We studied the evolution of cooperation in the prisoner’s dilemma game on a square lattice where the size of the interaction neighborhood is considered. Firstly, the effects of noise and the cost-to-benefit ratio on the maintenance of cooperation were investigated. The results indicate that the cooperation frequency depends on the noise and cost-to-benefit ratio: cooperation reaches a climax as noise increases, but it monotonously decreases and even vanishes with the ratio increasing. Furthermore, we investigated how the size of the interaction neighborhood affects the emergence of cooperation in detail. Our study demonstrates that cooperation is remarkably enhanced by an increase in the size of the interaction neighborhood. However, cooperation died out when the size of the interaction neighborhood became too large since the system was similar to the mean-field system. On this basis, a cluster-forming mechanism acting among cooperators was also explored, and it showed that the moderate range of the neighborhood size is beneficial for forming larger cooperative clusters. Finally, large-scale Monte Carlo simulations were carried out to visualize and interpret these phenomena explicitly.
prisoner’s dilemma game emergence of cooperation size of interaction neighborhood
Wang Z, Du W B, Cao X B, et al. Integrating neighborhoods in the evaluation of fitness promotes cooperation in the spatial prisoner’s dilemma game. Physica A, 2011, 390: 1234–1240CrossRefGoogle Scholar
Chen Y, Qin S M, Yu L C, et al. Emergence of synchronization induced by the interplay between two prisoner’s dilemma games with volunteering in small-world networks. Phys Rev E, 2008, 77: 032103CrossRefGoogle Scholar
Liu Z L, Peng C H, Xiang W H, et al. Application of artificial neural networks in global climate change and ecological research: An overview. Chin Sci Bull, 2010, 55: 3853–3863CrossRefGoogle Scholar
Liu H T, Li W W. Language clusters based on linguistic complex networks. Chin Sci Bull, 2010, 55: 3458–3465CrossRefGoogle Scholar
Chang S, Gong X Q, Jiao X, et al. Network analysis of protein-protein interaction. Chin Sci Bull, 2010, 55: 814–822CrossRefGoogle Scholar
Liu H T. Statistical properties of Chinese semantic networks. Chin Sci Bull, 2009, 54: 2781–2785CrossRefGoogle Scholar
Liu T, Li X, Liu X P. Integration of small world networks with multiagent systems for simulating epidemic spatiotemporal transmission. Chin Sci Bull, 2010, 55: 1285–1293CrossRefGoogle Scholar
Xia C Y, Sun S W, Liu Z X, et al. Epidemics of SIRS model with nonuniform transmission on scale-free networks. Int J Mod Phys B, 2009, 23: 2203–2213CrossRefGoogle Scholar
Santos F C, Pacheco J M. Scale-free networks provide a unifying framework for the emergence of cooperation. Phys Rev Lett, 2005, 95: 098104CrossRefGoogle Scholar
Wu Z X, Rong Z H, Holme P. Diversity of reproduction time scale promotes cooperation in spatial prisoner’s dilemma games. Phys Rev E, 2009, 80: 036106CrossRefGoogle Scholar
Szolnoki A, Szabó G. Cooperation enhanced by inhomogeneous activity of teaching for evolutionary prisoner’s dilemma games. Europhys Lett, 2007, 77: 30004CrossRefGoogle Scholar
Chen X J, Wang L. Cooperation enhanced by moderate tolerance ranges in myopically selective interactions. Phys Rev E, 2009, 80: 046109CrossRefGoogle Scholar
Perc M, Wang Z. Heterogeneous aspirations promote cooperation in the prisoner’s dilemma game. PLoS ONE, 2010, 5: e15117CrossRefGoogle Scholar
Szabó G, Vukov J, Szolnoki A. Phase diagrams for an evolutionary prisoner’s dilemma game on two-dimensional lattices. Phys Rev E, 2005, 72: 047107CrossRefGoogle Scholar
Zhang H F, Liu R R, Wang Z, et al. Aspiration-induced reconnection in spatial public goods game. Eur Phys Lett, 2011, 94: 18006CrossRefGoogle Scholar
Wang Z, Murks A, Du W B, et al. Coveting the neighbors fitness as a means to resolve social dilemmas. J Theor Biol, 2011, 277: 19–26CrossRefGoogle Scholar
Szabó G, Szolnoki A. Cooperation in spatial prisoner’s dilemma games with two types of players for increasing number of neighbors. Phys Rev E, 2009, 79: 016106CrossRefGoogle Scholar
Xu Z J, Wang Z, Zhang L Z. Bounded rationality in volunteering public goods games. J Theor Biol, 2010, 264: 19–23CrossRefGoogle Scholar
Szolnoki A, Perc M, Szabó G. Phase diagrams for three-strategy evolutionary prisoner’s dilemma games on regular graphs. Phys Rev E, 2009, 80: 056104CrossRefGoogle Scholar
Open Access This article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
Open AccessThis is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.