The Study On Cooperative Evolution Dynamics On Complex Networks

From cooperation between countries such as “the Belt and Road” initiative to mutual benefit and win-win among individuals,from group hunting in ancient times to cooperation innovation in today's society,social development and human progress are inseparable from cooperation.As of today,experts and scholars in many fields including sociology,economics,environmentology and psychology have carried out a mount of theoretical research and practical exploration on the generation and maintenance of cooperation,mainly focusing on individuals,networks and behavioral experiments,and the three aspects have achieved rich results,but “how does human cooperative behavior develop?” is still a most challenging scientific question.Relying on the analysis framework of evolutionary game theory and the Monte Carlo method,this paper continues to explore the dynamic mechanism of the generation,maintenance and development of cooperative behavior in the crowd through a large number of computer simulations.First,we continue to analyze the role of heterogeneity in the evolution of cooperation from the enduring and expanding periods of cooperation.Whether heterogeneity is manifested in the individual,the network,or other aspects such as the type of game,the role of heterogeneity in cooperative evolution needs to be analyzed in combination with the specific performance of heterogeneity or the updated rules of strategy,we cannot comprehensively attribute the promotion and suppression of cooperation to the emergence of heterogeneity.In the prisoner's dilemma game,we design a co-evolutionary model of individual learning abilities in accordance with the rule of “winner-weaken-loser-strengthen”,and explore the impact of heterogeneity of learning abilities on cooperation.According to the applicable population of the co-evolutionary rule,we discuss in three conditions,simulation results find thatcooperation can be promoted if only the cooperators in the crowd perform co-evolution(Condition II),and when the entire population(Condition I)or only the defectors(Condition III)co-evolve,cooperation is significantly inhibited.The snapshots reveal that the cooperators in Condition II have lower learning abilities than the defectors in the enduring period,this creates conditions for the evolution of cooperation in the expanding period and enhances the network reciprocity.In the other two conditions,the cooperators in the enduring period have difficulty in surviving due to their high learning abilities,eventually the defectors take over almost the entire crowd.All three conditions show heterogeneity in individual learning ability,but due to the different performances of individuals with different strategies,the final results are greatly different,which verifies the previous conclusions about heterogeneity and also helps to deepen understanding the role of heterogeneity in cooperative evolution.Second,we explore the impact of resource allocation on cooperative evolution in interdependent networks.The most critical point in interdependent networks is to establish the relationship between the two layers through a certain coupling relationship,the previous coupling relationships are mainly reflected by the corresponding individual payoff(or fitness),the synergy of strategy will generally occur on both networks,which will affect the cooperation among the crowd.This article creatively introduces resource allocation to the investment stage of the public goods game,two networks represent that each individual is in different fields of investment,the resource allocation is based on the historical payoff information of individuals in different fields of investment,and according to differences in time span and measurement methods,three rules of resource allocation have been formulated.The simulation results show that the introduction of resource allocation,although there is no traditional synergy phenomenon,can greatly promote the level of cooperation among the crowd.In rule I,the higher the proportion of individuals who can allocate resources,the higher the level of cooperation,the variance of the proportion factors of cooperators explains the change of the level of cooperation.Thesnapshot reveals that individuals who can allocate resources have greater advantages in cooperation than traditional individuals because they have more flexible investment strategies;In rule II,within a reasonable range,the influence of the adjustment coefficient on the cooperation is monotonic,the larger the adjustment coefficient,the higher the density of cooperation;In rule III,we extend the one-step historical information to the all historical information.The greater the selection intensity,the higher the density of cooperation.The snapshot reveals that a synergistic phenomenon can occur at the later stage of the evolution process when the selection intensity is larger.The larger or smaller scale factors of the cooperators outside the cluster can not only effectively protect the cooperators inside,but also act as "arrows" for the cooperators to expand their own areas outward.This article further enriches the evolutionary game theory,deepens our understanding of the role of heterogeneity in evolutionary games,and creatively introduces resource allocation to interdependent networks and preliminarily explores the role of resource allocation on cooperative development.The results contribute to the integration and development of economics,sociology,and psychology to a certain extent,and provide some ideas for solving the practical dilemmas faced by the environment and resources,and also have certain reference significance in terms of disease prevention,traffic control and network security.