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We investigate the spatial distribution and the global frequency of agents who can either cooperate or defect. The agent interaction is described by a deterministic, non-iterated prisoner's dilemma game, further each agent only locally…

Statistical Mechanics · Physics 2007-05-23 Frank Schweitzer , Laxmidhar Behera , Heinz Muehlenbein

Recent studies in the spatial prisoner's dilemma games with reinforcement learning have shown that static agents can learn to cooperate through a diverse sort of mechanisms, including noise injection, different types of learning algorithms…

Artificial Intelligence · Computer Science 2025-07-08 Gustavo C. Mangold , Heitor C. M. Fernandes , Mendeli H. Vainstein

Exploring the possible consequences of spatial reciprocity on the evolution of cooperation is an intensively studied research avenue. Related works assumed a certain interaction graph of competing players and studied how particular…

Populations and Evolution · Quantitative Biology 2021-02-09 B. F. de Oliveira , A. Szolnoki

The effects of an unconditional move rule in the spatial Prisoner's Dilemma, Snowdrift and Stag Hunt games are studied. Spatial structure by itself is known to modify the outcome of many games when compared with a randomly mixed population,…

Populations and Evolution · Quantitative Biology 2009-02-25 Estrella A. Sicardi , Hugo Fort , Mendeli H. Vainstein , Jeferson J. Arenzon

The effects of payoffs and noise on the maintenance of cooperative behavior are studied in an evolutionary Prisoner's Dilemma game with players located on the sites of different two-dimensional lattices. This system exhibits a phase…

Statistical Mechanics · Physics 2009-11-11 Gyorgy Szabo , Jeromos Vukov , Attila Szolnoki

We address the problem of how the survival of cooperation in a social system depends on the motion of the individuals. Specifically, we study a model in which Prisoner's Dilemma players are allowed to move in a two-dimensional plane. Our…

Physics and Society · Physics 2015-05-13 S. Meloni , A. Buscarino , L. Fortuna , M. Frasca , J. Gomez-Gardenes , V. Latora , Y. Moreno

The Prisoner's dilemma is the main game theoretical framework in which the onset and maintainance of cooperation in biological populations is studied. In the spatial version of the model, we study the robustness of cooperation in…

Disordered Systems and Neural Networks · Physics 2009-11-07 Mendeli H. Vainstein , Jeferson J. Arenzon

We study the effects of mobility on the evolution of cooperation among mobile players, which imitate collective motion of biological flocks and interact with neighbors within a prescribed radius $R$. Adopting the prisoner's dilemma game and…

Physics and Society · Physics 2011-02-22 Zhuo Chen , Jian-Xi Gao , Yun-Ze Cai , Xiao-Ming Xu

We investigate two paradigms for studying the evolution of cooperation--Prisoner's Dilemma and Snowdrift game in an online friendship network obtained from a social networking site. We demonstrate that such social network has small-world…

Physics and Society · Physics 2009-11-13 Feng Fu , Xiaojie Chen , Lianghuan Liu , Long Wang

The spatial Prisoner's Dilemma is a prototype model to show the emergence of cooperation in very competitive environments. It considers players, at site of lattices, that can either cooperate or defect when playing the Prisoner's Dilemma…

Computational Physics · Physics 2007-09-18 Marcelo Alves Pereira , Alexandre Souto Martinez , Aquino Lauri Espindola

Synchronization, cooperation, and chaos are ubiquitous phenomena in nature. In a population composed of many distinct groups of individuals playing the prisoner's dilemma game, there exists a migration dilemma: No cooperator would migrate…

Populations and Evolution · Quantitative Biology 2021-02-22 Shubhadeep Sadhukhan , Rohitashwa Chattopadhyay , Sagar Chakraborty

We present a detailed study of prisoner's dilemma game with stochastic modifications on a two-dimensional lattice, in presence of evolutionary dynamics. By very nature of the rules, the cooperators have incentive to cheat and the fear to…

Statistical Mechanics · Physics 2015-05-14 M. Ali Saif , Prashant M. Gade

The effects of an additional strategy or character called loner in the snowdrift game are studied in a well-mixed population or fully-connected network and in a square lattice. The snowdrift game, which is a possible alternative to the…

Physics and Society · Physics 2007-05-23 Li-Xin Zhong , Da-Fang Zheng , B. Zheng , Chen Xu , P. M. Hui

In times of plenty expectations rise, just as in times of crisis they fall. This can be mathematically described as a Win-Stay-Lose-Shift strategy with dynamic aspiration levels, where individuals aspire to be as wealthy as their average…

Physics and Society · Physics 2016-10-04 Marco A. Amaral , Lucas Wardil , Matjaz Perc , Jafferson K. L. da Silva

We study a spatial two-strategy (cooperation and defection) Prisoner's Dilemma game with two types ($A$ and $B$) of players located on the sites of a square lattice. The evolution of strategy distribution is governed by iterated strategy…

Physics and Society · Physics 2009-01-15 Gyorgy Szabo , Attila Szolnoki

Introducing strategy complexity into the basic conflict of cooperation and defection is a natural response to avoid the tragedy of the common state. As an intermediate approach, quasi-cooperators were recently suggested to address the…

Physics and Society · Physics 2024-04-24 Hsuan-Wei Lee , Colin Cleveland , Attila Szolnoki

In Evolutionary Dynamics the understanding of cooperative phenomena in natural and social systems has been the subject of intense research during decades. We focus attention here on the so-called "Lattice Reciprocity" mechanisms that…

Physics and Society · Physics 2009-11-13 L. M. Floria , C. Gracia-Lazaro , J. Gomez-Gardenes , Y. Moreno

A two-dimensional small-world type network, subject to spatial prisoners' dilemma dynamics and containing an influential node defined as a special node with a finite density of directed random links to the other nodes in the network, is…

Disordered Systems and Neural Networks · Physics 2009-11-07 Beom Jun Kim , Ala Trusina , Petter Holme , Petter Minnhagen , Jean S. Chung , M. Y. Choi

We investigate an evolutionary prisoner's dilemma game among self-driven agents, where collective motion of biological flocks is imitated through averaging directions of neighbors. Depending on the temptation to defect and the velocity at…

Physics and Society · Physics 2015-03-13 Zhuo Chen , Jian-Xi Gao , Yun-Ze Cai , Xiao-Ming Xu

The emergence of mutual cooperation is studied in a spatially extended evolutionary prisoner's dilemma game in which the players are located on the sites of cubic lattices for dimensions d=1, 2, and 3. Each player can choose one of the…

Statistical Mechanics · Physics 2009-10-31 Gyorgy Szabo , Tibor Antal , Peter Szabo , Michel Droz
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