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

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 (mathop {lim }limits_{n to infty } v_n) exists,v _n being the value of the game withn repetitions. Two functional equations are given for which (mathop {lim }limits_{n to infty } v_n) is the only simultaneous solutions. We also find the least upper bound for the error term (left| {v_n - mathop {lim }limits_{n to infty } v_n } right|) .