Characterization and incentive compatibility of Walrasian expectations equilibrium in infinite dimensional commodity spaces

Abstract

We consider a differential information economy with infinitely many commodities and analyze the veto power of the grand coalition with respect the ability of blocking non-Walrasian expectations equilibrium allocations. We provide two different Walrasian expectations equilibrium equivalence results. First by perturbing the initial endowments in a precise direction we show that an allocation is a Walrasian expectations equilibrium if and only if it is not “privately dominated” by the grand coalition. The second characterization deals with the fuzzy veto in the sense of Aubin but within a differential information setting. This second equivalence result provides a different characterization for the Walrasian expectations equilibrium and shows that the grand coalition privately blocks in the sense of Aubin any non Walrasian expectations equilibrium allocation with endowment participation rate arbitrarily close to the total initial endowment participation for every individual. Finally, we show that any no free disposal Walrasian expectations equilibria is coalitional Bayesian incentive compatible. Since the deterministic Arrow-Debreu-McKenzie model is a special case of the differential information economy model, one derives new characterizations of the Walrasian equilibria in economies with infinitely many commodities. Copyright Springer-Verlag Berlin/Heidelberg 2005Differential information economy, Walrasian expectations equilibrium, Radner equilibrium, Privately non-dominated allocations, Private core, Aubin private core, Coalitional Bayesian incentive compatibility.,

The Aubin private core of differential information economies

“…The main motivation for studying the private core stems from recent literature on differential information economies with a finite number of commodities which has shown several interesting properties of this solution concept: it is non-empty under standard continuity and concavity assumptions (Yannelis (1991), and Einy, Moreno and Shitovitz (2001)); it is coalitionally incentive compatible and it rewards the informational superiority of traders (Koutsougeras and Yannelis (1993)). The extensions of these properties to infinite dimensional models are discussed in Hervés-Beloso, Moreno-García and Yannelis (2005b) and Meo (2002).…”

“…Therefore, it applies to infinite-dimensional commodity spaces, even if the Lyapunov convexity theorem does not hold, provided that the separability assumption is satisfied. Note that, in Hervés-Beloso, Moreno-García and Yannelis (2005b), a characterization of Radner equilibria via privately nondominated allocations is provided when the space of commodities is l ∞ endowed with the Mackey topology by using a approach like that of Vind.…”

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

“…Finally, we will say that an allocation x is private c-fair relative to T 1 and T 0 if it is private c-fair relative to S 1 and S 2 , for all S 1 ∈ T 1 and S 2 ∈ T 0 . From an Aubin-like perspective, the notion of generalized coalition is as follows (compare [9], [10], [12], [13]). Definition 2.9.…”

“…We will assume that relevant allocations are measurable with respect to the private information of agents: that is, no coalition whose members use only their private information, could redistribute the net trade of any other disjoint coalition in a way which would assign a preferred bundle to each of its members. This allows us to compare c-fair allocations with the private core introduced by Yannelis [21] and the Aubin private core introduced in [9], [10] and [12]. As a first consequence, we get characterizations of Walrasian expectations equilibria in terms of suitable notions of coalitionally fair allocations, even when the set of large traders is non empty.…”

Walrasian analysis via two-player games

“…In Hervés-Beloso et al (2005a, 2005b, we provide characterizations of Walrasian allocations in terms of the blocking power of the "society" called "grand coalition." Precisely, in Hervés-Beloso et al (2005b), it is shown that the set of Walrasian allocations coincides with the set of allocations which are not blocked, in the sense of Aubin, by the society. Therefore, in order to obtain the equilibria it suffices to consider the Aubin blocking power of just one coalition, namely, the society formed by all the individuals in the economy.…”