关键词: 粗糙集, 粒子群算法, 混合策略纳什均衡, Vague集

Abstract: There is at least one mixed strategy Nash equilibrium in continuous game, but there are little related research results in existing literature about infinite mixed strategy Nash equilibrium and uncertainty game problem. The uncertainty game refers to the game equilibrium problem that the players’ strategy set or benefit function are uncertainty. This paper creates an approximation algorithm of infinitely mixed strategy Nash equilibrium, using the advantages of particle swarm optimization, fewer parameters, simple coding and not strictly required to objective function. This paper also proposes the concept of rough game theory, and gives a method converting rough game to a classic game theory based on rough set and vague set theory. This paper provides a theoretical basis for game problem when the strategy sets and benefit function problem are fuzzy. The examples show that the approximation algorithm of infinite mixed strategy Nash equilibrium based on improved particle swarm algorithm and rough game theory solution are feasible and effective.

Key words: rough set, particle swarm optimization, mixed strategy Nash equilibrium, Vague set