Under the assumption that the range of varying uncertain parameters is known, some results of existence and stability of equilibria for population games with uncertain parameters are investigated in this paper. On the basis of NS equilibria in classical noncooperative games, the concept of NS equilibria for population games with uncertain parameters is defined. Using some hypotheses about the continuity and convexity of payoff functions, the existence of NS equilibria in population games is also proved by Fan–Glicksberg fixed point theorem. Furthermore, we establish a bounded rationality model of population games with uncertain parameters, and draw the conclusions about the stability of NS equilibrium in this model by constructing the rationality function and studying its properties.

中文翻译：

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有限理性下具有不确定参数的种群博弈的均衡稳定性

在已知不确定参数变化范围的前提下，研究了具有不确定参数的种群博弈的均衡存在性和稳定性的一些结果。基于经典非合作博弈的NS均衡，定义了不确定参数种群博弈的NS均衡概念。使用关于收益函数的连续性和凸性的一些假设，Fan-Glicksberg不动点定理也证明了种群博弈中NS均衡的存在。此外，我们建立了具有不确定参数的种群博弈的有界理性模型，并通过构造理性函数并研究了其性质，得出了该模型中NS均衡稳定性的结论。