Evolutionary Strategy Based On Complex Network Game And Its Application

This paper studies the application of the evolution game based on the complex network. The main contents and contributions of this paper are stated as follows:1. Consider the problem of the strategy adopted by individuals in the vertices of the network for evolution on the lattice of the Prisoner’s Dilemma Game. Based on the WSLS strategy (Win-Stay-Lose-Shift), then propose a new strategy that if the payoff of the individual is larger than the neighbor’s, it will keep its strategy, otherwise, it will imitate the strategy of the directly interacted individual of its neighbors randomly. As the imitating strategy rule adopted, though the simulations, find that the results of the evolution game are related to the parameter b which is the element of the payoff matrix. Furthermore, with the value of b being increased, the percentage of the cooperators in the network will also raise. This situation is opposite to the previous concept that the higher the b is, the smaller the fraction of the cooperator is.2. Present the problem about the effect of the punishment (the payoff for the two players both choose defection) in the Prisoner’s Dilemma Game. In order to study it. we propose a new evolution strategy rule which can reflect the external factor for both players in the evolution game. For generally, if the punishment exists, the D (Defection)-D (Defection) structure (the two players both choose D strategy) which is the Nash equilibrium for the game can keep stable and never let the cooperation emerge. With the particular evolution strategy rule adopted, though the simulations, we find that the D-D structure can not keep stable and it will decrease during the game for the evolution strategy rule. Actually the punishment mainly affects the C (Cooperation)-D (Defection) structure in the network. After the fraction of the C-D structure achieved some levels, the punishment can keep the C-D structure stable and prevent it transforming to C (Cooperation)-C (Cooperation) structure. Moreover, from the aspect of the stability of structure and though the payoff the individual gains, we also find that the probability which is related to the payoff can affect the result of the evolution game.3. Present the problem about the punishment and feedback mechanism with the topology changed on small-world network. Base on the strategy updating rule, then propose a new punishment and feedback mechanism that all the individuals in the network will play a n-round Prisoner’s Dilemma Game firstly and then for the most defectors, its neighbors will punish it and break the connecting tie with it and set up the connecting for themselves. The mechanism can make the degree of the whole network decrease. And find that the mechanism can help keeping the cooperators surviving and avoiding them wiped out by the defectors. With the mechanism adopted, the number of n-round PDG almost has no effect for the evolution game. Furthermore, the probability, the average connecting<k> and the scale of the network are related to the result of the evolution game.