Evolutionary Game Dynamics On Complex Networks:a Perspective Of Heterogeneity

The emergence and maintenance of cooperative behaviors among selfish individuals has been a frontier and hot topic in many disciplines such as evolutionary biology and sociology.According to the fundamental principles of Darwinian selection "Survival of the fittest in natural selection",cooperation extinction is inevitable,and selfish behavior will be naturally chosen in biological evolution.This contradicts with the fact that cooperation is common between individuals of the same species and between individuals of different species.The evolutionary game dynamics on complex networks is a research topic for exploring the evolution of cooperation and can help individuals out of various cooperative dilemmas.Evolutionary game theory and complex networks provide a powerful theoretical framework to interpret the subtleties of cooperative behaviors among selfish individuals.In recent years,scholars in many fields such as game theory,statistical physics,statistics,network science,evolutionary biology,behavioral science,and experimental economics,have studied the evolutionary game dynamics on complex networks from the perspective of heterogeneity or asymmetry.It provides a new idea to solve the dilemmas of cooperation.Based on the previous achievements,this dissertation studies the evolutionary game dynamics on complex networks from two perspectives of heterogeneity.The main results are as follows:(1)Sorting out the research ideas and summarizing the previous research achievements.Through reading previous massive literature,we find that evolutionary game dynamics on complex networks is studied by computer simulation and experimental economics.So,we review recent classical findings of evolutionary game dynamics on complex networks from these two aspects,and give some thoughts on "the three routes of researching evolutionary game dynamics on complex networks along computer simulation" summarized by the former.First,the influence of network structure on the evolution of cooperation behaviors.Complex networks is an angle and method to understand many natural and social complex systems(such as economic system,ecological and biological,social system,etc.)and various dynamic processes(such as games,propagation,synchronization,and control).It is the basis of understanding the nature and function of complex systems,and mainly paid close attention to the topological structure,the function of the system and the relationship between the two.How collective behaviors evolves on complex systems is affected not only by the network structure of the system,but also by some of its characteristics(such as average degree,degree correlation,community structure,clustering coefficient,etc.).The second is to design dynamical mechanism by adjusting game model,strategy update rules and so on.This aspect mainly includes the expansion of strategic space(such as the introduction of isolated strategy and zero determinant strategy,etc.),dynamic payoff matrix,comparing and integrating of synchronous and asynchronous(random sequential)update modes,the selection of various strategy update rules,non-equal probability selection of strategy update objects,heterogeneous measures of individual fitness,and numerous social mechanisms(such as reputation,reward,punishment,conformity,win-stay lose-shift,tit for tat etc.).The third is to consider the coevolution of complex networks topology and game dynamics,which mainly considers not only the impact of network structure on game dynamics based on it,but also the one of dynamics process on the network structure.That is,besides that the strategies of players evolve in time,the network structure may simultaneously evolve as well.(2)In computer simulation regard,we do two things: one the one hand,we give the basic steps for the research on evolutionary game dynamics on complex networks with the Monte Carlo simulation method.On the other hand,we design two mechanisms for measuring heterogeneous environment to explore how heterogeneous integration environment affects the evolution of cooperative behavior in structured population.These two mechanisms are as follows: "When the environment of the focal individual is dominant,its environment is measured as the difference between its payoff and the average payoffs of its all neighbors " and "the environment of the focal individual is measured as some weighted average payoffs of its all neighbors".What these two mechanisms have in common is that they both incorporate the environment into the individual fitness.The difference includes two aspects.One is that the environment is measured in different ways.The individual environment of the former is the difference between the average accumulated payoffs of its all neighbors and its accumulated payoffs.While the individual environment of the latter is the some weighted average accumulated payoffs of all its neighbors.The second is that the timing of considering the environment is different.The former only integrates the environment when the environment is dominant,while the latter has no time limit.We use the Monte Carlo simulation method to verify the following conclusions from different perspectives.In these two mechanisms,the heterogeneous measurement environment enhances the mutual spatial reciprocity(the cooperators form cluster to protect themselves against the exploitation by defectors),and makes the cooperative level the negative feedback phenomenon.In addition,we have verified that the mechanism influences cooperative behavior,and the impact of these mechanisms on evolution of cooperation has consistency and universality for different network structures and different game models.(3)In experimental economics,we introduce the collective-risk social dilemma and simulate it by designing the climate game experiment to prevent dangerous climate change.Through real-life experiments on college students,we explore the impact of the factors such as group communication status,group size,and group gender structure on group cooperative behavior.In reality,differences in the cultural background,gender structure,number,and communication status of group members have different effects on group behavior decisions.Based on this,we randomly select student groups in the undergraduate group of Yunnan University of Finance and Yunnan University to conduct the climate game,explore the evolution of undergraduate cooperation behavior by statistical methods.First,we use the descriptive statistics to find that the communication groups has higher target attainment rates than the non-communication groups;the greater number of the group members,the lower the group's target attainment rate.Then,we use the Contingency Table's independence test to reach a conclusion that the group goal achievement rate is related to the group size,but not group gender or group communication status.Finally,we reach a conclusion through logistic regression analysis modeling: if "group size","group gender" and "group communication status" are used as explanatory variables,and "group goal achievement rate" is used as a forecast variable,then only "the group size" has a significant effect on " the group target attainment rate".Therefore,the cooperation behavior of college students is closely related to the number of groups,and the larger the number of groups is,the lower the target achievement rate of the group is.