Abstract:

 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 e>0, e-optimal strategies with finite memory. In fact, we show that there is an e-optimal strategy that depends on the clock and three states of memory.