With Kareen Rozen

Abstract: We study optimal contracting in teams with peer monitoring and moral hazard, featuring stylized aspects of production environments with complex tasks. Agents have many opportunities to shirk, task-level monitoring is needed to provide useful incentives, and because 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 “empty promises” and endogenous supervision structures. Agents optimally make more promises than they intend to keep, leading to the concentration of supervisory responsibility in the hands of one or two agents.

Working paper 1/16/2012

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Tags: Contracts, Moral hazard, Mechanism design, Peer monitoring, Partnership, Teams, Principal-Agent, Bounded memory, Cooperation

With Joel Watson

Abstract: This paper proposes a new approach to the problem of equilibrium selection in repeated games with transfers, by supposing that in each period the players bargain over how to play. Although the bargaining phase is cheap talk (which follows 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 satisfying these axioms exist for all discount factors and are simple to construct, and all equilibria attain the same joint value. Optimal play under agreement generally requires suboptimal play under disagreement. Whether patient players attain efficiency depends on both the stage game and the bargaining power that they derive from the details of 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.

Working paper 10/13/2011

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Tags: Repeated games, Bargaining, Negotiation, Renegotiation, Relational contracts, Principal-Agent, Cooperation

With Heidi Gjertsen, Theodore Groves, Eduard Niesten, Dale Squires, and Joel Watson

Abstract: We model conservation agreements using contractual equilibrium, a concept introduced by Miller and Watson (2010) to model dynamic relationships with renegotiation. The setting takes the form of a repeated principal-agent problem, where the principal must pay to observe a noisy signal of the agent's effort. Lacking a strong external enforcement system, the parties rely on self-enforcement for their relational contract. We characterize equilibrium play (including how punishments and rewards are structured) and we show how the parties' relative bargaining powers affect their ability to sustain cooperation over time. We argue that the model captures important features of real conservation agreements and reveals the ingredients required for successful agreements.

Working paper 9/23/2010 (stay tuned for an updated version in fall 2011)

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Tags: Repeated games, Community enforcement, Conservation Agreements, Monitoring, Bargaining, Negotiation, Renegotiation, Principal-Agent, Cooperation, Forest Protection, Cambodia, Coral Reefs, Fiji, Sea Turtles, Solomon Islands, Grey Whales, Baja California

Nageeb Ali and I have been awarded a three-year grant from the National Science Foundation Economics Program, entitled “Enforcing Cooperation in Networked Societies.” Stay tuned for our first working paper soon, and lots of great projects to follow after that.

Abstract excerpt: The foundation of economic activity and growth is in the ability of individuals to trust and trade with each other over time. Throughout human history, much of economic activity occurs in realms where formal legal institutions are unwilling or unsuited to enforce cooperative behavior. A growing literature on informal enforcement suggests that the networked pattern of social relationships plays a key role in supporting cooperation: as information about past behavior diffuses through the network, an individual who deviates in a partnership is punished not only by her partner but also by those who come to learn about it. Our research program studies how communities enforce cooperation through their social networks.Permalink

Tags: Social Networks, Cooperation, Community enforcement

Published in The Review of Economic Studies, 2011.

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.

Note: This is a major update of the paper formerly titled "Optimal ex post incentive compatible equilibria in repeated games of private information” and “The dynamic cost of ex post incentive compatibility in repeated games of private information."

Free-access link to published version

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Tags: Collusion, Price wars, Repeated games, Private information, Mechanism design, Ex post incentive compatibility, Folk theorem

My four most current working papers, listed below, are all under active revision right now. Several of them may undergo a change of title as well. Check back soon for updates. If you really want the latest version of one of them right now, you may request it by email.

1. Robust collusion with private information (Published 9/28/2011)
2. A theory of disagreement in repeated games with bargaining (with Joel Watson, Updated 10/13/2011)
3. Optimally empty promises and endogenous supervision (with Kareen Rozen, Updated 9/30/2011)
4. Enforcing cooperation in networked societies (with Nageeb Ali)

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This spring I'll be presenting seminars at the following universities near you:

• March 15: Università Bocconi, Milan
• March 16: Collegio Carlo Alberto, Turin
• March 18: Universität Zürich
• March 23: European University Institute, FlorencePermalink

With Nageeb Ali

Abstract: We endogenize social network formation and collective enforcement using a model in which players interact bilaterally and repeatedly along costly links. Players observe only their own partners' actions, so collective punishments that support cooperation must spread endogenously through the network, as a contagion. Our model features asynchronous interaction, variable stakes in each relationship, and transferable utilities. With these properties, for any network there exists a contagion equilibrium in which incentive constraints bind along the equilibrium path. Among symmetric networks, the optimal network topology in a large society features many identical, independent cliques. We conjecture that such a network is also Pareto optimal among all (symmetric and asymmetric) networks. Our results formalize the notion that when collective enforcement is decentralized, the level of social cooperation, or "social capital," is maximized in tight-knit, highly clustered groups.

Working paper coming soon

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Tags: Repeated games, Social Networks, Community enforcement, Network Formation, Cooperation, Contagion, Small Worlds, Cliques

Note: Satoru Takahashi discovered an error in a previous version of this paper. I am working on figuring out how to correct it. For now, I am posting a shorter version that contains only the correct results. Please do not cite, circulate, or refer to any version of the paper dated prior to 2009.

Abstract: This paper proves folk theorems for repeated games with private information, communication, and monetary transfers, in which signal spaces may be arbitrary, signals may be statistically interdependent, and payoffs for each player may depend on the signals of other players.

Working paper 1/13/2009

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Tags: Repeated games, Private information, Mechanism design, Folk theorem

The New York TImes published a nice article today on David Kirsch and the Dot-Com Archive that he curates at the University of Maryland. The article briefly mentions a paper that David, Brent Goldfarb, and I published in the Journal of Financial Economics a few years ago. As the article mentions, our paper interprets the Dot-Com bubble as a strategy gone wrong—too many startup firms adopted "Get Big Fast" strategies (trying to emulate Yahoo!, Google, eBay, and Amazon), when they would have had better success targeting smaller niche markets.

However, the article does not mention that our paper also makes a broader contribution to the theory of investment bubbles and crashes in general—one that can help us interpret more recent events in markets like residential housing, public equities, and mortgage backed securities. The basic insight is that straightforward herding behavior among the relatively well-informed financial fund managers (like venture capitalists, hedge funds, and investment banks) can lead to a boom-bust cycle because these intermediaries are managing the funds of less informed investors (like pension funds, institutional investors, and individuals). A herd forms among the fund managers when enough of them decide that a certain kind of security or asset is a good investment that the rest find it optimal to "pile on" without investigating the fundamentals any further. Such a herd can be temporary and self-correcting, as the fund managers learn about the investment over time. However, investors on the outside, like you and me, don't know as much as the people we hired to manage our funds, and we don't fully trust them either because they're not playing with their own money. What Brent, David, and I showed in the paper is that once a bubble starts to pop, we (the investors) may find it optimal to withdraw our funds entirely, just as our fund managers have corrected their strategies to account for the collapse of the bubble.

In the current financial crisis, we can see these kinds of effects, as banks raise their interest rates and collateral requirements, investors "flee to quality" and seek refuge in treasury securities, and investment banks fail one after another. To make these ideas concrete in the context of a current crisis, we can think of AAA-rated corporate bonds (rather than equity shares in Dot-Com startups) as the overvalued security, mutual fund managers (instead of venture capitalists) as the well-informed intermediaries, and blindly trusting the bond rating agencies (rather than Get Big Fast) as the misguided strategy. According to our theory, once we see corporate bonds starting to crumble, we investors can find it optimal to withdraw from the corporate bond market in favor of Treasury bills, even though our mutual fund managers are learning to do a better job gauging the default risk of bond-issuing firms.

What does it take to get the market started again under this theory? We investors need to see some evidence that the financial intermediaries are investing wisely again. An infusion of government equity into the financial industry may help, if it gives the intermediaries a chance to demonstrate that they can be trusted once again. Otherwise we can get stuck in a bad equilibrium in which nobody invests because the intermediaries haven't demonstrated that they are trustworthy, and the intermediaries can't demonstrate that they are trustworthy because nobody is investing. So the theory suggests that the kinds of financial bailouts currently underway might actually be useful.

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Tags: Venture capital, Herding, Bubbles, Finance, Financial crisis