in human societies, and it has been proposed as an explanation for the evolution of cooperation. While the majority of previous studies equates reputation with a transparent and complete history of players'…

Physics and Society · Physics 2025-08-20 Valerio Capraro , Francesca Giardini , Daniele Vilone , Mario Paolucci

Social norms are stable behavioral patterns that emerge endogenously within economic systems through repeated interactions among agents. In online market economies, such norms -- like fair exposure, sustained participation, and balanced…

Machine Learning · Computer Science 2026-03-06 Xiangning Yu , Qirui Mi , Xiao Xue , Haoxuan Li , Yiwei Shi , Xiaowei Liu , Mengyue Yang

Cooperation is of utmost importance to society as a whole, but is often challenged by individual self-interests. While game theory has studied this problem extensively, there is little work on interactions within and across groups with…

Physics and Society · Physics 2010-10-14 Dirk Helbing , Anders Johansson

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

Sustaining cooperation among self-interested agents is critical for the proliferation of emerging online social communities, such as online communities formed through social networking services. Providing incentives for cooperation in…

Social and Information Networks · Computer Science 2011-03-08 Yu Zhang , Jaeok Park , Mihaela van der Schaar

It is well-known that population structure is a catalyst for the evolution of cooperation since individuals can reciprocate with their neighbors through local interactions defined by network structures. Previous research typically relies on…

Physics and Society · Physics 2021-12-16 Anzhi Sheng , Aming Li , Long Wang

Multi-agent reinforcement learning serves as an effective tool for studying strategy adaptation in evolutionary games. Although prior work has integrated Q-learning with reputation mechanisms to promote cooperation, most existing algorithms…

Computational Physics · Physics 2026-04-10 An Li , Wenqiang Zhu , Chaoqian Wang , Longzhao Liu , Hongwei Zheng , Yishen Jiang , Xin Wang , Shaoting Tang

Recent research has identified the heterogeneity as crucial for the evolution of cooperation in spatial population. However, the influence of heterogeneous noise is still lack. Inspired by this interesting question, in this work, we try to…

Physics and Society · Physics 2015-06-18 Y. Yao , S. -S. Chen

In this work we have used computer models of social-like networks to show by extensive numerical simulations that cooperation in evolutionary games can emerge and be stable on this class of networks. The amounts of cooperation reached are…

Physics and Society · Physics 2012-07-12 Alberto Antonioni , Marco Tomassini
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