Solving Nash Equilibrium for Non-cooperative Game Based on the Particle Swarm Optimization Integrating Multiply Strategies

In order to solve Nash equilibrium problem of n-person finite non-cooperative game, this paper involved adaptive adjustment of inertia weight, dynamic reverse learning and local mutation search strategy into the basic particle swarm optimization (PSO), and proposed a particle swarm optimization integrating multiply strategies algorithm(IMSPSO). This algorithm introduces the state information of individual particles into the inertial weight strategy, independently adjusts the inertial weight of each particle, and reflects the difference of individual particles' weight requirements. When the algorithm is detected to be in the local optimum, a dynamic reverse learning strategy is introduced to expand the search area and enhance the algorithm's global exploration ability. At the same time, the small-scale mutation search operation of individual local neighborhood is used to guide the local learning and search of particles, so as to enhance the mining ability of particles in local space. The algorithm is used to solve two Nash equilibrium problems of non-cooperative games. The experimental results show that the algorithm can achieve good results and its performance is better than the basic particle swarm optimization algorithm.