Catálogo de publicaciones - libros

We summarize here basic cooperative and noncooperative equilibrium concepts, in the context of differential information economies with a finite number of agents. These, on the one hand, game theoretic, and, on the other hand, Walrasian equilibrium type concepts are explained, and their relation is pointed out, in the context of specific economies with one or two goods and two or three agents. We analyze the incentive compatibility of several cooperative and noncooperative concepts, and also we discuss briefly the possible implementation of these concepts as perfect Bayesian equilibria through the construction of relevant game trees. This possibility is related to whether the allocation is incentive compatible. This depends on whether there is free disposal or not.

The meaning of exchange efficiency is examined in the context of an economy in which agents differ in their endowments of information. Definitions of efficiency, and of the core, are proposed which emphasize the role of communication. Opportunities for insurance are preserved by restricting communication, or in a market system by restricting insider trading, prior to the pooling of information for the purposes of production.

in which different agents have different information. I propose a definition of exchange efficiency and I characterize the efficient allocations. I then examine an analogous definition of the core and I demonstrate that the core is not empty if the usual regularity conditions are satisfied. An example, however, illustrates that a market process may fail to yield an efficient allocation. In fact, in this example the market allocation is not even individually rational for the agents. Also, in this example the core is empty if there are opportunities for communication which disrupt arrangements for mutual insurance.

Shortest distances, grey weighted distances and ultrametric distance are classically used in mathematical morphology. We introduce a lexicographic distance, for which any segmentation with markers becomes a Voronoï tessellation.

We introduce a new core concept for an exchange economy with differential information which is contained in the coarse core concept of Wilson (1978). We prove the existence of (i) a core allocation for an exchange economy with differential information and; (ii) an -core strategy for a game in normal form with differential information.

We focus on the private core (Yannelis [19]) of an economy with a finite number of agents with differential information, a continuum of states and an infinite number of commodities. We state a nonemptiness result for the private core and provide a proof based on a fixed-point argument.

We provide necessary and sufficient conditions for weak (semi)continuity of the expected utility. Such conditions are also given for the weak compactness of the domain of the expected utility. Our results have useful applications in cooperative solution concepts in economies and games with differential information, in noncooperative games with differential information and in principal-agent problems.

We provide an alternative proof of the existence of core allocations in exchange economies with differential information and infinite dimensional commodity spaces. We also identify a critical feature of information sharing rules that ensures nonemptiness of the core. In essence, the only condition we require on the sharing rules is that profitable “insider trading” be prohibited. In the absence of insider trading, balancedness is guaranteed and core nonemptiness follows.

We introduce a new core concept, called the two-stage core, which is appropriate for economies with sequential trade. We prove a general existence theorem and present two applications of the two-stage core: (i) In asset markets economies where we extend our existence proof to the case of consumption sets with no lower bound, in order to capture the case of arbitrary short sales of assets. Further, we show that the two-stage core is non empty in the Hart (1975) example where a rational expectations equilibrium fails to exist. (ii) In differential information economies where we provide sufficient conditions for the incentive compatibility of trades. Namely, that no coalition of agents can misreport the true state and provide improvements to all its members, even by redistributing the benefits from misreporting.

A condition is given that is equivalent to balancedness of all NTU-games derived from an exchange economy with asymmetric information when endowments are variable. The condition is applicable to the ex-ante model with expected utilities, but also to the more general model of Arrow-Radner type economies without subjective probabilities. Differences in the interpretation of measurability assumptions between these two models are discussed, and another model with information consistent utility functions is developed in which the result would also hold.

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.