Research

Published Papers

On the Existence of Monotone Pure-Strategy Perfect Bayesian Equilibrium in Games with Complementarities (Online Appendix) Journal of Economic Theory, May 2020

(An older version of this paper can be viewed here.)

Abstract: Many important economic situations can be modelled as dynamic games of incomplete information with strategic complementarities of actions and types. In this paper, we extend the results of Athey (2001) and Reny (2011) from static Bayesian games to dynamic environments, providing conditions that guarantee the existence of monotone equilibria in types in such games. A feature that distinguishes this environment from those of previous results is the endogeneity of beliefs, which can complicate continuity of payoffs, needed to find a fixed point. To address this, we define an auxiliary static game which pins down beliefs while preserving continuity of payoffs. We also provide conditions which guarantee that there will exist monotone best-replies to monotone strategies of one's opponents in a dynamic environment. Applications are given to signaling games and stopping games such as auctions, wars of attrition, and joint research projects.

Rational Inattention and the Monotone Likelihood Ratio Property ( Journal of Economic Theory, September 2021)

Abstract: A commonly assumed feature of games with complementarities is that players have noisy signals of the underlying state of the world that are ordered by the monotone likelihood ratio property (MLRP). At the same time, a large literature has recently explored the behavior of rationally inattentive agents. I provide a connection between these two literatures, showing that a decision maker with payoffs that satisfy increasing differences (ID) will always acquire signals that are ordered by the MLRP if and only if he has attention costs proportional to entropy reduction. I extend this result to games, providing conditions under which players first acquire MLRP-ordered signals, and then choose higher actions given higher realizations of the signals. Applications are given to global games and independent private-value auctions.

Monotone Persuasion (Games and Economic Behavior, November 2021)

Abstract: We explore when it is optimal in Bayesian persuasion environments for senders to commit to signal structures which induce the receiver to take higher actions when the underlying state is higher. Building on the literature on monotone comparative statics, we provide a technique to compute the optimal monotone signal structure. We also identify primitive conditions that guarantee that these are optimal among all (possibly non-monotone) signal structures. When the action space is binary, supermodularity of the sender’s and receiver’s preferences suffices for the optimal signal to have a monotone structure. With a continuum of actions, the conditions are more intriguing. We identify a novel single-crossing condition using a virtual utility representation of the sender’s payoff. Applications are given to quadratic loss functions with biases and to credit ratings.

Screening Inattentive Buyers (American Economic Review, June 2022)

(This paper was previously circulated under the title, "Screening Inattentive Agents.")

Abstract: Information plays a crucial role in mechanism design problems. A potential complication is that this information may endogenously and flexibly depend on what options they are offered. I show that it is without loss to look at contour mechanisms, which comprise triplets of allocation probabilities, prices, and beliefs, and are uniquely determined by a single such point. The mechanism design problem then reduces to Bayesian persuasion along the optimal contour. The reduction to contour mechanisms has significant implications for both implementation of the optimal mechanism, and the revenues that can be achieved.

Working Papers

Monopoly, Product Quality, and Flexible Learning (joint with Doron Ravid)

Abstract: A seller offers a buyer a schedule of transfers and associated product qualities, as in Mussa and Rosen (1978). After observing this schedule, the buyer chooses a flexible costly signal about his type. We show it is without loss to focus on a class of mechanisms that compensate the buyer for his learning costs. Using these mechanisms, we prove the quality always lies strictly below the efficient level. This strict downward distortion holds even if the buyer acquires no information or when the buyer’s posterior type is the highest possible given his signal, reversing the “no distortion at the top” feature that holds when information is exogenous. 

Posterior-Mean Separable Costs of Information Acquisition (joint with Komal Malik)

Abstract: We analyze a problem of revealed preference given state-dependent stochastic choice data in which the payoff to a decision maker (DM) only depends on their beliefs about posterior means. Often, the DM must also learn about or pay attention to the state; in applied work on this subject, a convenient assumption is that the costs of such learning are linearly dependent in the distribution over posterior means. We provide testable conditions to identify whether this assumption holds. This allows for the use of information design techniques to solve the DM's problem.

Cardinal Representations of Information 

Abstract: In the spirit of von Neumann and Morgenstern (1947), this paper provides an axiomatic representation of information. Under the von Neumann-Morgenstern axioms, along with an additional continuity axiom and a Blackwell informativeness axiom, I show that any ordering over information can be essentially uniquely represented as, equivalently: (a) a strictly increasing cost of information acquisition; (b) the expected utility from a decision problem; (c) for a given prior, an additive posterior-separable measure of uncertainty; and (d) a separable cost of signals. I discuss the implications of the results for the rational inattention literature.

Nonlinear Pricing and Coasian Dynamics

Abstract: The Coase conjecture states that, when a monopolist faces a continuum of consumers with varying valuation for a durable good, the monopolist cannot exploit his monopoly power if he cannot commit not to make future offers. This paper examines whether this is true when the monopolist can endogenously contract on the quality of the good, as in Mussa and Rosen (1978). We find that the monopolist retains full commitment power, as any other solution unravels: all consumers are afraid of having the lowest remaining valuation in any future period, and so will accept any offer that gives them positive payoff immediately.

Works in Progress

Posterior-Separable Information Costs and Menu Preferences (joint with Henrique de Oliveira)

Revealed Preference Tests for Bayesian Persuasion