Evolutionary Donation Game On Comples Network

In the nature,various systems can be characterized as complex network interacting among themselves,such as human societies,protein interactions in biology,air routes and so on.The best formulation of network were nodes representing entities and links representing relationships between entities.Recently,network science has developed rapidly.Understanding the behaviors of the system represented by the network,establishing the connections between the structures and functions of the network,predicting and inferring the operation rules of the whole system are the ultimate purposes of studying the network.Regardless of competition,cooperation and symbiotic,entities interact each other all the time.Complex network does not exist independently,they are closely related to the dynamics of interactions between entities,the interaction between entities forms the network and it also feeds back into this interaction.Hence,finding the proper models of these dynamics is crucial for the further study of network.Fortunately,evolutionary game theory,which is regarded as the most powerful tool to study cooperative behavior,can solve this problem effectively.In addition,evolutionary game theory is helpful for understanding the emergence and maintenance of cooperative behavior among selfish individuals.Therefore,we’re more interested in evolutionary game theory.For one thing,we propose a new strategy transfer rule for network evolutionary game and verify its performance on different networks.When players participate in a network game,they gain payoffs by playing games with their neighbors according to their different choices.Inspired by the human behavior,we focus on two interesting human behaviors:transcendental behavior and disturbance behavior.The former means that players will choose a proper strategy if they recognize global information,which emphasizes goodness,creativity,and potential for self-development.The latter describes the influence from the neighbors,which emphasizes conformity and dependence.To explore our proposed mechanisms,we introduce new transfer rules in the framework of memory-based donation game and observe their final cooperation rates and payoff distribution.In detail,we come up with the transcendental probability Tp and the amendatory Fermi rule W’(ai←aj)=E+W/E+1,with the introduction of the disturbance E=(b/c)/(b/c+k)in Fermi rule W =W(ai ←aj).The results from simulations and human experiments show that the introduction of new mechanisms will promote the emergence and maintenance of cooperation,then promote the reasonable distribution of payoffs.Our method provides new insights into the evolution of network evolutionary game,and we hope that this work can inspire more studies on resolving the social dilemmas.For another,we extend the framework of multichannel game to structured population,and explore the influence of the structure,the size,the closeness and the cognitive level of the population on the evolution process.Individuals interact in various areas which may interact with others.In this paper,in view of the limitation of interactive ability of individuals,we extend the multichannel game to structured population,simulate the multichannel game with different structures,sizes,closeness and cognitive levels of the population.We find that the coupling between games can improve the tendency of choosing cooperation,promote the emergence and maintenance of cooperation,and improve the individuals’payoffs.With the introduction of population structures,the coupling between games still has the advantage,but the different population structures have no essential influence on the evolution process.In addition,the expansion of the population size will inhibit the emergence and maintenance of cooperation,which further leads to the collapse of cooperative clusters and defection occupy the whole population finally.On the contrary,the closeness of the population is favor of the evolution process.The closer the interaction between individuals,the easier the cooperation emerge and maintain,and the higher the individual payoffs will be.In addition,the cognitive level of the population also affect the evolution process,only when the cognitive level is appropriate,the population’s benefits can be maximized.Finally,we explore the conditions of cooperation emergence in the population of all defectors.For the above results,we give the corresponding theoretical analysis through the analysis of income distribution and fixed probability Our study provides a framework for multichannel game with structured population,and provides corresponding theoretical analysis,which can provide certain theoretical support for subsequent research.