Abstract:

We study the problem of npersons’ noncooperative finite game with multiple Nash equilibrium points. Firstly, we construct a mathematical programming model and prove that the solution to this model is equal to that of the npersons’ noncooperative finite game. We also propose a simulated annealing algorithm with selfadaption neighborhood for such problems. Based on this algorithm, we solve the multisolution problem without reducing the number of solutions. Numerical experiments show that the proposed algorithm is convergent and stable, and it outperforms the particle swarm algorithm, the immune particle swarm algorithm and the traditional simulated annealing algorithm.

Key words: npersons noncooperative finite game, simulated annealing algorithm, selfadaption neighbourhood, continuous variable, global optimization, multisolution problem