集值支付博弈中强Nash平衡的存在性定理
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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)


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

    Abstract:

    [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.

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王能发,杨哲,刘自鑫.集值支付博弈中强Nash平衡的存在性定理[J].重庆师范大学学报自然科学版,2023,40(1):139-144

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  • 在线发布日期: 2023-05-05