Research On The Evolution Of Cooperation Based On Popularity Of Strategy In Local And Global Environments

From lowly groups of organisms to complex human societies,cooperative behavior that benefits others at a cost is ubiquitous.Cooperative behavior can promote the reproduction of life,the evolution of species,the development of society,and the progress of civilization,and only by cooperating can we win together.However,Darwin believed that only competition could survive,which would result in cooperative behavior being unable to actively form,stabilize,and spread in a competitive group of selfish individuals.Therefore,it is the top priority for people from all walks of life to reveal the causes of the independent emergence of cooperation and explore the mechanism to promote the evolution of cooperation.Currently,evolutionary game theory and complex network theory provide an important framework for exploring the evolution of cooperation.Based on the objective fact that the popularity of strategy in local and global environments affects the survival and development of individuals,this paper applies evolutionary game theory to construct models and conduct numerical simulation in the regular network,introduces local and global popularity in the fitness function and strategy update probability function to study the influence of the strategy popularity in local and global environments on cooperation in social dilemmas from both macro and micro perspectives.Firstly,the effect of introducing local popularity and global popularity into the fitness calculation on the cooperation in the prisoner’s dilemma game is studied.In this model,the local popularity and global popularity are quantitatively described based on the number of players who hold the same strategy with the central or target agent in different environments,and the individual’s final popularity is determined according to the weight of local popularity.The scaling index is used to reflect the influence of popularity on fitness,and the power function of popularity is combined with the individual interaction payoff function to get the final fitness function.The numerical experiment mainly explored the influence of the weight of local popularity and the scaling index of popularity on the evolution of cooperation.The results showed that: when the more popular individuals get more fitness,there exists the optimal value of the scaling index for the cooperative behavior,and the higher the local popularity is,the more beneficial to cooperation;when high popularity is unfavorable for fitness,the greater the absolute value of the scaling index is,the more conducive it is to the cooperation,and the global popularity is more conducive to cooperation in this case.Secondly,a spatial multi-game model in which popularity and payoff jointly driven update is proposed.In this model,based on local popularity and global popularity,the concept of popularity expectation is proposed,which is used as a reference for the level of popularity.In the multi-games,individuals will consider both the difference of popularity in the environment and the difference of their own payoff when updating,and use the weight factor to describe the intensity of the influence of popularity when updating strategy.The simulation results show that for the update rule in the multi-games,in the case of very small weight of popularity: local popularity is beneficial for cooperation when the social dilemma is strong,while global popularity can promote cooperation only when the temptation to defect is small;in the case of larger popularity influence weight: the local popularity is more conducive to cooperation regardless of the strength of the social dilemma.On the other hand,the influence of popularity-driven updating on cooperation is double-edged,but increasing the weight factor of popularity-driven updating can weaken the intensity of prisoner’s dilemma to a large extent and narrow the gap of survival pressure of cooperators in multi-dilemmas.Finally,the paper prospects for future research.In the future,the influence of popularity on cooperation can be studied from a multidimensional perspective in different networks and different models.