Dubins and Savage (How to gamble if you must: inequalities for stochastic processes, McGraw-Hill, New York, 1965) found an optimal strategy for limsup gambling problems in which a player has at most two choices at every state x at most one of which could differ from the point mass \(\delta (x)\). Their result is extended here to a family of two-person, zero-sum stochastic games in which each player is similarly restricted. For these games we show that player 1 always has a pure optimal stationary strategy and that player 2 has a pure \(\epsilon \)-optimal stationary strategy for every \(\epsilon > 0\). However, player 2 has no optimal strategy in general. A generalization to n-person games is formulated and \(\epsilon \)-equilibria are constructed.

杜宾斯与野人（如何赌博：如果必须的话：随机过程的不平等，McGraw-Hill，纽约，1965年）找到了一种解决limsup赌博问题的最佳策略，其中玩家在每个州最多有两种选择x在以下一种情况下最多这可能不同于点质量\（\ delta（x）\）。他们的结果在这里扩展到一个两人，零和的随机游戏家族，其中每个玩家都受到类似的限制。对于这些游戏，我们显示出玩家1始终具有纯粹的最佳固定策略，而玩家2对于每个\（\ epsilon> 0 \）都有纯粹的\（\ epsilon \）-最优固定策略。但是，玩家2通常没有最佳策略。拟定了n人游戏的概化并\（\ epsilon \）构造了平衡点。