An active-contracting perspective on equilibrium selection in relational contracts

With Joel Watson

Journal of Institutional and Theoretical Economics, 179(3–4):530–561, December 2023
Symposium on the Economics of Relational Contracts: Past and Future Developments

Abstract: Miller and Watson (2013) introduced contractual equilibrium for repeated games with recurrent bargaining, axiomatizing how parties in a relational contract interpret the outcome of their negotiation. We show that modeling elements the previous literature used to study negotiation – elements that would seem to capture bargaining power and impose structure on equilibrium – actually do not affect the set of equilibrium payoffs, so that predictions depend on arbitrary equilibrium selection by the analyst. In contrast, contractual equilibrium puts equilibrium selection in the parties’ hands, leading to sharp predictions. In a principal–agent setting, increasing the agent’s bargaining power causes the equilibrium effort to rise, and play under disagreement depends on the history of effort choices.

Open Access (CC BY 4.0): Published article

Seeking Relationship Support: Strategic network formation and robust cooperation

With Xu Tan

Abstract: We study cooperation on social networks with private monitoring and communication. For arbitrary networks, we construct a class of equilibria that attain high cooperation on all supported links, in a way that is robust to social contagion, bilaterally renegotiation proof, and in which players need only local information about the network. In these equilibria, guilty players exert high effort for their innocent partners, and are willing to do so because they are compensated for their effort costs. Anticipating cooperation, players in a network formation game with random opportunities to form links will strategically form a network with realistic “small worlds” properties, including high “support” but relatively low clustering.

Working paper, draft available on request

Renegotiation-proof multilateral enforcement

With S. Nageeb Ali and David Yilin Yang

Abstract: In multilateral enforcement, a player who cheats on one partner is punished by many partners. But renegotiation might subvert the threat of multilateral punishment. We consider renegotiation proofness in multilateral enforcement games with public monitoring, and also introduce the notion of “bilateral renegotiation proofness” for games with private monitoring. With public monitoring, renegotiation proofness does not impede multilateral enforcement at all; even with private monitoring, bilateral renegotiation imposes no cost when a principal interacts with many agents who can communicate with each other. For community enforcement games with private monitoring, players’ ability to renegotiate bilaterally has some cost, but this cost is relatively small in large communities.

Working paper July 2016

When to behave badly and when to behave well under disagreement

With Alexandra Charbi

Abstract: In a repeated principal-agent problem in which the agent has private information about her i.i.d. cost of effort (à la Levin 2003), we analyze relational contracts that the parties can renegotiate in a way that respects their relative bargaining power. We show that if a disagreement arises in a state in which she was to be rewarded, then it is optimal for the agent to destroy surplus, exerting costly effort to hurt the principal. In such an event, her counter-productive effort is optimally constant regardless of her effort cost, the principal does not fire her, and both parties anticipate agreeing to reward the agent in the next period. In contrast, on the equilibrium path as well as under disagreement in a state in which the agent was to be punished, the agent exerts productive effort that is decreasing in her effort cost.

Working paper June 2016

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. 

Working paper November 2013

Attainable payoffs in repeated games with interdependent private information

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.

Dormant working paper January 2009