Incentive Optimization For The Emergence Of Cooperation In Structured Populations

In recent years,the emergence of cooperative behavior among a large population of individuals has attracted extensive attention from experts and scholars in applied mathematics,biology,control science,computer science and so on.Previous research results have shown that the emergence of cooperative behavior can be efficiently promoted by prosocial incentives.However,the total budget is limited for the institution to implement incentive.Therefore,it is worth studying how to allocate the limited total incentive budget by exploring the optimal incentive strategy for promoting the emergence of cooperation.However,previous theoretical studies on incentive policies mostly focused on well-mixed populations.Thus far there are just a few studies which have investigated the consequence of an optimal incentive allocation protocol with which cooperation can be best promoted in structured populations.Based on this,this thesis supposes that the institution allocates a limited budget to reward cooperators and punish defectors,depending on the actual cooperation level in the population,for exploring the optimal incentive protocol which can best promote cooperation.The main work and research results are as follows:Firstly,this thesis explores the optimal incentive allocation protocol on the basis of minimizing the average payoff differences between defectors and cooperators.Concretely,under the framework of spatial public good games with institutional incentives,this thesis assumes that the total budget of incentives used for rewarding cooperators and punishing defectors in an interaction group is fixed.Furthermore,this thesis derives the dynamical equation for characterizing the dynamical changes of the fraction of cooperators by using the pair approximation approach.Subsequently,this thesis formulates an optimal allocation problem by minimizing the average payoff differences between defectors and cooperators.The optimal allocation protocol has been obtained through theoretical analysis.The results show that the optimal policy depends sensitively on the efficiency ratio of reward to punishment.When the efficiency ratio is low,the optimal incentive policy is pure punishment.For an intermediate level of the efficiency ratio,the optimal protocol is adaptive hybrid.When the efficiency ratio is high,pure reward is proved to be optimal.In addition,our conclusions are verified by numerical calculations.Secondly,this thesis explores the optimal incentive allocation protocol on the basis of maximizing the gradient of the selection.The results show that the optimal policy depends sensitively on the efficiency ratio of reward to punishment.When the efficiency ratio is low,the optimal incentive policy is pure punishment.For an intermediate level of the efficiency ratio,the optimal protocol is adaptive hybrid.When the efficiency ratio is high,pure reward is proved to be optimal.In addition,the above theoretical results are verified numerically.