Absorbing games with a clock and finite memory

We prove that an absorbing game with either finite or compact action sets, and a repeated game with symmetric incomplete information, have, for each e>0, e-optimal strategies that depend on the clock and finitely many states of memory. Specifically, we show that in the case of an absorbing game there is an e-optimal strategy that depends on the clock and three states of memory, and in the case of a repeated game with symmetric incomplete information there is an e-optimal strategy that depends on the clock and k(e) states of memory, where k(e) is independent of e in the deterministic signal case. 

Joint work with Kristoffer Arnsfeld Hansen and Rasmus Ibsen-Jensen.