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.

An equivalence theorem for a differential information economy

“…It follows from the continuity of U i (ω, x) in x and measurability in ω that U i (·, ·) is jointly measurable. Hence, under (A.2) and (A.3), the associated continuum economy E c satisfies all the assumptions of the equivalence theorem of Radner equilibria and private core (see Einy et al, 2001). …”

“…The argument is not straightforward and requires the private core-equivalence theorem (Einy et al, 2001). However, our proof has a big payoff.…”

Incentives and the core of an exchange economy: a survey

“…Alternatively, one can follow Radner (1968) and impose the requirement that an agent's trades be measurable with respect to her private information. Equilibrium allocations so defined bear the standard relationship with the private core (see Section 1.1.3), which similarly imposes such measurability restrictions; see Einy et al (2001a). 37 When the economy is replicated in the way proposed by Gul and Postlewaite, on the other hand, each individual's information remains private even in the large economy and we need a notion of competitive equilibrium which takes incentives into account.…”

The bargaining set of a large economy with differential information

“…Throughout the paper we assume that for all t ∈ T and ω ∈ Ω the function u t (ω, ·) is strictly increasing and continuous on l Einy, Moreno and Shitovitz (1998) have shown that if the utility functions of the traders are continuous and strictly increasing, and if every commodity is present in the market (i.e., T e(t, ω)d µ 0 for all ω ∈ Ω), then a competitive equilibrium (in the sense of Radner) exists when the economy is irreducible (see Theorem A in Einy, Moreno and Shitovitz, 1998). Since in our model the initial endowments of the traders are in l ++ , the economies we consider here are irreducible (see Proposition 3.1 in Einy, Moreno and Shitovitz, 1998), and therefore always have a competitive equilibrium.…”