Relational contracting, negotiation, and external enforcement

With Trond Olsen and Joel Watson

Abstract: We study relational contracting and renegotiation in environments with external enforcement of long-term contractual arrangements. An external, long-term contract governs the stage games the contracting parties will play in the future (depending on verifiable stage-game outcomes) until they renegotiate. In a contractual equilibrium, the parties choose their individual actions rationally, they jointly optimize when selecting a contract, and they take advantage of their relative bargaining power. Our main result is that in a wide variety of settings, in each period of a contractual equilibrium the parties agree to a semi-stationary external contract, with stationary terms for all future periods but special terms for the current period. In each period the parties renegotiate to this same external contract, effectively adjusting the terms only for the current period. For example, in a simple principal-agent model with a choice of costly monitoring technology, the optimal contract specifies mild monitoring for the current period but intense monitoring for future periods. Because the parties renegotiate in each new period, intense monitoring arises only off the equilibrium path after a failed renegotiation.

Working Paper March 2018

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 7/31/2016

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 6/6/2016

The optimal structure of conservation agreements and monitoring

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

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 11/20/2013

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.

Working paper 1/13/2009