效用函数与纳什均衡

UTILITY FUNCTION AND NASH EQUILIBRIUM

本文引入效用函数将博弈问题描述为收入形式和效用形式两种模型 ,使得纳什均衡与参与人效用函数联系起来 ,并得到结论 :(1)效用函数的变化对纯策略纳什均衡不产生影响 ,却改变真混合策略纳什均衡 ;(2 )效用函数严格拟凹时 ,真混合策略纳什均衡是稳定的 ;(3)效用函数严格拟凸时 ,真混合策略纳什均衡不存在 .

In this paper,using utility functions we describe game as income and utility models,establish relations of Nash equilibria and utility functions of players,and obtain the conclusions:(1)changes of utility functions dont alter the equlibria of pure strategies,but do alter those of proper mixed stategies;(2)when utility functions of players are quasiconcave,the equlibria of proper mixed stategies are stable;(3)when utility functions of players are quasiconvex,the equilibria of proper mixed stategies do not exist.