On repeated games with general information function

For a class of repeated two-person zero-sum games with incomplete information it was proved byAumann andMaschler that limνn exists,νn being the value of the game withn repetitions. If the players know at each stage the moves done by both players at all previous stages,Aumann andMaschler could prove that the error termδn=¦νn — limνn¦ satisfiesδn≤c/√n for somec>0. It was then shown byZamir that this bound is the lowest possible. In this paper it is shown that if previous moves are not always announced,δn may be of higher order of magnitude e.g.δn≥c/n1/3 for somec>0. New upper bounds forδn are given for two classes of games.