Long deliberation times promote cooperation in the prisoner’s dilemma game

Abstract Some individuals could be quite cautious when making decisions and do not update their strategy frequently in the prisoner’s dilemma game. That is, instead of updating their strategy immediately after the game, they make decisions only after a certain period of deliberation. Moreover, individuals’ strategy update is based on the cumulative payoffs they got from their prior update. Since individuals in a group could be homogeneous or heterogeneous, their strategy can depend on two aspects: the initial time of the update and the length of its delay time. In this paper, three different cases that may lead to the delay of strategy update are taken into consideration. We find that introducing a deliberation mechanism can promote cooperation, that this effect could be greater when the delay time is extended, and that heterogeneity among individuals also has a positive effect on cooperation.

[1]  Qiuhui Pan,et al.  Cooperation in spatial prisoner’s dilemma game with delayed decisions , 2013 .

[2]  G. Szabo,et al.  Diversity of reproduction rate supports cooperation in the prisoner's dilemma game on complex networks , 2008, 0802.2807.

[3]  Danyang Jia,et al.  Effects of inertia on the evolution of cooperation in the voluntary prisoner’s dilemma game , 2018, Physica A: Statistical Mechanics and its Applications.

[4]  Guangming Xie,et al.  Inertia in strategy switching transforms the strategy evolution. , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[5]  G. Szabó,et al.  Impact of aging on the evolution of cooperation in the spatial prisoner's dilemma game. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[6]  Jacek Miekisz,et al.  Stochasticity and Time Delays in Evolutionary Games , 2011, Dyn. Games Appl..

[7]  J. Neumann,et al.  Communication on the Borel Notes , 1953 .

[8]  Alexander J. Stewart,et al.  Extortion and cooperation in the Prisoner’s Dilemma , 2012, Proceedings of the National Academy of Sciences.

[9]  W. Hamilton,et al.  The Evolution of Cooperation , 1984 .

[10]  James M. Allen,et al.  Asynchronous updates can promote the evolution of cooperation on multiplex networks , 2017 .

[11]  Han-Xin Yang,et al.  Heterogeneous Aspirations Promote Cooperation in the Public Goods Game , 2013 .

[12]  Wenxu Wang,et al.  Memory-based snowdrift game on networks. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[13]  Daizhan Cheng,et al.  Dynamics and stability for a class of evolutionary games with time delays in strategies , 2016, Science China Information Sciences.

[14]  Duncan J. Watts,et al.  Collective dynamics of ‘small-world’ networks , 1998, Nature.

[15]  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.

[16]  Albert,et al.  Emergence of scaling in random networks , 1999, Science.

[17]  Attila Szolnoki,et al.  A double-edged sword: Benefits and pitfalls of heterogeneous punishment in evolutionary inspection games , 2015, Scientific Reports.

[18]  Matjaz Perc,et al.  Effects of compassion on the evolution of cooperation in spatial social dilemmas , 2018, Appl. Math. Comput..

[19]  Attila Szolnoki,et al.  Information sharing promotes prosocial behaviour , 2013, ArXiv.

[20]  Yongkui Liu,et al.  Memory-based prisoner’s dilemma on square lattices , 2010 .

[21]  M. Perc,et al.  Towards effective payoffs in the prisoner’s dilemma game on scale-free networks , 2007, 0711.4028.

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

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

[24]  Matjaz Perc,et al.  Evolutionary mixed games in structured populations: Cooperation and the benefits of heterogeneity , 2016, Physical review. E.

[25]  Zhuxi Zhang,et al.  Heterogeneous investments promote cooperation in evolutionary public goods games , 2018, Physica A: Statistical Mechanics and its Applications.

[26]  Changwei Huang,et al.  Preferential selection based on strategy persistence and memory promotes cooperation in evolutionary prisoner’s dilemma games , 2018, Physica A: Statistical Mechanics and its Applications.

[27]  Wenxing Ye,et al.  Memory-based prisoner's dilemma game with conditional selection on networks , 2017, Appl. Math. Comput..

[28]  Binghong Wang,et al.  Cooperation in spatial evolutionary games with historical payoffs , 2016 .

[29]  Martin A Nowak,et al.  Comparing reactive and memory-one strategies of direct reciprocity , 2016, Scientific Reports.

[30]  Luís Correia,et al.  The Influence of the Update Dynamics on the Evolution of Cooperation , 2009, Int. J. Comput. Intell. Syst..

[31]  Paul E. Turner,et al.  Prisoner's dilemma in an RNA virus , 1999, Nature.

[32]  T. Yi,et al.  Effect of time delay and evolutionarily stable strategy. , 1997, Journal of theoretical biology.

[33]  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.

[34]  Thomas Lux,et al.  Financial systems: Ecology and economics , 2011, Nature.

[35]  W. Press,et al.  Iterated Prisoner’s Dilemma contains strategies that dominate any evolutionary opponent , 2012, Proceedings of the National Academy of Sciences.

[36]  J M Smith,et al.  Evolution and the theory of games , 1976 .

[37]  Attila Szolnoki,et al.  Decelerated invasion and waning moon patterns in public goods games with delayed distribution , 2013, Physical review. E, Statistical, nonlinear, and soft matter physics.

[38]  Attila Szolnoki,et al.  Knowing the past improves cooperation in the future , 2019, Scientific Reports.