The role of generosity on the evolution of cooperation

Abstract Cooperation between non-kin is a mysterious phenomenon and needs explanation from evolutionary perspective. The mechanism under which players choose to keep or stop the interaction with the current partner based upon what the current partner does can facilitate the evolution of cooperation. Animals including humans are error prone and sometimes fail in cooperating even when they intend to cooperate. In the presence of such an error, those who defected are not always players who intended to defect; therefore, it is not obvious whether stopping the interaction with a player who defected is a nice option or not. Additionally, are cooperators more or less likely to evolve when execution errors are present? By using a simple mathematical model, we reveal that generosity who misses defection by the partner and keeps the interaction can facilitate the evolution of cooperation and that mistakes can facilitate the evolution of cooperation.

[1]  C. A. Aktipis,et al.  Is cooperation viable in mobile organisms? Simple Walk Away rule favors the evolution of cooperation in groups. , 2011, Evolution and human behavior : official journal of the Human Behavior and Evolution Society.

[2]  Chaitanya S. Gokhale,et al.  Evolutionary games in the multiverse , 2010, Proceedings of the National Academy of Sciences.

[3]  F. A. Chalub,et al.  Fixation in large populations: a continuous view of a discrete problem , 2014, Journal of mathematical biology.

[4]  J. Wakano,et al.  Generous cooperators can outperform non-generous cooperators when replacing a population of defectors. , 2010, Theoretical population biology.

[5]  M. Nowak,et al.  Tit for tat in heterogeneous populations , 1992, Nature.

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

[7]  Segismundo S. Izquierdo,et al.  Leave and let leave: A sufficient condition to explain the evolutionary emergence of cooperation , 2014 .

[8]  C Athena Aktipis,et al.  Know when to walk away: contingent movement and the evolution of cooperation. , 2004, Journal of theoretical biology.

[9]  Peter Kollock,et al.  "An Eye for an Eye Leaves Everyone Blind": Cooperation and Accounting Systems , 1993 .

[10]  P. F. Slade Dominant Cubic Coefficients of the ‘1/3-Rule’ Reduce Contest Domains , 2019, Mathematics.

[11]  C. Hauert,et al.  Replicator dynamics for optional public good games. , 2002, Journal of theoretical biology.

[12]  A. Griffin,et al.  Cooperation and Competition Between Relatives , 2002, Science.

[13]  Tianguang Chu,et al.  Rare but severe concerted punishment that favors cooperation. , 2012, Theoretical population biology.

[14]  A. Traulsen,et al.  How Life History Can Sway the Fixation Probability of Mutants , 2016, Genetics.

[15]  M A Nowak,et al.  The arithmetics of mutual help. , 1995, Scientific American.

[16]  Richard McElreath,et al.  Mathematical models of social evolution: A guide for the perplexed , 2007 .

[17]  Arne Traulsen,et al.  Extrapolating Weak Selection in Evolutionary Games , 2013, PLoS Comput. Biol..

[18]  Roderick M. Kramer,et al.  When in Doubt... , 1991 .

[19]  W. Hamilton The genetical evolution of social behaviour. I. , 1964, Journal of theoretical biology.

[20]  林 直保子 TIT-FOR-TATからOUT-FOR-TATへ , 1993 .

[21]  P. Molander The Optimal Level of Generosity in a Selfish, Uncertain Environment , 1985 .

[22]  K. Foster,et al.  Kin selection is the key to altruism. , 2006, Trends in ecology & evolution.

[23]  S. Kurokawa Payoff non-linearity sways the effect of mistakes on the evolution of reciprocity. , 2016, Mathematical biosciences.

[24]  Segismundo S. Izquierdo,et al.  The option to leave: conditional dissociation in the evolution of cooperation. , 2010, Journal of theoretical biology.

[25]  Q. Pan,et al.  Aspiration promotes cooperation in the prisoner's dilemma game with the imitation rule. , 2016, Physical review. E.

[26]  Huanren Zhang,et al.  Errors can increase cooperation in finite populations , 2018, Games Econ. Behav..

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

[28]  Yi Tao,et al.  Opting out against defection leads to stable coexistence with cooperation , 2016, Scientific Reports.

[29]  Sabin Lessard,et al.  On the Robustness of the Extension of the One-Third Law of Evolution to the Multi-Player Game , 2011, Dyn. Games Appl..

[30]  Yi Tao,et al.  A simple rule of direct reciprocity leads to the stable coexistence of cooperation and defection in the Prisoner's Dilemma game. , 2017, Journal of theoretical biology.

[31]  R. Trivers The Evolution of Reciprocal Altruism , 1971, The Quarterly Review of Biology.

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

[33]  R. May More evolution of cooperation , 1987, Nature.

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

[35]  Yi Tao,et al.  Cooperation evolves more when players keep the interaction with unknown players , 2019, Appl. Math. Comput..

[36]  Jonathan Bendor,et al.  Uncertainty and the Evolution of Cooperation , 1993 .

[37]  Shun Kurokawa,et al.  Evolution of social behavior in finite populations: a payoff transformation in general n-player games and its implications. , 2013, Theoretical population biology.

[38]  R. Axelrod,et al.  The Further Evolution of Cooperation , 1988, Science.

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

[40]  S. Frank Foundations of Social Evolution , 2019 .

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

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