On repeated games with general information function

For a class of repeated two-person zero-sum games with incomplete information it was proved by Aumann and Maschler that lim ν_n exists, ν_n being the value of the game with n repetitions. If the players know at each stage the moves done by both players at all previous stages, Aumann and Maschler could prove that the error term δ_n=|ν_n - lim ν_n| satisfies δ_n≤c/√n for some c>0. It was then shown by Zamir that this bound is the lowest possible. In this paper it is shown that if previous moves are not always announced, δ_n may be of higher order of magnitude e.g. δ_n≥c/n^1/3 for some c>0. New upper bounds for δ_n are given for two classes of games.