Research On Evolution Dynamics Based On Asymmetric Game

As an important part of game,asymmetric game is realistic,which exists in daily life and widely used in biological system,economic system,social network and other fields.Evolutionary game dynamics organically combines dynamics and game theory,and considers the variation of game strategies' frequencies from the perspective of dynamics,which is a powerful tool to solve game problems.In this paper,under the influence of environmental feedback mechanism,the dynamic evolution behavior of asymmetric division of labor games in which the game roles and their strategies are the same is studied by dynamic method,and the evolutionary behavior of asymmetric trust games in which the game roles and their strategies are different under the influence of punishment mechanism is also considered.The research contents of this paper are divided into two parts.The dynamic evolution behavior of two kinds of asymmetric games that whether the game roles and their strategies are different are analyzed,and sufficient conditions of equilibrium stability are given.In the first part,this paper analyze the influence of environmental factors on the asymmetric division of labor games from three aspects.First,environment directly affect the game's payoffs.Unlike zero supply in poor patch,populations in game have additional benefits provided by the rich patch,through imitative dynamics find that the stability of the strategies' frequencies depends on environment factors,task costs and benefits,we also obtain the change of each strategies' frequency under different environmental through experiment;Second,environment affects the strength of players.The cost of the stronger and the weaker depend on their strength,and costs are inversely proportional to their strength.Using imitative dynamics to study the evolution of strategies' frequencies stability,find that strategies' frequencies depend on the task cost,value and the power gap between players,and through the experiment find that the strength gap will affect the strategy stable results;Third,the change of environment leads to asymmetric game payoffs.The environment under two extreme states: deplete and replete correspond to two types of division of labor game,the influence of environment variables on the evolutionary stability of game strategy are discussed by replicator dynamics,find that environment changes will affect the original evolution results,new steady state occur in game.In the second part,this paper consider asymmetric trust game,where the game roles and their strategies are different.First of all,we introduce punish into the two population asymmetric trust game model,study the influence of punishment intensity on the game evolution results,which show that when punishment is big enough,it can promote the emergence of cooperation,indicate the necessity of introducing punishment mechanism.Finally,the regulatory population is introduced to implement the punishment mechanism.Through investigation,we find that the intensity of supervision in the three population trust game and the payoff required to maintain the operation of the regulatory agency determine the evolution trend of the trust game.