基于烟花算法的非合作博弈Nash均衡问题求解

SOLVING NASH EQUILIBRIUM OF NON-COOPERATIVE GAME BASED ON FIREWORKS ALGORITHM

提出一种求解N人有限非合作博弈Nash均衡的群体智能算法—烟花算法(FWA)。烟花爆炸后产生爆炸火花和高斯变异火花,根据火花的适应度值的好坏产生下一代烟花,适应度值较好的火花在较小范围内产生较多的爆炸火花,反之,适应度值较差的火花在较大范围内产生较少的爆炸火花。通过高斯变异火花增加种群的多样性,这种爆炸搜索机制对较好火花附近的区域搜索更加彻底并且避免过早陷入局部寻优。实验结果表明,烟花算法在求解N人有限非合作博弈Nash均衡问题上优于免疫粒子群算法。

The fireworks algorithm(FWA)is proposed to solve finite non-cooperative game among N people.The fireworks generate explosive and gaussian mutation sparks,then the next sparks are generated based on fitness.Sparks with higher fitness will generate more explosive sparks in smaller scope while sparks with lower fitness will generate less explosive sparks in larger scope.This explosive searching mechanism can provide a more complete search in area of greater sparks and avoid falling into local optimum based on the increased group diversity by Gaussian mutation.The results demonstrate that the proposed algorithm is effective and superior to the immune particle swarm algorithm in solving Nash equilibrium of non-cooperative game among N people.