集值支付博弈中强Nash平衡的存在性定理

The Existence Theorems of Strong Nash Equilibria for Games with Set-Valued Payoffs

[目的]研究具有集值支付的博弈问题中强Nash平衡的存在性。[方法]分别基于非传递效用与可传递效用的假定,引入强Nash非传递效用平衡和强Nash可传递效用平衡的概念。[结果]在一些常规条件下,得到强Nash非传递效用平衡和强Nash可传递效用c*-平衡的存在性定理。[结论]扩展了集值支付博弈的研究范围,并把合作解存在性推广到了集值支付博弈中,为集值支付博弈的应用提供了理论支撑。

[Purposes]The existence of strong Nash equilibrium in game problems with set-valued payoffs is discussed.[Methods]By considering nontrasferable and transferable utilities,the notions of strong Nash nontransferable utility equilibria and strong Nash transferable utility equilibria for games with set-valued payoffs are introduced.[Findings]Under the regular conditions,the existence theorems of strong Nash nontransferable utility equilibria and strong Nash transferable utility c*-equilibria are obtained.[Conclusions]This work extends the research scope of set-valued payoff games and extends the existence of cooperative solutions to set-valued payoff games,which provides theoretical support for the application of set-valued payoff games.