The Study Of Cooperative Behavior Evolution In Complex Network

Recently,the outbreak of the US-China trade war and the conflict over the effective allocation of public resources have attracted attention and discussion.Without exception,cooperation is the best way to solve these problems.However,each individual is rational.Therefore,how to maintain cooperation to maximize the collective interest is an issue that has attracted in-depth studies by economists and experts in the field of behavioral science.Evolutionary game theory has become the mainstream method to solve this problem.Based on the prisoner's dilemma game and public goods game,this paper studies the evolution of cooperative behavior on a regular square lattice network.First,we incorporate neighbors' wisdom to the calculation of players' replicate ability via a single parameter in the prisoner's dilemma game.Through extensive numerical simulations,we find that positive modifies players' reproductive ability,where cooperative clusters become more compact and can attract more defectors to follow them.Cooperation evolves with the support of this enhanced network reciprocity.For example,we can still observe full cooperation state even at the extremely bad condition that natural selection strongly favors defection.Then,considering real-world strategy adjustments,we optimized the mechanism and defined neighbors' wisdom as the average of Fermi function values of the neighbors with different strategies and the average of Fermi function values of the neighbors with same strategies.It is concluded through comparison that defining the neighbors' wisdom as the average Fermi function value of the neighbors with different strategies promotes cooperation best,the effect of all neighbors is second,and the effect of the neighbors with same strategies is the worst.Finally,a third strategy(loner)is added to the traditional public goods game to generate a voluntary public goods game.Based on the spatial voluntary public goods games,we investigated how loners' payoff affects the evolution of cooperation on square lattice.In the voluntary model,loners can exit the game by hold a small fixed payoff.By introducing a tunable parameter,we make loner's payoff positively related to the synery factor r.Through Monte Carlo simulations,we found that higher loners' income essentially weakens their own survivability,but strengthens the competitiveness of cooperators.Through the analysis of the evolution process,we clarify the reasons how low-income loner totally dominate the population.For other results,we have studied from the perspective of spatial distribution,and find that higher loners' payoff leads to more intense strategies transition during the loop dominance process.Further we have made statistics on the strategies transition in the process of active stationary state along the path of strategic cycle dominance.The quantitative results once again prove that the higher income of the loner leads to more efficient strategy transformation.Although the model studied in this paper is simple,it can provide another insight into how cooperation can maintain this open issue,and it is a supplement and improvement to the existing mechanism.On the other hand,it provides a good theoretical framework for solving the problems of economics and trade,resource allocation,etc.,and can be widely used in various business problems and economics-related issues.Of course,it also provides some inspiration for the prevention and control of infectious diseases.