Is multilateral enforcement vulnerable to bilateral renegotiation?

With S. Nageeb Ali and Yilin David Yang

Abstract: In a multilateral enforcement regime, a player who cheats on one partner is punished by many partners. But if partners can renegotiate in private, they can subvert the power of the multilateral punishment. We introduce a new notion of "bilateral renegotiation proofness" that applies to multilateral games with private monitoring. For symmetric networked environments, we characterize an optimal bilateral renegotiation proof equilibrium. While players’ ability to renegotiate bilaterally is indeed socially costly, it is perhaps not as costly as one might expect. In densely connected communities, the proportional cost imposed by bilateral renegotiation declines as the number of participants grows, and vanishes in the limit.

Working paper 1/10/2016

Ostracism and forgiveness

With S. Nageeb Ali

Conditionally accepted by The American Economic Review

Abstract: Many communities rely upon ostracism to enforce cooperation: if an individual shirks in one relationship, her innocent neighbors share information about her guilt in order to shun her, while continuing to cooperate among themselves. However, a strategic victim may herself prefer to shirk, rather than report others' deviations truthfully. If guilty players are to be permanently ostracized, then such deviations are so tempting that cooperation in any relationship is bounded by what the partners could obtain through bilateral enforcement. We show that ostracism can improve upon bilateral enforcement if it is tempered by forgiveness, through which guilty players are eventually readmitted to cooperative society.

Major update: Working paper 7/7/2015

Wasteful sanctions, underperformance, and endogenous supervision

With Kareen Rozen

Published in The American Economic Journal: Microeconomics, 6(4):326–361, November 2014

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.

Published article (restricted access)

Published article and Supplementary Appendix (free access)

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

Moving to Michigan

I am leaving UCSD to join the Economics Department at the University of Michigan, effective July 1, 2013. I will miss my San Diego colleagues very much, but I’m excited to work with the faculty and students at Michigan.

Enforcing cooperation in networked societies

With S. Nageeb Ali

Abstract: Which social norms and networks maximize cooperation in bilateral relationships? We study a network of players in which each link is a repeated bilateral partnership with two-sided moral hazard. The obstacle to community enforcement is that each player observes the behavior of her partners in their partnerships with her, but not how they behave in other partnerships. We introduce a new metric for the rate at which information diffuses in a network, which we call viscosity, and show that it provides an operational measure for how conducive a network is to cooperation. We prove that clique networks have the lowest viscosity and that the optimal equilibrium of the clique generates more cooperation and higher average utility than any other equilibrium of any other network. This result offers a strategic foundation for the perspective that tightly knit groups foster the most cooperation. We apply this framework to analyze favor exchange arrangements, decentralized trade in networked markets, and social collateral.

Working paper 10/31/2012

Visiting Microsoft Research, 2012-2013

For the 2012–2013 school year, I am visiting Microsoft Research New England. I’m looking forward to lots of productive interactions with the permanent researchers, postdocs, and other visitors!

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)

A contract-theoretic model of conservation agreements

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)

NSF award on social networks

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 (Update: now available), 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.

Attainable payoffs in repeated games with interdependent private information

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

NY Times on the Dot-Com bubble, with lessons for today

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.