Relational contracts with hidden information and renegotiation

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. On the equilibrium path, the agent’s productive effort is decreasing in her effort cost; in many cases with pooling for low-cost types and separating for high-cost types. 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. The welfare of the parties is increasing in the agent’s bargaining power; the principal, if he could choose, would elect to give the agent some bargaining power, but less than would be jointly optimal.

Working paper coming in June 2016

Is multilateral enforcement vulnerable to bilateral renegotiation?

With S. Nageeb Ali and David Yilin 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

(New version coming in June 2016)

A contract-theoretic model of conservation agreements

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

Abstract: We examine the structure and performance of conservation agreements, which are used across the world to protect natural resources. Key elements of these agreements are: (1) they are ongoing arrangements between a local community and an outside party, typically a non-governmental organization (NGO); (2) they feature payments in exchange for conservation services; (3) the prospects for success depend on the NGO engaging in costly monitoring to detect whether the community is foregoing short-term gains to protect the resource; (4) lacking a strong external enforcement system, they rely on self-enforcement; and (5) the parties have the opportunity to renegotiate at any time. We provide a novel model that contains these ingredients and we apply the model to assess the workings of real conservation agreements, using three case studies as representative examples. 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. The model captures important features of real conservation agreements and identifies some of the features required for successful agreements.

Working paper 4/21/2016

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