Real world players often increase their payoÞs by voluntarily committing to play a .xed strategy, prior to the start of a strategic game. In fact, the players may further bene.t from commitments that are conditional on the commitments of others. This paper proposes a model of conditional...

Aumann has shown that agents who have a common prior cannot have common knowledge of their posteriors for event $E$ if these posteriors do not coincide. But given an event $E$, can the agents have posteriors with a common prior such that it is common knowledge that the posteriors for $E$...

We study two-player discounted repeated games in which one player cannot monitor the other unless he pays a fixed amount. It is well known that in such a model the folk theorem holds when the monitoring cost is on the order of magnitude of the stage payoff. We analyze high frequency games in...

We introduce the concepts of joint games and compatibility. In a joint game, members of the grand coalition have the option to split and maximize their total worths, over different games. In order to determine whether the grand coalition will remain intact, we introduce the notion of...

An administrator is provided with data collected by several practitioners. These data may include inconclusive observations. The administrator is required to form a frequency distribution on the states of nature that would be approved by external auditors as long as it is compatible with the...