Evolution of cooperation in a spatial structure with compensation mechanisms

Abstract We study the evolution of cooperation by modeling interactional individuals with compensation mechanism on a two-dimensional square lattice. In this model, the payoff to cooperators is the same no matter what types their neighbors are, while the payoff to defectors depends on whether there exists cooperative neighbor. In addition, cooperators will obtain some compensation from the payoffs of defectors. We find that a larger compensation coefficient in the model leads to the higher cooperation, which means the compensation mechanism partly promotes cooperation. In addition, the simulation results suggest that decreasing either the payoff of defectors without cooperative neighbors or the payoff of defectors with cooperative neighbors will promote cooperation.

[1]  Attila Szolnoki,et al.  Reward and cooperation in the spatial public goods game , 2010, ArXiv.

[2]  W. Hamilton.  The Evolution of Altruistic Behavior , 1963, The American Naturalist.

[3]  R. Seyfarth,et al.  Vocal recognition in free-ranging vervet monkeys , 1980, Animal Behaviour.

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

[5]  R. Boyd,et al.  Explaining altruistic behavior in humans , 2003 .

[6]  M. Nowak,et al.  Stochastic dynamics of invasion and fixation. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[7]  Attila Szolnoki,et al.  Rewarding evolutionary fitness with links between populations promotes cooperation , 2014, Journal of theoretical biology.

[8]  Arne Traulsen,et al.  Fixation probabilities of random mutants under frequency dependent selection. , 2010, Journal of theoretical biology.

[9]  R. Seyfarth,et al.  Vocal development in vervet monkeys , 1986, Animal Behaviour.

[10]  E. Fehr,et al.  Altruistic punishment in humans , 2002, Nature.

[11]  Yiping Fang,et al.  Promotion of cooperation in aspiration-based spatial prisoner’s dilemma game , 2011 .

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

[13]  Cendri A. C. Hutcherson,et al.  A Neurocomputational Model of Altruistic Choice and Its Implications , 2015, Neuron.

[14]  Attila Szolnoki,et al.  Evolutionary advantages of adaptive rewarding , 2012, 1208.3457.

[15]  Zhihai Rong,et al.  Effects of aspiration on public cooperation in structured populations , 2012 .

[16]  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.

[17]  Attila Szolnoki,et al.  Antisocial pool rewarding does not deter public cooperation , 2015, Proceedings of the Royal Society B: Biological Sciences.

[18]  Darrel D. Muehling,et al.  “I Eat Organic for My Benefit and Yours”: Egoistic and Altruistic Considerations for Purchasing Organic Food and Their Implications for Advertising Strategists , 2014 .

[19]  Jörg Oechssler,et al.  Cooperation as a Result of Learning with Aspiration Levels , 2002 .

[20]  S. Tipper,et al.  I Want to Help You, But I Am Not Sure Why: Gaze-Cuing Induces Altruistic Giving , 2013, Journal of experimental psychology. General.

[21]  Arne Traulsen,et al.  Pairwise comparison and selection temperature in evolutionary game dynamics. , 2007, Journal of theoretical biology.

[22]  Christine Taylor,et al.  COOPERATION MAINTAINED BY FITNESS ADJUSTMENT. , 2007, Evolutionary ecology research.

[23]  S. Kurokawa,et al.  Emergence of cooperation in public goods games , 2009, Proceedings of the Royal Society B: Biological Sciences.

[24]  Tadeusz Platkowski,et al.  Enhanced cooperation in prisoner's dilemma with aspiration , 2009, Appl. Math. Lett..

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

[26]  Mauro Mobilia,et al.  Reply to "Comment on 'Stochastic dynamics of the prisoner's dilemma with cooperation facilitators' ". , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[27]  Zhi-Xi Wu,et al.  Promotion of cooperation by aspiration-induced migration , 2011 .

[28]  M. Tomasello,et al.  Altruistic Helping in Human Infants and Young Chimpanzees , 2006, Science.

[29]  R. Boyd,et al.  The evolution of altruistic punishment , 2003, Proceedings of the National Academy of Sciences of the United States of America.

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

[31]  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.

[32]  L. Imhof,et al.  Stochasticity and evolutionary stability. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[33]  D. D. de Quervain,et al.  The Neural Basis of Altruistic Punishment , 2004, Science.

[34]  Deborah A. Small,et al.  Selfish or selfless? On the signal value of emotion in altruistic behavior. , 2014, Journal of personality and social psychology.

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

[36]  E. Bárány.  SIMULTANEOUS MEASUREMENT OF CHANGING INTRAOCULAR PRESSURE AND OUTFLOW FACILITY IN THE VERVET MONKEY BY CONSTANT PRESSURE INFUSION. , 1964, Investigative ophthalmology.