Research On Cooperative Game Theory Based On Complexity Of Network Structure

Charles Darwin proposed that selfish individual prefers to choose betrayal strategy to increase its payoff,thus betrayal strategy will be widely spread in the population.However,cooperation exists in almost all fields in real life.Game theory provides a powerful framework for the study of the evolution of cooperative behavior.People can always find the application of game theory in their lives,including chess,war decision-making,commercial cooperation,and biological evolution.Complex networks can represent many complex systems in the real world,including urban power networks,the World Wide Web,and ecological networks.These networks have different characteristics,for example,the interpersonal network has a small-world characteristic,and the computer network has a scale-free characteristic.Different network structures have different effects on game evolution.In order to explore the relationship between network structure and game evolution,people introduced complex networks into game theory.The network model in this paper are the most widely used small-world network model and scale-free network model.Compared with random network and regular network,these two models are closer to the real-world network.Complex networks have some common structural characteristics.When how network structure affects cooperative evolution has been concerned,some scholars have studied the impact of structural characteristics,such as average degree and clustering coefficient on cooperative evolution.However,cooperation should be related to the complexity of the network.Therefore,this paper uses network structure entropy to characterize the complexity of the network,and studies its relationship with the level of cooperation in games on complex networks.In the process of real-world games,individuals will not only change their strategies,but also their own game relationships.That is,in the game,the network topology is constantly changing.Therefore,games based on dynamic networks should also be valued.The game model is also closely related to the evolutionary behavior of cooperation.In this paper,the classic game model in the two-player game—the prisoner’s dilemma model and the classicmodel in the multiplayer game—the public good game model are used.We first introduce the prisoner’s dilemma game and public goods game based on complex network,and then introduce the prisoner’s dilemma game model based on dynamic topology,where the network topology and game dynamics evolve together.The experiment uses the Monte Carlo method.The results show that in the BA and NW networks,there is an appropriate network structure entropy for both the Prisoner’s Dilemma Game Model based on Dynamic topology and Static topology,so that the cooperation rate in the network reaches the highest level.In the public goods game experiment,there is no significant difference in the experimental results on the BA and NW networks.Regardless of the network structure characteristics,when the gain coefficient is small,the larger the network structure entropy,the smaller the cooperation rate.When the gain coefficient is large,there is medium-sized network structure entropy,which makes the network cooperation level optimal.Results show that network structure entropy is an important feature of network evolutionary games and is suitable for describing the impact of network structure on cooperation.