The value of two-person zero-sum repeated games with lack of information on both sides

Abstract

Abstract." We consider repeated two-person zero-sum games in which each player has only partial information about a chance move that takes place at the beginning of the game. Under some conditions on the information pattern it is proved that lira v, exists, v, being the value of the game with n repetin~c~ tions. Two functional equations are given for which lira v, is the only simultaneous solutions. We n~m also find the least upper bound for the error term Iv, -lira v,.

Minmax and maxmin of repeated games with incomplete information

“…Kohlberg/Zamir [1974] and Mertens/Zamir[1977]]. From these results it is already clear that both the condition for the existence of v and the asymptotic value lim v n are quite different from the corresponding results for the games studied in this'paper.…”

Stochastic Games with a Single Controller and Incomplete Information

“…The main results in this framework are related to the case |Ω| = 1 (repeated games with incomplete information) and are due to Aumann, Maschler, and Stearns [3] (see also Aumann and Maschler [2]) and Mertens and Zamir [11,12]. As in the case of incomplete information on one side, we denote by u(p, s) the value of the matrix game with action sets I and J and matrix payoff (p, s, ω)) in which player 1 (resp., player 2) is informed of k (resp., l) while his opponent gets no information.…”

What restrictions do Bayesian games impose on the value of information?

“…7.4 On one-shot incomplete information zero-sum games Mertens and Zamir (1971) showed that the values of one-shot incomplete information zero-sum games with state space K form a lattice and is closed under addition. It is therefore dense in the set of all continuous functions over ∆(K).…”