不确定性下非合作博弈强Nash均衡的存在性

Existence of strong Nash equilibrium for non-cooperative games under uncertainty

在已知不确定参数变化范围的假设下,研究了非合作博弈强Nash均衡的存在性问题.基于经典非合作博弈的强Berge均衡及帕雷托均衡的概念,结合非合作博弈NS均衡,定义了不确定性下非合作博弈的帕雷托强Berge和强Nash均衡的概念,并借助Ky Fan不等式证明其存在性.最后利用算例验证了其可行性和有效性.

Under the assumption that the domain of the undetermined parameters is known,the existence of strong Nash equilibrium for non-cooperative games is investigated.Combined the concept of strong Berge equilibrium and Pareto equilibrium with NS-equilibrium for non-cooperative games,the notions of Pareto strong Berge equilibrium and strong Nash equilibrium under uncertainty are defined,and the existence theorem of the equilibrium is also provided by means of the Ky Fan inequality.Finally,a numeric example illustrates the effectiveness and feasibility of the proposed method.