Payoff Continuity in Incomplete Information Games

An incomplete information game is defined by a probability distribution + over a type space and payoff functions u. Probability distribution +$ is strategically close to + if, for any bounded payoff functions u and any equilibrium of the game (+, u), there exists an approximate equilibrium of the game (+$, u) under which all players get approximately the same payoffs. This note shows that two probability distributions are strategically close if and only if (1) they assign similar ex ante probability to all events; and (2) with high ex ante probability, it is approximate common knowledge that they assign similar conditional probabilities to all events. Journal of Economic Literature Classification Numbers: C72, D82. 1998 Academic Press