The Research Of Co-Evolution Mechanism Between Complex Networks And Game Learning Based On Individual Preference

The 21 st century is the era of Internet. Human society has been developed rapidly because of the development of science and technology, and all kinds of systems that exist in the nature and society also tend to be complicated. The complexity systems can be abstracted as a complex network, so the study of complex networks is more meaningful. It can help us understand the evolution regularity of the complex system and more easily adapt to social life by studying complex networks.There are interaction relationships between human and animal relationships and this kind of interaction relationship is called a game. Game theory is a subject focusing on behaviors and decisions of rational players involved in competitive and interactive activities. In the game, players aim at maximum profits. By combining the game theory with dynamic evolution, the evolution game theory is produced. The player will continue to learn and change their strategies in order to obtain higher profit in the evolution game. The study of game theory can help us better understand the cooperation phenomena in the social.At present, the study of evolution game on complex networks has been an upsurge in the research. With deepening of the research, the complex network model is more and more close to the real networks and the game model is close to real game in the nature. The study of evolution game model on complex networks regards nodes as participants and edges as a link between the participants, then participants can play a game while there is a edge between them. Participants can obtain profits through the game and the change of profits will lead to the change of the network structure. Meanwhile, the change of network structure will affect the game process, and then it will affect the participants' benefits and game learning process. Therefore, it is a co-evolution relationship between the network structure and preference of game learning. Through the research of the co-evolution relationship, it can help us better understand the complexity of the interaction of individuals in society.This article builds a model of evolution game based on complex networks. The initial network is a small world network, and all the nodes in the network have the property of preference. In the evolution process, there will be a new node to join in, and the way to add edges for nodes is based on the priority connection. At the same time, the players will learn the study probability? and the network will adjust with the adjustment probability ?. In the process of the calculation about the profit, when the selected strategy of the two players is same, the profit will be controlled by the profit ratio parameter ?. The selection of the strategies for the players is according to the Nash equilibrium, and compared with the traditional game model based on the strategy choice function. In a word, the theory and experiment data proves that the game model based on the Nash equilibrium is more close to the real network.According to the results of computer simulation, for the game model based on the strategy choice function, the degree distribution is similar to the BA scale-free network and obeys power-law distribution, at the same time, with the evolution of the network, the average degrees of the network also presents the phenomenon of rising rapidly, falling fast and rising stable, average profits and modularity has a rapid growth phase, then remains stable. For the game model based on the Nash equilibrium, the degree distribution is similar to the real network Facebook. With the evolution of the network, the average degree of the network increases gradually, and it can reach equilibrium earlier than the model based on the strategy choice function. Although the modularity of the game model based on the Nash equilibrium is small, it can reflect the features of the real networks. For parameter involved in the network, such as game learning parameter, network adjustment parameter and profit ratio parameter, the influence of these parameters to the result of the network evolution will no longer apparent when the duty is greater than 0.5. With the increase of the strategy space set k, the modularity of the game model based on the strategy selection function is increasing, but the modularity of the game model based on the Nash equilibrium is decreasing. In a word, we believe that the game model based on the Nash equilibrium is more close to the real networks, which is to say that the changes we did in this paper are practical and necessary.