Synergy punishment promotes cooperation in spatial public good game

Abstract In previous work, punishment has been proved to an effective way to promote cooperation, and punish is introduced as a strategy just like cooperate or defect. In this paper, however, we introduce a new synergy punishment mechanism into a spatial public good game which is different from the previous works, every cooperator has a probability to be a punisher, additionally if punishment is carried out by several punishers, the cost of punishment will be reduced by synergistic effect. The simulation results show that punishment can promote cooperation and the synergistic effect has an obvious influence on cooperation for a small punishment fine but has little influence for a big punishment fine.

[1]  Xiaoping Li,et al.  Asymmetric evaluation promotes cooperation in network population , 2017 .

[2]  J. Kagel,et al.  Handbook of Experimental Economics , 1997 .

[3]  F. C. Santos,et al.  Social diversity promotes the emergence of cooperation in public goods games , 2008, Nature.

[4]  Matjaz Perc,et al.  Aspiring to the Fittest and Promotion of Cooperation in the Prisoner's Dilemma Game , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[5]  Long Wang,et al.  Promotion of cooperation induced by appropriate payoff aspirations in a small-world networked game. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[6]  Attila Szolnoki,et al.  Competition and cooperation among different punishing strategies in the spatial public goods game , 2015, Physical review. E, Statistical, nonlinear, and soft matter physics.

[7]  Mao-Bin Hu,et al.  Asymmetric cost in snowdrift game on scale-free networks , 2009 .

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

[9]  Josef Hofbauer,et al.  Evolutionary Games and Population Dynamics , 1998 .

[10]  Y. Lai,et al.  Diversity-optimized cooperation on complex networks. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[11]  Feng Qi,et al.  Randomness enhances cooperation: a resonance-type phenomenon in evolutionary games. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[12]  Zhen Wang,et al.  If players are sparse social dilemmas are too: Importance of percolation for evolution of cooperation , 2012, Scientific Reports.

[13]  K. C. Smith,et al.  Alleles of the NRAMP1 gene are risk factors for pediatric tuberculosis disease. , 2005, Proceedings of the National Academy of Sciences of the United States of America.

[14]  Martin A. Nowak,et al.  Indirect reciprocity provides a narrow margin of efficiency for costly punishment , 2008, Nature.

[15]  Chen Shen,et al.  Does coevolution setup promote cooperation in spatial prisoner's dilemma game? , 2016, Appl. Math. Comput..

[16]  R. Zecchina,et al.  Exact solution of a modified El Farol's bar problem: Efficiency and the role of market impact , 1999, cond-mat/9908480.

[17]  M. Small,et al.  Adjusting learning motivation to promote cooperation , 2010 .

[18]  Attila Szolnoki,et al.  Correlation of positive and negative reciprocity fails to confer an evolutionary advantage: Phase transitions to elementary strategies , 2013, ArXiv.

[19]  Chen Shen,et al.  Environment promotes the evolution of cooperation in spatial voluntary prisoner's dilemma game , 2017, Appl. Math. Comput..

[20]  Attila Szolnoki,et al.  Evolutionary dynamics of group interactions on structured populations: a review , 2013, Journal of The Royal Society Interface.

[21]  Xinyang Deng,et al.  A novel framework of classical and quantum prisoner’s dilemma games on coupled networks , 2016, Scientific Reports.

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

[23]  Attila Szolnoki,et al.  Restricted connections among distinguished players support cooperation. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[24]  Attila Szolnoki,et al.  Topology-independent impact of noise on cooperation in spatial public goods games. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[26]  Chen Shen,et al.  Incorporating dominant environment into individual fitness promotes cooperation in the spatial prisoners' dilemma game , 2017 .

[27]  Attila Szolnoki,et al.  Probabilistic sharing solves the problem of costly punishment , 2014, ArXiv.

[28]  Zhen Wang,et al.  Heterogeneous Aspirations Promote Cooperation in the Prisoner's Dilemma Game , 2010, PloS one.

[29]  Attila Szolnoki,et al.  Phase Diagrams for the Spatial Public Goods Game with Pool-Punishment , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[30]  Zhi-Xi Wu,et al.  Spatial prisoner's dilemma game with volunteering in Newman-Watts small-world networks. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[31]  Attila Szolnoki,et al.  Impact of Critical Mass on the Evolution of Cooperation in Spatial Public Goods Games , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[32]  Attila Szolnoki,et al.  Punish, but not too hard: how costly punishment spreads in the spatial public goods game , 2010, 1007.0431.

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

[34]  Zhen Wang,et al.  Cooperation and age structure in spatial games. , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[36]  Matjaz Perc,et al.  Evolution of public cooperation in a monitored society with implicated punishment and within-group enforcement , 2015, Scientific Reports.

[37]  Torsten Röhl,et al.  Extortion subdues human players but is finally punished in the prisoner’s dilemma , 2014, Nature Communications.

[38]  Han-Xin Yang,et al.  Promoting cooperation by punishing minority , 2018, Appl. Math. Comput..

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

[40]  H. Qian,et al.  Fixation, transient landscape, and diffusion dilemma in stochastic evolutionary game dynamics. , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[41]  D. Fudenberg,et al.  Emergence of cooperation and evolutionary stability in finite populations , 2004, Nature.

[42]  Wen-Xu Wang,et al.  Cascade of elimination and emergence of pure cooperation in coevolutionary games on networks. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[43]  Attila Szolnoki,et al.  Phase diagrams for three-strategy evolutionary prisoner's dilemma games on regular graphs. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.