On the core of an economy with differential information

We show that the fine core of an atomless exchange economy with differential information is a subset of the ex-post core of the economy. (This inclusion may be proper, and it does not hold for economies with a finite number of traders.) Consequently, every fine core allocation is a selection from the equilibrium corre- spondence of the associated family of full information economies. Moreover, when each trader knows his or her own utility function and his of her own endowment, every fine core allocation is a rational expectations equilibrium allocationPublicad

On the core of an economy with differential information.

We show that the (interim) fine core of an atomless exchange economy with differential information is a subset of the ex-post core of the economy. Moreover, the interim fine core may be empty, and therefore it may be a proper subset of the ex-post core. The inclusion relation does not hold for economies with a finite number of traders.Atomless exchange economies; Differential information; Fine core; Ex-poxt core;

On the core of an economy with differential information

We show that the (interim) fine core of an atomless exchange economy with differential information is a subset of the ex-post core of the economy. Moreover, the interim fine core may be empty, and therefore it may be a proper subset of the ex-post core. The inclusion relation does not hold for economies with a finite number of traders

Theorems on the core of an economy with infinitely many commodities and consumers

Cataloged from PDF version of article.It is known that the classical theorems of Grodal [Grodal, B., 1972. A second remark on the core of an atomless economy. Economettica 40, 581-583] and Schmeidler [Schmeidler, D., 1972. A remark on the core of an atomless economy. Econometfca 40, 579-580] on the veto power of small coalitions in finite dimensional, atomless economies can be extended (with some minor modifications) to include the case of countably many commodities. This paper presents a further extension of these results to include the case of uncountably many commodities. We also extend Vind's [Vind, K., 1972. A third remark on the core of an atomless economy. Econometrica 40, 585-586] classical theorem on the veto power of big coalitions in finite dimensional, atomless economies to include the case of an arbitrary number of commodities. In smother result, we show that in the coalitional economy defined by an atomless individualistic model, core-Walras equivalence holds even if the commodity space is non-separable. The above-mentioned results are also valid for a differential information economy with a finite state space. We also extend Kannai's [Kannai, Y., 1970. Continuity properties of the core of a market. Econometfca 38, 791-815] theorem on the continuity of the core of a finite dimensional, large economy to include the case of an arbitrary number of commodities. All of our results are applications of a lemma, that we prove here, about the set of aggregate alternatives available to a coalition. Throughout the paper, the commodity space is assumed to be an ordered Banach space which has an interior point in its positive cone. (c) 2008 Elsevier B.V. All rights reserved

Optimality of equilibria in differential information economies with restricted coalitions

It is well known that the set of unblocked allocations, the core, and the set of Walras allocations coincide in an atomless economy when all measurable coalitions are allowed to form. Clearly, if only a subset of the set of all coalitions is allowed to form, the set of unblocked allocations enlarges, and generally we can merely say that this larger set contains the set of Walrasian allocations. In reality the lack of communication restricts the set of coalitions that can be formed. The purpose of our work is investigate the Core-Walras equivalence by imposing to the set of all coalitions some restrictions. The notion of the core is based on the premise that any group of agents can cooperate and agree upon a coordinated set of actions which can then be enforced. In the context of a differential information economy, an allocation should be seen as a state-contingent allocation satisfying physical resource constraints in each information state. A central role is played by the information set of each agent. Agents which enter into a coalition contract at the ex-ante stage, i.e. before any agents receives private information, or at the interim, i.e. after each agent has received her private information. It is well known that the ex-post stage, i.e. decisions are made after the information state is known, is no different from a model with complete information. An appropriate notion of the core must take into account of whether the coalition decisions stage is ex-ante or interim. In our work we specially deal with the private core which is an ex-ante concept. It has some interesting properties: it exists under standard continuity and concavity assumptions on utility functions, it is coalitionally incentive, i.e. there is truthful revelation of information in each coalition, and it takes into account the information superiority of traders. From the non cooperative side, we deal with two main equilibrium concepts: • the rational expectations equilibrium which is an interim concept in which prices are referred to as signals reflecting and transferring information; • the competitive private equilibrium, which is closer to the Walrasian equilibrium notion in the deterministic case: this non-cooperative solution concept presumes that agents maximize their ex-ante expected utility subject to their budget constraint in which information constraints, besides the classical ones, are considered. We will consider a differential information exchange economy obtained by introducing in the classical Arrow-Debreu model both uncertainty and asymmetries in information. In these model, uncertainty is exogenous and is represented by a measure space (Ω,F) where Ω denotes the finite set of all possible states of nature and F is the set of all possible events. We will assume that agents make coalitional decisions at the ex-ante stage but each agent receives private information which is not publicly verifiable before consumption takes place. In particular, agents trades with the anonymous market rather than with other agents directly and it becomes very natural to require that agents' trade be measurable with respect to their private information. We characterize in terms of decentralizing prices several notions of core allocations resulting from different possible restrictions imposed to the set of blocking coalitions. Reciprocal relations among cores are also studied. Another issue we have investigated in our work, starting from the reality restrictions of coalitions due by various rules imposed over the society (i.e. information, transportation, legal and institutional constraints), is the number and composition of the set of blocking coalitions

Theorems on the core of an economy with infinitely many commodities and consumers

It is known that the classical theorems of Grodal [Grodal, B., 1972. A second remark on the core of an atomless economy. Econometrica 40, 581-583] and Schmeidler [Schmeidler, D., 1972. A remark on the core of an atomless economy. Econometrica 40, 579-580] on the veto power of small coalitions in finite dimensional, atomless economies can be extended (with some minor modifications) to include the case of countably many commodities. This paper presents a further extension of these results to include the case of uncountably many commodities. We also extend Vind's [Vind, K., 1972. A third remark on the core of an atomless economy. Econometrica 40, 585-586] classical theorem on the veto power of big coalitions in finite dimensional, atomless economies to include the case of an arbitrary number of commodities. In another result, we show that in the coalitional economy defined by an atomless individualistic model, core-Walras equivalence holds even if the commodity space is non-separable. The above-mentioned results are also valid for a differential information economy with a finite state space. We also extend Kannai's [Kannai, Y., 1970. Continuity properties of the core of a market. Econometrica 38, 791-815] theorem on the continuity of the core of a finite dimensional, large economy to include the case of an arbitrary number of commodities. All of our results are applications of a lemma, that we prove here, about the set of aggregate alternatives available to a coalition. Throughout the paper, the commodity space is assumed to be an ordered Banach space which has an interior point in its positive cone. © 2008 Elsevier B.V. All rights reserved

Listing Price and Non-Price-Taking behavior in market mechanisms with differential information

Abstract 1 This work investigates the optimal initial public offering mechanism (IPO) comparing the book-building, the fixed price offer and the auction to understand if the supremacy of the first mechanism is economically justified or if there are other motivations behind. In the first chapter, a survey of the theories concerning the underpricing and a general overview of the market evolution are presented. Later, let us present a theoretical model in which the listing methods are compared basis on the firm’s profit. It examines what are the key variables studied by the issuer to decide the mechanism maximizing its revenue. The information cost and the reservation utility of the investors turn out the most significant variables. Abstract 2 This work considers an exchange economy with a finite number of agents and a finite number of goods where the agents are arbitragers. The general equilibrium theory borrows the notion of arbitrage to the finance for showing how the consumers move in an economy closer to the real world with uncertainty and differential information. The first chapter describes the notion of arbitrage, its evolution during the years through the eyes of several authors. The second chapter analyses the main aspects of a differential information economy, studying the concept of core and competitive equilibrium in the ex-ante, in the interim and in the ex-post stage. In the last chapter, the arbitrage condition becomes the guideline for defining new notions of competitive equilibrium when the economy is characterized by uncertainty and differential information

The bargaining set of a large economy with differential information

We study the Mas-Colell bargaining set of an exchange economy with differential information and a continuum of traders. We established the equivalence of the private bargaining set and the set of Radner competitive equilibrium allocations. As for the weak fine bargaining set, we show that it contains the set of competitive equilibrium allocations of an associated symmetric information economy in which each trader has the “joint information” of all the traders in the original economy, but unlike the weak fine core and the set of fine value allocations, it may also contain allocations which are not competitive in the associated economy.Publicad

On the continuity of equilibrium and core correspondences in economies with differential information

We study upper semi-continuity of the private core, the coarse core, and the Radner equilibrium correspondences for economies with differential information, with Boylan (1971) topology on agents' information fields

Competitive and core allocations in large economies with differential information

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 (1968, 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.Publicad