An absorbing game is a two-person zero-sum repeated game. Some of the entries are “absorbing” in the sense that, following the play of an absorbing entry, with positive probability all future payoffs are equal to that entry's payoff. The outcome of the game is the long-run average payoff. We prove that a two-person zero-sum absorbing game, with either finite or compact action sets, has, for each $\epsilon >0$, ε-optimal strategies with finite memory. In fact, we show that there is an ε-optimal strategy that depends on the clock and three states of memory.

中文翻译：

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带有时钟和两位记忆的游戏

吸引人的游戏是两人零和重复游戏。某些条目是“吸收”的，这是指在进行吸引人的条目之后，所有将来的收益都等于该条目的收益的可能性为正。游戏的结果是长期的平均收益。我们证明了具有有限或紧凑动作集的两人零和吸收博弈对每个博弈都有$\epsilon >0$，ε-具有有限记忆的最优策略。实际上，我们表明存在一种ε最佳策略，该策略取决于时钟和内存的三个状态。