On the relations between the values of a game and its information structure

In deterministic zero-sum two-person games, the upper and lower values move towards each other as the information available to the players is increased. This basic fact still holds, with appropriate interpretation, even when the closed loop equations fail to have a unique solution for all pairs of strategies, a hypothesis that would at times be overly restrictive.In particular, if a saddle-point exists for some information pattern, then it remains a saddle-point when the information available is increased. In that case, the additional information can only enable a player to come closer to the ideal of permanent optimality.These results, though, fail to hold in an essential way when the game is stochastic