We consider a finitely defined game where the payoff for each player at each terminal point of the game is not a fixed quantity but varies according to probability distributions on the terminal points induced by the strategies chosen. We prove that if these payoffs have an upper-semicontinuous and convex valued structure then the game has an equilibrium. For this purpose the concept of a myopic equilibrium is introduced, a concept that generalizes that of a Nash equilibrium and applies to the games we consider. We answer in the affirmative a question posed by A. Neyman: if the payoffs of an infinitely repeated game of incomplete information on one side are a convex combination of the undiscounted payoffs and payoffs from a finite number of initial stages, does the game have an equilibrium?

我们考虑一个有限定义的游戏，其中每个玩家在游戏每个终点的收益不是固定数量，而是根据所选策略在终点上的概率分布而变化。我们证明，如果这些收益具有上半连续和凸值结构，那么博弈就具有均衡性。为此目的，引入了近视平衡的概念，该概念概括了纳什平衡的概念并适用于我们考虑的游戏。我们肯定地回答A.内曼（N. Neyman）提出的一个问题：如果一侧不完整信息的无限重复博弈的收益是未折扣收益和有限初始阶段收益的凸组合，则该游戏是否具有平衡？