Competitive and core allocations in large economies with differential information

Abstract

Summary.We study the core and competitive allocations in exchange economies with a continuum of traders and differential information. We show that if the economy is "irreducible", then a competitive equilibrium, in the sense of Radner (1968Radner ( , 1982, exists. Moreover, the set of competitive equilibrium allocations coincides with the "private core" (Yannelis, 1991). We also show that the "weak fine core" of an economy coincides with the set of competitive allocations of an associated symmetric information economy in which the traders information is the joint information of all the traders in the original economy.

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

“…In the case of atomless economies (i.e., T 1 = ∅), the previous inclusions and the private core equivalence Theorem (see [6]) ensure that private c-fair allocations are exactly private core allocations. Proof.…”

“…Notice that we assume free-disposal in the feasibility requirement. It is indeed well known that, with non-free disposal, a Walrasian expectations equilibrium might not exist with positive prices (see [6] and the references quoted there).…”

Exchange economies with asymmetric information: competitive equilibrium and core

“…The list of contributions on the relationship between Radner equilibrium and ex-ante core concept with asymmetric information comprises two other recent papers by Einy, Moreno and Shitovitz [4,5], working with a continuum of agents. In [4] they show that in an ex-ante model, if the economy is 'irreducible', then a Radner equilibrium exists and the set of Radner competitive equilibrium allocations coincides with the private core.…”

“…In [4] they show that in an ex-ante model, if the economy is 'irreducible', then a Radner equilibrium exists and the set of Radner competitive equilibrium allocations coincides with the private core. It is also shown, that the weak fine core corresponds to competitive equilibria of an economy, where the symmetric information of the agents is their pooled private information.…”

“…In the presented paper, resource feasibility will be considered as denoting strict equality of the sum of the allocated commodities and the sum of the initial endowments. This complicates the existence of an equilibrium considerably, since existence results from the theory of production economies such as employed in Radner [12] or Einy, Moreno and Shitovitz [4] cannot be used. The reason for that is that the proofs of these existence results rely on the assumption that production sets have a nonempty relative interior.…”