Payoff Continuity in Incomplete Information Games

An incomplete information game is defined by a probability distributionμover a type space and payoff functionsu. Probability distributionμ′ isstrategically closetoμif, for any bounded payoff functionsuand any equilibrium of the game (μ, u), there exists an approximate equilibrium of the game (μ′, 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 similarconditionalprobabilities to all events.Journal of Economic LiteratureClassification Numbers: C72, D82.