Françoise Forges

Incentives and the core of an exchange economy: a survey

This paper provides a general overview of the literature on the core of an exchange economy with asymetric information. Incentive compatibility is emphasized in studying core concepts at the ex ante and the interim stage.The analysis includes issues of non emptiness of the core as wellas core convergence to price equilibrium allocations.

The Ex Ante Incentive Compatible Core in the Absence of Wealth Effects

In a differential information economy with quasi-linear utilities, monetary transfers facilitate the fulfillment of incentive compatibility constraints: the associated ex ante core is generically non-empty. However, we exhibit a wellbehaved exchange economy in which this core is empty, even if goods are allocated through random mechanisms.

Correlated Equilibrium and Sunspot Equilibrium

SummaryWe show by an example that the sunspot equilibria of a competitive economy are not equivalent to the correlated equilibria if sunspots generate transfers between (extrinsic) states of nature (through a contingent commodities market). Nevertheless, we prove that the sunspot equilibrium allocations of a standard overlapping generations economy coincide with the (strategic form) correlated equilibrium allocations of a natural market game mimicking the economy.

Extensive-Form Correlated Equilibrium: Definition and Computational Complexity

This paper defines the extensive-form correlated equilibrium (EFCE) for extensive games with perfect recall. The EFCE concept extends Aumanns strategic-form correlated equilibrium (CE). Before the game starts, a correlation device generates a move for each information set. This move is recommended to the player only when the player reaches the information set. In two-player perfect-recall extensive games without chance moves, the set of EFCE can be described by a polynomial number of consistency and incentive constraints. Assuming P is not equal to NP, this is not possible for the set of CE, or if the game has chance moves.

Long persuasion games

This paper characterizes geometrically the set of all Nash equilibrium payoffs achievable with unmediated communication in persuasion games, i.e., games with an informed expert and an uninformed decisionmaker in which the experts information is certifiable. The first equilibrium characterization is provided for unilateral persuasion games, and the second for multistage, bilateral persuasion games. As in Aumann and Hart (2003), we use the concepts of diconvexification and dimartingale. A leading example illustrates both geometric characterizations and shows how the expert, whatever his type, can increase his equilibrium payoff compared to all equilibria of the unilateral persuasion game by delaying information certification.

A Note on the Incentive Compatible Core

We identify particular exchange economies with asymmetric information in which the ex ante incentive compatible core is nonempty provided that coalitions can allocate goods by means of random mechanisms. Both the use of random mechanisms and the restriction to a specific class of economies are crucial for the result. Indeed, the ex ante incentive compatible core can be empty (i) in our class of economies if coalitions can only use deterministic mechanisms and (ii) outside this class, even if random mechanisms are allowed.

Core-stable rings in auctions with independent private values

We propose a semi-cooperative game theoretic approach to check whether a given coalition is stable in a Bayesian game with independent private values. The ex ante expected utilities of coalitions, at an incentive compatible (noncooperative) coalitional equilibrium, describe a (cooperative) partition form game. A coalition is core-stable if the core of a suitable characteristic function, derived from the partition form game, is not empty. As an application, we study collusion in auctions in which the bidders’ final utility possibly depends on the winner’s identity. We show that such direct externalities offer a possible explanation for cartels’ structures (not) observed in practice.

Ex post individually rational trading mechanisms

We model the trading possibilities of one seller and n potential buyers as a strategic game, which extends the two-person sealed-bid double auction. We introduce particular communication equilibria for this game, the self-fulfilling equilibria. In the case of arbitrary informational externalities, we show that self-fulfilling equilibria are euqivalent to veto-incentive compatible mechanisms.

Correlated equilibria in repeated games with lack of information on one side: A model with verifiable types

Games with lack of information on one side are considered where the uncertainty of the uniformed player concerns the (verifiable) identity of his opponent. Two solution concepts are compared: the correlated equilibrium and the noisy channel equilibrium. The analysis shows in particular that correlated equilibria behave differently in the model with verifiable types and in the one with unverifiable types.

Implementation of Communication Equilibria by Correlated Cheap Talk: The Two-Player Case

We show that essentially every communication equilibrium of any finite Bayesian game with two players can be implemented as a strategic form correlated equilibrium of an extended game, in which before choosing actions as in the Bayesian game, the players engage in a possibly infinitely long (but in equilibrium almost surely finite), direct, cheap talk.