This paper shows that, indeed , Aumann's classical existence and equivalence theorems depend on there being many more agents than commodities. We show that for an arbitrary atomless measure space of agents three is a fixed non-separable infinite dimensional commodity space in which one can...

Investors often wish to insure themselves against the payoff of their portfolios falling below a certain value. One way of doing this is by purchasing an appropriate collection of traded securities. However, when the derivatives market is not complete, an investor who seeks portfolio insurance...

This paper presents a surprising example. It shows that lattice theoretic properties in Mas-Colell's (1986) seminal work are relevant to the existence of equilibrium problem even when commodity space is finite dimensional. The paper provides an example of an economy with three commodities and...

We prove Aliprantis, Brown, and Burkinshaw's (1987) theorem on the equivalence of Edgeworth production equilibria and pseudo-equilibria in a more general setting. We consider production economies with unordered preferences and general consumption sets in a vector lattice commodity space. We...

We present a complete, separable and metrizable topology on the product space of information and (subjective) beliefs. Such a topology formalizes similarity of differential information without the assumption of a common prior, but under the assumption that objectively impossible events are...