Ezra Einy

Competitive and core allocations in large economies with differential information

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 (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.

The desirability relation of simple games

Abstract We prove some properties of simple games with a complete desirability relation, and investigate the relationships between the desirability of a simple game G and that of some simple games that are derived from G . We also provide an example of a proper simple game that has a complete and acyclic desirability relation but is not a weighted majority game.

Information Advantage in Cournot Oligopoly

We model an oligopolistic industry where a number of firms that are asymmetrically informed about the environment compete via quantities, and we study how the information available to a firm affects its equilibrium profits. Indeed we find that if all firms have access to the same constant returns to scale technology, in any Bayesian equilibrium the information advantage of a firm is rewarded.

Rational expectations equilibria and the ex-post core of an economy with asymmetric information

We study the relationship between the rational expectations equilibrium allocations and the ex -post core of exchange economies with asymmetric information.

On connected coalitions in dominated simple games

In a book by Axelrod it is claimed that, in the presence of well defined policy order, only connected coalitions form. Here we investigate the compatability of Axelrods hypothesis with several hypotheses (about coalition formation in dominated simple game) that were formulated by Peleg.

Regular simple games

Using Kelleys intersection number (and a variant of it) we define two classes of simple games, the regular and the strongly regular games. We show that the strongly regular games are those in which the set of winning coalitions and the set of losing coalitions can be strictly separated by a finitely additive probability measure. This, in particular, provides a combinatorial characterization for the class of finite weighted majority games within the finite simple games. We also prove that regular games have some nice properties and show that the finite regular games are exactly those simple games which are uniquely determined by their counting vector. This, in particular, generalizes a result of Chow and Lapidot.

On the existence of Bayesian Cournot equilibrium

We show that even in very simple oligopolies with differential information a (Bayesian) Cournot equilibrium in pure strategies may not exist, or be unique. However, we find sufficient conditions for existence, and for uniqueness, of Cournot equilibrium in a certain class of industries. More general results arise when negative prices are allowed.

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.

Compound voting and the Banzhaf index

Abstract We present three axioms for a power index defined on the domain of simple (voting) games. Positivity requires that no voter has negative power, and at least one has positive power. Transfer requires that, when winning coalitions are enhanced in a game, the change in voting power depends only on the change in the game, i.e., on the set of new winning coalitions. The most crucial axiom is composition : the value of a player in a compound voting game is the product of his power in the relevant first-tier game and the power of his delegate in the second-tier game. We prove that these three axioms categorically determine the Banzhaf index.

The value of public information in a Cournot duopoly

We derive alternative sufficient conditions for the value of public information to be either positive or negative in a Cournot duopoly where firms technology exhibits constant returns to scale.