A Note on the Private Core and Coalitional Fairness under Asymmetric Information

Abstract

We study relations among Walrasian expectations allocations, coalitional fair allocations and the private core of economies with uncertainty and asymmetric information. Our analysis covers finite exchange models, as well as models of mixed markets consisting of some large traders and an ocean of small traders. The adopted notion of coalitional fairness requires that: 1. Under a “c-fair” allocation, no coalition could benefit from achieving the net trade of some other disjoint coalition; 2. Coalition bargaining takes place without information sharing among agents. We introduce a notion of restricted Walrasian expectations allocation and examine its relations with c-fairness.