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

作　　者：王能发 杨哲[3] 刘自鑫 WANG Nengfa;YANG Zhe;LIU Zixin(School of Mathematics and Statistics,Guizhou University of Finance and Economics,Guiyang 550025;Guizhou Key Laboratory of Big Data Statistical Analysis,Guiyang 550025;School of Economics,Shanghai University of Finance and Economics,Shanghai 200433,China)

机构地区：[1]贵州财经大学数学与统计学院 [2]贵州省大数据统计分析重点实验室,贵阳550025 [3]上海财经大学经济学院,上海200433

出　　处：《重庆师范大学学报（自然科学版）》2023年第1期139-144,共6页Journal of Chongqing Normal University:Natural Science

基　　金：国家自然科学基金(No.62062018);贵州大数据统计分析重点实验室项目(No.黔科合平台人才[2019]5103);贵州省高层次创新型人才项目(No.黔科合平台人才-GCC[2022]020-1);贵州财经大学创新探索及学术新苗项目(No.2022XSXMB22)。

摘　　要：[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.

关 键 词：集值支付博弈 强Nash平衡 非传递效用 可传递效用 

分 类 号：O225[理学—运筹学与控制论]