混合Nash均衡策略的随机化模拟

For a two-person complete information static game, any mixed Nash equilibrium is a probability distribution on the strategy space in theory. But, in practice, it is difficult for players to randomize their strategies according to the probability distribution.The main reason is people do not know how to randomize their own strategies. In order to improve the practical feasibility of mixed Nash equilibria, this paper adopts the method of Monte Carlo. Firstly, transform the strategies into numbers and solve the probabilites distribution of mixed Nash equilibria. Secondly, design two random variables which respectively obey a specific distribution law for each player. Lastly, simulate the random numbers which are dynamically shown to the players and players just chose the corresponding strategy to the number. It can be proven theoretically the probability value, according to which the strategies are randomized, is consistent with the probability of the mixed Nash equilibria. A numerical example of the sex battle game show that this paper can help the player simply randomize their own strategy choices according to the mixed Nash equilibrium, and the coincident rate is above 94% .