Wasteful sanctions, underperformance, and endogenous supervision

With Kareen Rozen

Forthcoming in The American Economic Journal: Microeconomics.

Abstract: We study optimal contracting in team settings where agents have many opportunities to shirk, task-level monitoring is needed to provide useful incentives, and it is difficult to write individual performance into formal contracts. Incentives are provided informally, using wasteful sanctions like guilt and shame, or slowed promotion. These features give rise to optimal contracts with underperformance, forgiving sanctioning schemes, and endogenous supervision structures. Agents optimally take on more assigned tasks than they intend to complete, leading to the concentration of supervisory responsibility in the hands of one or two agents.

Working paper 8/09/2013

A theory of disagreement in repeated games with bargaining

With Joel Watson

Published in Econometrica, 81(6):2303–2350, November 2013.

Abstract: This paper proposes a new approach to equilibrium selection in repeated games with transfers, supposing that in each period the players bargain over how to play. Although the bargaining phase is cheap talk (following a generalized alternating-offer protocol), sharp predictions arise from three axioms. Two axioms allow the players to meaningfully discuss whether to deviate from their plan; the third embodies a “theory of disagreement”—that play under disagreement should not vary with the manner in which bargaining broke down. Equilibria that satisfy these axioms exist for all discount factors and are simple to construct; all equilibria generate the same welfare. Optimal play under agreement generally requires suboptimal play under disagreement. Whether patient players attain efficiency depends on both the stage game and the bargaining protocol. The theory extends naturally to games with imperfect public monitoring and heterogeneous discount factors, and yields new insights into classic relational contracting questions.

Published article

Supplemental material

Robust collusion with private information

Published in The Review of Economic Studies, 79(2):778–811, April 2012.

Abstract: The game-theoretic literature on collusion has been hard pressed to explain why a cartel should engage in price wars, without resorting to either impatience, symmetry restrictions, inability to communicate, or failure to optimize. This paper introduces a new explanation that relies on none of these assumptions: if the cartel's member firms have private information about their costs, price wars can be optimal in the face of complexity. Specifically, equilibria that are robust to payoff-irrelevant disruptions of the information environment generically cannot attain or approximate efficiency. An optimal robust equilibrium must allocate market shares inefficiently, and may call for price wars under certain conditions. For a two-firm cartel, cost interdependence is a sufficient condition for price wars to arise in an optimal robust equilibrium. That optimal equilibria are inefficient generically applies not only to collusion games, but also to the entire separable payoff environment (Chung & Ely 2006)—a class that includes most typical economic models.

Published article (free access)

Invention under uncertainty and the threat of ex post entry

Published in the European Economic Review, 52(3):387–412, April 2008

Abstract: This paper proposes a theoretical framework for studying the invention of new products when demand is uncertain. In this framework, under general conditions, the threat of ex post entry by a competitor can deter invention ex ante. Asymmetric market power in the ex post market exacerbates the problem. The implications of these general results are examined in a series of examples that represent important markets in the computer industry. The first is a model that shows how an operating system monopolist, by its mere presence, can deter the invention of complements, to its own detriment as well as that of society. The implications of policies such as patent protection, price regulation, and mandatory divestiture are considered. Three additional examples consider the ability of a monopolist in one market to commit to bundling an unrelated product, a pair of horizontally differentiated firms that can add a new feature to their products, and a platform leader that can be challenged in its base market by the supplier of a complementary product.

Published article (ScienceDirect subscribers only)

Working paper 8/24/2006 (older version but freely distributable)

Was there too little entry during the Dot Com Era?

With Brent Goldfarb and David Kirsch

Published in the Journal of Financial Economics, 86(1):100-144, October 2007

Abstract: We present four stylized facts about the Dot Com Era: (1) there was a widespread belief in a "Get Big Fast" business strategy; (2) the increase and decrease in public and private equity investment was most prominent in the internet and information technology sectors; (3) the survival rate of dot com firms is on par or higher than other emerging industries; and (4) firm survival is independent of private equity funding. To connect these findings we offer a herding model that accommodates a divergence between the information and incentives of venture capitalists and their investors. A Get Big Fast belief cascade may have led to overly focused investment in too few internet startups and, as a result, too little entry.

Covered by The New York Times (Leslie Berlin, "Lessons of survival from the Dot-Com attic," p. BU4, 11/23/2008)

Covered by The Wall Street Journal (Lee Gomes, "The Dot-Com Bubble is reconsidered—and maybe relived," p. B1, 11/8/2006)

Covered by Inc.com (Leslie Taylor, "The dot-com bust? Not as bad as you think," 12/4/2006)

Published article (ScienceDirect subscribers only)

Working paper 12/13/2005 (older version but freely distributable)

Efficiency in repeated trade with hidden valuations

With Susan Athey

Published in Theoretical Economics, 2(3):299-354, September 2007

Abstract: We analyze the extent to which efficient trade is possible in an ongoing relationship between impatient agents with hidden valuations (i.i.d. over time), restricting attention to equilibria that satisfy ex post incentive constraints in each period. With ex ante budget balance, efficient trade can be supported in each period if the discount factor is at least one half. In contrast, when the budget must balance ex post, efficiency is not attainable, and furthermore for a wide range of probability distributions over their valuations, the traders can do no better than employing a posted price mechanism in each period. Between these extremes, we consider a "bank" that allows the traders to accumulate budget imbalances over time, but only within a bounded range. We construct non-stationary equilibria that allow traders to receive payoffs that approach efficiency as their discount factor approaches one, while the bank earns exactly zero expected profits. For some probability distributions there exist equilibria that yield exactly efficient payoffs for the players and zero profits for the bank, but such equilibria require high discount factors.

Published article (free access)

“Token” equilibria in sensor networks with multiple sponsors

With Sameer Tilak and Tony Fountain

Published in the Proceedings of the Workshop on Stochasticity in Distributed Systems (StoDiS'05), San Jose, CA, December 19, 2005

Abstract: When two sponsoring organizations, working towards separate goals, employ wireless sensor networks for a finite period of time, it can be efficiency-enhancing for the sponsors to program their sensors to cooperate. But if each sensor privately knows whether it can provide a favor in any particular period, and the sponsors cannot contract on ex post payments, then no favors are performed in any Nash equilibrium. Allowing the sponsors to contract on ex post payments, we construct equilibria based on the exchange of "tokens" that yield significant cooperation and increase expected sponsor payoffs. Increasing the sponsors' liability is beneficial because it enables them to use more tokens.

Working paper 5/22/2006 (newer and better than the StoDiS version)