Coalitions and recurrent negotiation in multilateral relational contracts

With Joel Watson

Abstract: We introduce a theory of coalitional governance of multilateral relational contracts. The coalition is a subset of the parties, called insiders. In an infinitely repeated game with voluntary transfers, the parties coordinate on an equilibrium that the coalition negotiates and renegotiates over time. The coalition's power derives exclusively from its ability to coordinate the behavior of both the insiders and outsiders, using promised rewards and punishments. We show that equilibrium contractual arrangements differ substantially between insiders and outsiders, due to the latter parties being unable to claim a share of surplus during the coalition's negotiations. Essentially, insiders create a long-term contract, with rewards and punishments extending beyond instances of renegotiation, whereas the relationship between insiders and outsiders can be characterized by a shorter-term contract in which rewards and punishments do not extend beyond instances of renegotiation. If renegotiation occurs each period, then the latter arrangements take the form of direct payments from insiders to outsiders.

To incorporate bargaining power in the theory and to explore applications, we develop the concept of coalition-directed contractual equilibrium. In the coalition directed equilibrium of a repeated public-goods game, the coalition maximizes surplus by outsourcing marginal contributions to outsiders—that is, if an insider is otherwise identical to an outsider, then in equilibrium the outsider makes greater contributions, while the insider obtains a higher payoff. We interpret our results in the context of two applications: global climate change negotiations, and partnership firms.

Working paper coming soon

Seeking Relationship Support: Strategic network formation and robust cooperation

With Xu Tan and Harry Kleyer

Abstract: We study cooperation on evolving social networks with private monitoring and communication. A multilateral restitution equilibrium attains high cooperation on links that are supported (contained in triangles), while preserving cooperation between innocent players off the equilibrium path, and remaining invariant to players’ beliefs about the network outside their local neighborhoods. When new players arrive, they strategically form links to players they meet, and seek mutual friends to support cooperation in their relationships. Using data from Banerjee, Chandrasekhar, Duflo and Jackson (2013), we estimate a structural model incorporating survey under-response, and find that both support-seeking and survey under-response are statistically relevant.

Working paper May 2026

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

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