Study on Mixed Strategy Nash Equilibrium Based on Rough Set Theory and Particle Swarm Optimization

Abstract

There is at least one mixed strategy Nash equilibrium in continuous game, but the existing literature does not provide a universal method of solving infinite strategy mixed strategy NASH equilibrium; this is also the issues to be ad- dressed in the paper. This paper creates a infinitely strategy mixed strategy Nash equilibrium's an approximation algo- rithm, using rough set theory and the advantages of particle swarm optimization. And proposes the concept of fuzzy game theory, gives a method converted fuzzy game to a classic game theory base on rough set and Vague set theory; The paper provides a theoretical basis for widespread problem in the applications field of game theory when strategy sets and the benefit function problem are fuzzy. The results of the algorithm example show, this paper created algorithm is feasible and effective. It can solve an infinite strategy mixed strategy Nash equilibrium, and equilibrium problem of fuzzy game model.