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


With S. Nageeb Ali

Abstract: Many communities rely upon ostracism to improve cooperation in bilateral relationships: if an individual deviates in one relationship, other innocent players come to learn about this deviation, and proceed to shun the guilty player while continuing to cooperate with each other. Typically, it is assumed that information spreads through word-of-mouth communication and that victims and third-parties have no incentive to lie about their experience with guilty players. We show, perhaps surprisingly, that innocent players may not have the incentive to communicate truthfully. Communication incentives are particularly severe in equilibria in which guilty players are permanently ostracized: such equilibria cannot support cooperation significantly beyond what each pair of players could obtain without community enforcement altogether. The challenge is that a victim of cheating prefers to cheat herself rather than to report her victimization to others. However, ostracism equilibria that feature forgiveness can foster truthful communication and thereby improve upon permanent ostracism. Our results suggest a new perspective on forgiveness and redemption in social norms.

Working paper 6/14/2013

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