Direct reciprocity with costly punishment: Generous tit-for-tat prevails

JOURNAL OF THEORETICAL BIOLOGY

卷:256

Article

Rand, David G.^1,2  Ohtsuki, Hisashi^1,3  Nowak, Martin A.^1,4,5 

[1] Harvard Univ, Program Evolutionary Dynam, Cambridge, MA 02138 USA

[2] Harvard Univ, Dept Syst Biol, Cambridge, MA 02138 USA

[3] Tokyo Inst Technol, Muguro Ku, Tokyo 1528552, Japan

[4] Harvard Univ, Dept Organism & Evolutionary Biol, Cambridge, MA 02138 USA

[5] Harvard Univ, Dept Math, Cambridge, MA 02138 USA

关键词: Cooperation;    Punishment;    Evolution;    Nash equilibrium analysis;    Finite population size analysis;    Computer simulation;    Reciprocity;   

DOI  :  10.1016/j.jtbi.2008.09.015

来源: Elsevier

【 摘 要 】

The standard model for direct reciprocity is the repeated Prisoner's Dilemma, where in each round players choose between cooperation and defection. Here we extend the standard framework to include costly punishment. Now players have a choice between cooperation, defection and costly punishment. We study the set of all reactive strategies, where the behavior depends on what the other player has done in the previous round. We find all cooperative strategies that are Nash equilibria. If the cost of cooperation is greater than the cost of punishment, then the only cooperative Nash equilibrium is generous-tit-for-tat (GTFT), which does not use costly punishment. If the cost of cooperation is less than the cost of punishment, then there are infinitely many cooperative Nash equilibria and the response to defection can include costly punishment. We also perform computer simulations of evolutionary dynamics in populations of finite size. These simulations show that in the context of direct reciprocity, (i) natural selection prefers generous tit-for-tat over strategies that use costly punishment, and (ii) that costly punishment does not promote the evolution of cooperation. We find quantitative agreement between our simulation results and data from experimental observations. Published by Elsevier Ltd.

【 授权许可】

Free