Random matching models with a continuum population are widely used in economics to study environments where agents interact in small coalitions. This paper provides foundations to such models. In particular, the paper establishes an existence result for random matchings that are universal in the...

We show that concepts introduced by Aumann more than thirty years ago throw a new light on purification in games with extremely dispersed private information. We show that one can embed payoff-irrelevant randomization devices in the private information of players and use these randomization...

We characterize the class of finite measure spaces which guarantee that for a correspondence [phi] from to a general Banach space the Bochner integral of [phi] is convex. In addition, it is shown that if [phi] has weakly compact values and is integrably bounded, then, for this class of measure...