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According to the standard imitation protocol, a less successful player adopts the strategy of the more successful one faithfully for future success. This is the cornerstone of evolutionary game theory that explores the vitality of competing…

Physics and Society · Physics 2019-09-27 Attila Szolnoki , Xiaojie Chen

Holding on to one's strategy is natural and common if the later warrants success and satisfaction. This goes against widespread simulation practices of evolutionary games, where players frequently consider changing their strategy even…

Populations and Evolution · Quantitative Biology 2012-05-04 Yongkui Liu , Xiaojie Chen , Lin Zhang , Long Wang , Matjaz Perc

Competition among cooperators, defectors, and loners is studied in an evolutionary prisoner's dilemma game with optional participation. Loners are risk averse i.e. unwilling to participate and rather rely on small but fixed earnings. This…

Disordered Systems and Neural Networks · Physics 2009-11-07 Gyorgy Szabo , Christoph Hauert

Punishment is a common tactic to sustain cooperation and has been extensively studied for a long time. While most of previous game-theoretic work adopt the imitation learning where players imitate the strategies who are better off, the…

Populations and Evolution · Quantitative Biology 2024-12-20 Chenyang Zhao , Guozhong Zheng , Chun Zhang , Jiqiang Zhang , Li Chen

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

Research has shown that the addition of abstention as an option transforms social dilemmas to rock-paper-scissor type games, where defectors dominate cooperators, cooperators dominate abstainers (loners), and abstainers (loners), in turn,…

Computer Science and Game Theory · Computer Science 2018-12-12 Marcos Cardinot , Josephine Griffith , Colm O'Riordan , Matjaz Perc

We study a modified prisoner's dilemma game taking place on two-dimensional disordered square lattices. The players are pure strategists and can either cooperate or defect with their immediate neighbors. In the generations each player…

Physics and Society · Physics 2007-05-23 Zhi-Xi Wu , Xin-Jian Xu , Zi-Gang Huang , Sheng-Jun Wang , Ying-Hai Wang

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

We study a spatial, one-shot prisoner's dilemma (PD) model in which selection operates on both an organism's behavioral strategy (cooperate or defect) and its choice of when to implement that strategy across a set of discrete time slots.…

Populations and Evolution · Quantitative Biology 2020-12-01 Tim Johnson , Oleg Smirnov

In recent years, Win-Stay-Lose-Learn rule has attracted wide attention as an effective strategy updating rule, and voluntary participation is proposed by introducing a third strategy in Prisoner's dilemma game. Some researches show that…

Computer Science and Game Theory · Computer Science 2021-08-18 Zhenyu Shi , Wei Wei , Xiangnan Feng , Ruizhi Zhang , Zhiming Zheng

Cyclic dominance has become a pivotal factor in sustaining cooperation within structured populations. However, this comprehension has predominantly revolved around node dynamics, where players are confined to employing the same strategy…

Physics and Society · Physics 2024-09-13 Danyang Jia , Chen Shen , Xiangfeng Dai , Junliang Xing , Pin Tao , Yuanchun Shi , Zhen Wang

Cooperation is a difficult proposition in the face of Darwinian selection. Those that defect have an evolutionary advantage over cooperators who should therefore die out. However, spatial structure enables cooperators to survive through the…

Physics and Society · Physics 2018-02-02 Attila Szolnoki , Matjaz Perc

We study the emergency of mutual cooperation in evolutionary prisoner's dilemma games when the players are located on a square lattice. The players can choose one of the three strategies: cooperation (C), defection (D) or "tit for tat" (T),…

Statistical Mechanics · Physics 2015-06-24 Gyorgy Szabo , Tibor Antal , Peter Szabo , Michel Droz

We consider the prisoner's dilemma being played repeatedly on a dynamic network, where agents may choose their actions as well as their co-players. This leads to co-evolution of network structure and strategy patterns of the players.…

Physics and Society · Physics 2007-06-26 Christoly Biely , Klaus Dragosits , Stefan Thurner

Evolutionary Prisoner's Dilemma games with quenched inhomogeneities in the spatial dynamical rules are considered. The players following one of the two pure strategies (cooperation or defection) are distributed on a two-dimensional lattice.…

Populations and Evolution · Quantitative Biology 2007-05-23 Attila Szolnoki , Gyorgy Szabo

Prisoner's dilemma game is the most commonly used model of spatial evolutionary game which is considered as a paradigm to portray competition among selfish individuals. In recent years, Win-Stay-Lose-Learn, a strategy updating rule base on…

Physics and Society · Physics 2021-01-27 Zhenyu Shi , Wei Wei , Xiangnan Feng , Xing Li , Zhiming Zheng

Spatial evolutionary games provide a valuable framework for elucidating the emergence and maintenance of cooperative behavior. However, most previous studies assume that individuals are profiteers and neglect to consider the effects of…

Computer Science and Game Theory · Computer Science 2025-11-25 Bin Pi , Minyu Feng , Liang-Jian Deng

In spatial games players typically alter their strategy by imitating the most successful or one randomly selected neighbor. Since a single neighbor is taken as reference, the information stemming from other neighbors is neglected, which…

Physics and Society · Physics 2012-11-01 Xiaofeng Wang , Matjaz Perc , Yongkui Liu , Xiaojie Chen , Long Wang

In the framework of the paradigmatic prisoner's dilemma, we investigate the evolutionary dynamics of social dilemmas in the presence of "cooperation facilitators". In our model, cooperators and defectors interact as in the classical…

Populations and Evolution · Quantitative Biology 2012-08-02 Mauro Mobilia

This paper studies scenarios of cyclic dominance in a coevolutionary spatial model in which game strategies and links between agents adaptively evolve over time. The Optional Prisoner's Dilemma (OPD) game is employed. The OPD is an extended…

Computer Science and Game Theory · Computer Science 2017-02-15 Marcos Cardinot , Josephine Griffith , Colm O'Riordan
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