Frédéric Koessler

Strategic knowledge sharing in Bayesian games

Abstract This paper provides a model for the study of direct, public and strategic knowledge sharing in Bayesian games. We propose an equilibrium concept which takes into account communication possibilities of exogenously certifiable statements and in which beliefs off the equilibrium path are explicitly deduced from consistent possibility correspondences, without making reference to perturbed games. Properties of such an equilibrium and of revised knowledge are examined. In particular, it is shown that our equilibrium is always a sequential equilibrium of the associated extensive form game with communication. Finally, sufficient conditions for the existence of perfectly revealing or non-revealing equilibria are characterized in some classes of games. Several examples and economic applications are investigated.

When does a firm disclose product information

A firm chooses a price and the product information it discloses to a consumer whose tastes are privately known. We provide a necessary and sufficient condition on the match function for full disclosure to be the unique equilibrium outcome whatever the costs and prior beliefs about product and consumer types. It allows for products with different qualities as well as some horizontal match heterogeneity. With independently distributed product and consumer types, full disclosure is always an equilibrium and a necessary and sufficient equilibrium condition is that all firm types earn at least the full-disclosure profit.

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.

Certifiable Pre‐Play Communication: Full Disclosure

This article asks when communication with certifiable information leads to complete information revelation. We consider Bayesian games augmented by a pre-play communication phase in which announcements are made publicly. We first characterize the augmented games in which there exists a fully revealing sequential equilibrium with extremal beliefs (i.e., any deviation is attributed to a single type of the deviator). Next, we define a class of games for which existence of a fully revealing equilibrium is equivalent to a richness property of the evidence structure. This characterization enables us to provide different sets of sufficient conditions for full information disclosure that encompass and extend all known results in the literature, and are easily applicable. We use these conditions to obtain new insights in games with strategic complementarities, voting with deliberation, and persuasion games with multidimensional types.

Optimal Delegation with Multi-Dimensional Decisions

This paper investigates optimal mechanisms in a principal–agent framework with a two-dimensional decision space, quadratic payoffs and no monetary transfers. If the conflicts of interest between the principal and the agent are different on each dimension, then delegation is always strictly valuable. The principal can better extract information from the agent by using the spread between the two decisions as a costly screening device. Delegation sets no longer trade off pooling intervals and intervals of full discretion but instead take more complex shapes. We use advanced results from the calculus of variations to ensure existence of a solution and derive sufficient and necessary conditions for optimality. The optimal mechanism is continuous and deterministic. The agentʼs informational rent, the average decision and its spread are strictly monotonic in the agentʼs type. The comparison of the optimal mechanism with standard one-dimensional mechanisms shows how cooperation between different principals controlling various dimensions of the agentʼs activities facilitates information revelation.

Persuasion Games with Higher Order Uncertainty

In persuasion games, it is well known that a perfectly revealing equilibrium may fail to exist when the decision maker is uncertain about the interested party\s payoff-relevant information. However, by explicitly integrating higher order uncertainty into the information structure, this paper shows that a perfectly revealing equilibrium does exist when disclosures are not restrained to intervals of the payoff-relevant state space. On the contrary, when payoff-irrelevant disclosures are impossible, a perfectly revealing equilibrium fails to exist as long as there is a strictly positive probability that the decision maker does not know whether the interested party is informed or not. In this case, a partially revealing equilibrium and associated inferences are characterized.

Informed seller with taste heterogeneity

Consider a seller with a single indivisible good facing a buyer whose willingness to pay depends on his privately-known taste and on product characteristics privately known by the seller. What selling procedure can arise as an equilibrium of the game in which the seller strategically chooses mechanisms conditional on his information? We characterize the set of equilibrium outcomes and establish that ex-ante revenue-maximizing mechanisms are in this set. There is generally a continuum of revenue-ranked equilibrium outcomes. Focusing on the revenue-maximizing equilibrium, we show that the seller, in general, benefits from private information and does not benefit from committing to a disclosure or a certification technology. We also provide conditions under which the privacy of the sellers information does not affect revenue.