# Ex-post core, fine core and rational expectations equilibrium allocations

## TL;DR

This paper explores the relationships between the ex-post core, fine core, and rational expectations equilibrium allocations in an asymmetric information oligopoly, establishing conditions for their inclusion and providing counterexamples.

## Contribution

It introduces new results on the non-emptiness of the ex-post core and its relation to rational expectations equilibria in complex economies with large and small agents.

## Key findings

- Ex-post core is non-empty under certain assumptions.
- The ex-post core contains all rational expectations equilibrium allocations.
- Counterexample shows ex-post core and rational expectations set can differ.

## Abstract

This paper investigates the ex-post core and its relationships to the fine core and the set of rational expectations equilibrium allocations in an oligopolistic economy with asymmetric information, in which the set of agents consists of some large agents and a continuum of small agents and the space of states of nature is a general probability space. We show that under appropriate assumptions, the ex-post core is not empty and contains the set of rational expectations equilibrium allocations. We provide an example of a pure exchange continuum economy with asymmetric information and infinitely many states of nature, in which the ex-post core does not coincide with the set of rational expectations equilibrium allocations. We also show that when our economic model contains either no large agents or at least two large agents with the same characteristics, the fine core is contained in the ex-post core.