The effects of heterogeneity of updating rules on cooperation in spatial network

Abstract The emergence and maintenance of cooperation remains to be one of the overreaching problems and a number of scholars have devoted endless efforts to resolve such problems. To further explore this issue, we focus on the impact of heterogeneity of updating rules on cooperative behavior in voluntary prisoner's dilemma; here, two types of strategy updating rules are considered to mimic social facts which are listed as strategy learning mechanism and strategy teaching mechanism. The stability of different mechanisms on promoting cooperation is thoroughly investigated in this manuscript. Numerical simulations are conducted while corresponding results are presented with sufficient clarifications. We find that the strategy learning mechanism can promote cooperation steadily. However, with the variance in the proportion of the two update rules in the investigated community, the strategy teaching mechanism seems to be more sensitive. Moreover, compared with strategy learning mechanism, strategy teaching mechanism plays a more important and apparent role in promoting cooperation. We also find that personal strategy is sensitive to the varying of Loner's payoff σ, especially when σ is close to 1. We hope our findings will shed some lights on resolving the social dilemmas.

[1]  Jun Tanimoto,et al.  A stochastic Pairwise Fermi rule modified by utilizing the average in payoff differences of neighbors leads to increased network reciprocity in spatial prisoner's dilemma games , 2019, Appl. Math. Comput..

[2]  Yangming Guo,et al.  Investing the effect of age and cooperation in spatial multigame , 2020 .

[3]  Hao Guo,et al.  The impact of loners’ participation willingness on cooperation in voluntary prisoner's dilemma , 2017 .

[4]  Jun Tanimoto,et al.  Network reciprocity by coexisting learning and teaching strategies. , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[5]  Jun Tanimoto,et al.  Coevolutionary, coexisting learning and teaching agents model for prisoner’s dilemma games enhancing cooperation with assortative heterogeneous networks , 2013 .

[6]  G. Szabó,et al.  Evolutionary prisoner's dilemma game on a square lattice , 1997, cond-mat/9710096.

[7]  Ángel Sánchez,et al.  Evolutionary game theory: Temporal and spatial effects beyond replicator dynamics , 2009, Physics of life reviews.

[8]  M. Perc,et al.  Social diversity and promotion of cooperation in the spatial prisoner's dilemma game. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[9]  G. Szabó,et al.  Cooperation for volunteering and partially random partnerships. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[10]  Jun Tanimoto,et al.  A game theoretic approach to discuss the positive secondary effect of vaccination scheme in an infinite and well-mixed population , 2019, Chaos, Solitons & Fractals.

[11]  Jun Tanimoto,et al.  Fundamentals of Evolutionary Game Theory and its Applications , 2015 .

[12]  Yoh Iwasa,et al.  The leading eight: social norms that can maintain cooperation by indirect reciprocity. , 2006, Journal of theoretical biology.

[13]  Y. Moreno,et al.  Dynamic instability of cooperation due to diverse activity patterns in evolutionary social dilemmas , 2015, 1502.07724.

[14]  Jörgen W. Weibull,et al.  Evolutionary Game Theory , 1996 .

[15]  Vivek Patel,et al.  An elitist teaching-learning-based optimization algorithm for solving complex constrained optimization problems , 2012 .

[16]  M. Nowak,et al.  Evolutionary Dynamics of Biological Games , 2004, Science.

[17]  G. Szabó,et al.  Phase diagrams for an evolutionary prisoner's dilemma game on two-dimensional lattices. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[18]  H. Ohtsuki,et al.  The replicator equation on graphs. , 2006, Journal of theoretical biology.

[19]  Víctor M Eguíluz,et al.  Cooperation, social networks, and the emergence of leadership in a prisoner's dilemma with adaptive local interactions. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[20]  Yoh Iwasa,et al.  Exploiting a cognitive bias promotes cooperation in social dilemma experiments , 2018, Nature Communications.

[21]  A. Sanchez,et al.  Co-evolution of strategies and update rules in the prisoner's dilemma game on complex networks , 2010, 1007.3626.

[22]  György Szabó,et al.  Phase transitions and volunteering in spatial public goods games. , 2002, Physical review letters.

[23]  Jun Tanimoto,et al.  Relationship between dilemma occurrence and the existence of a weakly dominant strategy in a two-player symmetric game , 2007, Biosyst..

[24]  Attila Szolnoki,et al.  Statistical Physics of Human Cooperation , 2017, ArXiv.

[25]  M. Perc,et al.  Coevolution of teaching activity promotes cooperation , 2008, 0803.4091.

[26]  G. Szabó,et al.  Cooperation enhanced by inhomogeneous activity of teaching for evolutionary Prisoner's Dilemma games , 2006, q-bio/0610001.

[27]  Jun Tanimoto,et al.  Various error settings bring different noise-driven effects on network reciprocity in spatial prisoner's dilemma , 2018, Chaos, Solitons & Fractals.

[28]  M. Nowak.  Five Rules for the Evolution of Cooperation , 2006, Science.

[29]  Hao Guo,et al.  Adaptive willingness resolves social dilemma in network populations. , 2019, Chaos.

[30]  C. Hauert,et al.  Volunteering as Red Queen Mechanism for Cooperation in Public Goods Games , 2002, Science.

[31]  György Szabó,et al.  Evolutionary prisoner's dilemma games with voluntary participation. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[32]  Attila Szolnoki,et al.  Reentrant phase transitions and defensive alliances in social dilemmas with informed strategies , 2015, ArXiv.

[33]  Yangming Guo,et al.  Investigation of epidemic spreading process on multiplex networks by incorporating fatal properties , 2019, Applied Mathematics and Computation.

[34]  Attila Szolnoki,et al.  Cyclic dominance in evolutionary games: a review , 2014, Journal of The Royal Society Interface.

[35]  Jun Tanimoto,et al.  Three-strategy and four-strategy model of vaccination game introducing an intermediate protecting measure , 2019, Appl. Math. Comput..

[36]  Jun Tanimoto,et al.  Evolutionary Games with Sociophysics: Analysis of Traffic Flow and Epidemics , 2018 .

[37]  M. Nowak,et al.  Evolutionary games and spatial chaos , 1992, Nature.

[38]  Wd Hamilton,et al.  The genetical theory of social behaviour. I, II , 1964 .

[39]  F. C. Santos,et al.  Evolutionary dynamics of social dilemmas in structured heterogeneous populations. , 2006, Proceedings of the National Academy of Sciences of the United States of America.

[40]  K. Sigmund.  The Calculus of Selfishness , 2010 .

[41]  Arne Traulsen,et al.  Repeated games and direct reciprocity under active linking. , 2008, Journal of theoretical biology.

[42]  Chao Luo,et al.  Chaotic evolution of prisoner's dilemma game with volunteering on interdependent networks , 2017, Commun. Nonlinear Sci. Numer. Simul..

[43]  F. C. Santos,et al.  Scale-free networks provide a unifying framework for the emergence of cooperation. , 2005, Physical review letters.

[44]  Attila Szolnoki,et al.  Zealots tame oscillations in the spatial rock-paper-scissors game. , 2016, Physical review. E.

[45]  Huijia Li,et al.  Punishment diminishes the benefits of network reciprocity in social dilemma experiments , 2017, Proceedings of the National Academy of Sciences.

[46]  G. Szabó,et al.  Evolutionary games on graphs , 2006, cond-mat/0607344.

[47]  Martin A. Nowak,et al.  Evolutionary dynamics on any population structure , 2016, Nature.