We study equilibrium concepts in non-cooperative games under uncertainty where both beliefs and mixed strategies are represented by non-additive measures (capacities). In contrast to the classical Nash framework based on additive probabilities and linear convexity, we employ capacities and max-plus integrals to model qualitative and idempotent decision criteria. Two equilibrium notions are investigated: Nash equilibrium in mixed strategies expressed by capacities, and equilibrium under uncertainty in the sense of Dow and Werlang, where players choose pure strategies but evaluate payoffs with respect to non-additive beliefs. For games with compact strategy spaces and continuous payoffs, we establish existence results for both equilibrium concepts using abstract convexity techniques and a Kakutani-type fixed point theorem.

翻译：本文研究不确定性条件下非合作博弈的均衡概念，其中信念与混合策略均采用非可加测度（容度）表示。与基于可加概率和线性凸性的经典纳什框架不同，我们采用容度与极大加积分来建模定性与幂等的决策准则。重点探究两种均衡概念：以容度表达的混合策略纳什均衡，以及Dow和Werlang意义下的不确定性均衡（参与者选择纯策略但通过非可加信念评估收益）。针对具有紧策略空间与连续支付函数的博弈，我们运用抽象凸性技术与Kakutani型不动点定理，为两种均衡概念建立了存在性结果。