Payoff Continuity in Incomplete Information Games
证明两个概率分布在策略上接近的充要条件是：它们对所有事件的先验概率相似，且高概率下近似共同知识认为它们对所有事件的条件概率也相似。
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.