In this paper, by virtue of the Kakutani–Fan–Glicksberg fixed point theorem and a nonlinear scalarization function, we first obtain an existence theorem of general n-person noncooperative games problems with set payoffs. Then, we also obtain existence theorems of minimax regret equilibria and ϵ-minimax regret equilibria with scalar set payoffs. Some examples are given to illustrate our results.

中文翻译：

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n人非合作游戏解的存在和极小极大值对设定收益的平衡感到遗憾

在本文中，借助Kakutani–Fan–Glicksberg不动点定理和非线性标量函数，我们首先获得了具有收益的一般n人非合作博弈问题的存在性定理。然后，我们还获得极小极大遗憾存在定理平衡和ε -minimax遗憾平衡与标设定的回报。给出了一些例子来说明我们的结果。