Research
Publications
A Revision Game of Strategic Experimentation on a Common Threshold (Journal of Economic Theory, March 2020)
A revision game of experimentation is examined in which players search for an unknown threshold. Each player encounters individual random opportunities to revise her own action. Lower action saves flow cost, but the player whose action falls below the threshold suffers a costly breakdown and exits the game. The set of symmetric pure-strategy Markov equilibria has a simple characterization. The difference between these equilibria vanishes as the revision opportunity becomes infinitely frequent. In all such equilibria, players revise actions gradually over time and, absent breakdowns, settle asymptotically. The asymptotic level of actions decreases with the patience of the players, and the speed of decline in actions decreases with the number of players. In equilibrium, the endogenous arrival rate of breakdown is decreasing over time. The model extends to incorporate collateral damage from breakdowns, where two competing externalities jointly shape the dynamics.
In this paper, I study the optimal dynamic contract in a principal-agent model wherein the agent with transparent preferences privately observes a persistently evolving state. Over time, the principal takes actions to match a state-dependent target, where actions are committed based on the agent's report history. I solve the optimal contract in closed-form, which sometimes prescribes actions that move in the opposite direction of the target. I provide a simple necessary and sufficient condition for that to occur. The principal generically fares better than babbling, but efficiency is not approached as players become patient. Over time, the principal is worse off in expectation, but the agent fares better or worse depending on the shape of the principal's state-dependent target. Mean reversion leads to more co-movement between the action and the target. A short horizon dampens the principal's response to information.
Optimal Dynamic Selling Mechanism and Deal Protections in Mergers and Acquisitions (Journal of Finance, August 2023), with Zhe Wang
We study the dynamic profit-maximizing selling mechanism in an M&A environment with costly bidder entry and without entry fees. Depending on the parameters, the optimal mechanism is implemented by a standard auction, or by a two-stage procedure with exclusive offers to one bidder followed by an auction potentially favoring that bidder. The optimal mechanism may involve common deal protections like termination fees, asset lockups, or stock option lockups. Our proposed procedures resemble sales of targets filing Chapter 11 bankruptcy or M&A involving public targets; they shed light on how to use deal protections in practice.
The Strategic Decentralization of Recruiting (Journal of Economic Theory, April 2023), with Thomas Jungbauer and Zhe Wang
We propose a model of strategic delegation in professional labor markets with heterogeneous workers. A big firm, competing with fringe firms, decides whether to exercise its market power to suppress wages. Alternatively, it may choose to delegate hiring to agents (divisions), thereby committing to bid more fiercely for workers. This reduces the incentive for fringe firms of going toe-to-toe with the big firm. In equilibrium, the big firm chooses to delegate unless (a) it is too large, (b) not productive enough, or (c) too productive. While a more productive big firm delegates more often, the optimal number of agents it delegates to decreases in the big firm’s productivity. The presence of big firms does not substantially lower social welfare, unless its size exceeds the tipping point beyond which it chooses not to delegate. The introduction of a minimum wage in a professional labor market induces the big firm to delegate more aggressively, increasing match quality. Thus, social welfare may increase despite a drop in employment.
Working Papers
Peer Learning, Enforcement, and Reputation (R&R at RAND Journal of Economics), with Kai Du, Phillip Stocken, and Zhe Wang
We consider a dynamic model featuring two firms that test a regulator’s enforcement propensity through their misconduct and a regulator that disciplines them to build a reputation for strict enforcement. We show that when the regulator has full discretion over the enforcement criterion, peer learning about each other’s enforcement outcome creates not only information externalities but also endogenous enforcement externalities, which increase misconduct when the regulator is sufficiently patient and reduce it otherwise. Without regulatory discretion, however, the enforcement externalities vanish and peer learning lowers misconduct. Our results have implications for enforcement transparency, regulatory decision horizons, and regulatory discretion.
Overcoming Discrimination: Harassment and Discrimination Dynamics, with Adam Dearing and Michael Waldman
A common feature of historical episodes in which integration was successful, as well as episodes where integration was unsuccessful, is the aggravated harassment of the early pathbreakers who put themselves at risk by violating the previous segregated norm. Examples abound including Jackie Robinson and Larry Doby in the case of Major League Baseball, Autherine Lucy who was the first Black student at the University of Alabama, and Jane Chastain and Melissa Ludtke who were early female sports reporters. In this paper, we explore from a theoretical perspective the role of harassment of what we refer to as integration pathbreakers in the success and speed with which integration occurs. In our model of labor market discrimination, harassment occurs because the harassers potentially receive direct and immediate utility from harassing, but also because harassment has the potential to slow down or even stop integration. Our main result is that such a setting can exhibit path dependence, where the success or failure of the early integration pathbreakers can be pivotal for the success and speed of the subsequent integration process. That is, early success is more likely to be followed by successful and faster integration than early failure, even when the early success is not due to aspects of the environment that make integration easier. In addition to our formal theoretical analysis of the role of harassment in the success and speed of integration, we apply our results to various historical episodes including the integration of Major League Baseball in the 1940s, 1950s, and 1960s.
We present a new theory of anticompetitive exclusive dealing. In it, exclusive deals do not serve to disadvantage rivals or exclude them from the market. In equilibrium, it is often the case that multiple suppliers each form their own exclusive networks, with other downstream firms remaining unaffiliated. Despite the lack of exclusion and competitor harm, competition is harmed: exclusive deals raise all prices and harm consumers. Both retailers and suppliers may benefit from the increase in industry profits. Indeed, exclusive deals may allow suppliers of homogenous goods to earn positive profits, whereas they would earn zero in the absence of exclusive deals.
Innovation often requires completing a series of steps, some of which are unmarketable and unpatentable. The first firm to complete all these steps profits either from a first-mover advantage or from patented components of the final product. Less innovative firms, unable to complete some of these steps, may resort to espionage to learn the missing steps and advance the development of their final product. We show that larger market rewards (e.g., stronger patents) or more efficient experimentation can harm innovation under espionage. We also investigate the role of a rival’s acquisition, third-party hackers, and different espionage methods.
We revisit the Sender-Receiver game of Crawford and Sobel (1982), and examine whether allowing for long cheap talk increases the set of payoffs. We show that it does, for biases in the range [1/8, 1/sqrt{8}], and explicitly derive the best equilibrium within some class. We show that the payoff increases with the length of the cheap talk phase, although there is no discontinuity at infinity. Because only finitely many messages (and two rounds) suffice for lower biases, this shows that the number of messages necessary to implement the best equilibrium is not increasing in the congruence of the players’ preferences, unlike what the static cheap talk game suggests.