We present a result on convexity and weak compactness of the range of a vector measure with values in a Banach space, based on the Maharam classification of measure spaces. Our result extends a recent result of Khan and Sagara [Illinois Journal of Mathematics, forthcoming].

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...

Maskin and Tirole have defined payoff-relevant states in discrete time dynamic games with observable actions in terms of a partition of the set of histories. Their proof that this partition is unique cannot be applied, when action spaces are infinite or when players are unable to condition on...

It is shown that core-Walras equivalence fails whenever the commodity space is a non-separable Banach space. The interpretation is that a large number of agents guarantees core-Walras equivalence only if there is actually a large number of agents relative to the size of the commodity space....

Balder's (2002) model of games with a measure space of players is integrated with the line of research on finite-player games with discontinuous payoff functions which follows Reny (1999). Specifically, we extend the notion of continuous security, introduced by McLennan, Monteiro and Tourky...

More importantly, it also provides foundations to random matching models of continuum populations with infinitely many types, which are currently used in the literature without an explicit justification.