Researches Of The Analysis Of Nash Equilibrium And The Design Of Mechanisms On The Networked Public Goods Game

In recent years,network security and social security issues have occurred frequently.Enterprises and individuals must install firewalls and vaccinate against viruses to achieve security investment.When the investment in the network meets specific requirements,the network reaches group immunity,while uninvested individuals will directly benefit.Therefore,individuals in the network have the motivation not to invest but to benefit directly from the investment of other individuals.However,this self-interested behavior of individuals can easily lead to group security investment failures,resulting in huge losses.These issues of conflict between personal and collective interests can be generally abstracted as the networked public goods game model for analysis.There has been a great deal of work to improve the solution quality of networked public goods games from the perspective of Nash equilibrium solutions and the introduction of mechanisms.On the Best-shot networked public goods games,however,few studies analyze from the perspective of optimal Nash equilibrium based on social welfare and designing the evolutionary mechanisms considering the information use,access range and access cost.While the social welfare,representing the total payoff of the community,is the most common and important index to measure the solution quality of networked public goods games.Based on the considerations above,on the best-shot networked public goods game model,the Nash equilibrium analysis and evolutionary mechanism design are carried out in this paper.The details are as follows:(1)From the perspective of classical game theory,Nash equilibrium analysis is conducted.And to improve the solution quality of the optimal Nash equilibrium,pruning algorithms based on the network topology are proposed.First,the optimal and worst Nash equilibria of the Best-shot network public goods game model in special graphs and the performance of maximum social welfare are analytically demonstrated.And the thresholds of the price of anarchy and the price of stability are measured.Subsequently,the basic model is expanded,and the access cost is introduced to transform the solution of the maximum social welfare of the basic model into the solution of the optimal Nash equilibrium of the extended model.Finally,based on the above theoretical analysis,three pruning algorithms based on the network topology are proposed to approximate the optimal Nash equilibrium,and the degree-based best response algorithms of the expanded model is proposed to approximate the maximum social welfare.The experimental results show that the quality of the optimal Nash equilibrium solution and the quality of the maximum social welfare solution are improved through the proposed algorithms.(2)From the perspective of evolutionary game theory,a mechanism design study is conducted to analyze the impact of mechanisms: access range(k-hop),information use strategy,and access cost in enhancing social welfare.Considering the uncertainty of information used by the bounded rational group in real society,we further extend the basic model by introducing the mechanisms of information use strategy and k-hop access cost,establish the k-hop evolutionary Best-shot networked public goods game model,and conduct experimental analysis by considering the network topology and investment cost parameter settings.The effects of the changes in hop range,information use strategy,and access cost on social welfare are first analyzed in detail in the lattice network.Then the effects of network topology and different levels of investment cost are considered.The experiments are extended in the ER random network and BA scale-free network,as well as different settings of investment cost levels,to analyze the effects of different mechanisms and parameter designs on the average social welfare.