The Impact Of Costly Defection On Evolutionary Stability Strategy And Cooperation In Indirect Reciprocal Population Game

The evolution of human society can be modeled as population evolutionary game,in which cooperation among people is often promoted by behaviors,reputations,indirect reciprocity and other mechanisms.Firstly,with the help of the social norms of the second-order reputation assessment mechanism,we introduce an action of costly defection into a classical population evolutionary game with donations,allow players to have a certain opportunity to participate in the population evolutionary game and make mistakes in the reputation evaluation,and propose a new kind of population evolutionary game model.Secondly,we define an equilibrium solution of the population evolutionary game,and then seek equilibrium conditions for some cooperative evolutionary stability strategies and discuss their average payoffs respectively,where these strategies are three strategies: donors always take cooperation toward a good recipient but take defection,punishment or silence toward a bad recipient.It shows that among these three cooperative evolutionary stability strategies,the average payoff of the strategy taking defection with lower cost toward bad recipients is lower than that of the strategy taking silence with no cost toward bad recipients but is higher than that of the strategy taking punishment with higher cost.Finally,computer simulation verifies the above conclusions.Our results will be helpful to understand the evolution mechanisms of human society and the emergence of cooperation.