Relational contracting, negotiation, and external enforcement

With Joel Watson and Trond Olsen

Abstract: We study relational contracting and renegotiation in environments with external enforcement of long-term contractual arrangements. A 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, jointly optimize when selecting a contract, and exercise their relative bargaining power. Our main result is that in a wide variety of settings, the optimal contract is semi-stationary, with stationary terms for all future periods but special terms for the current period. In each period the parties renegotiate to this same contract. 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 renegoti- ate in each new period, intense monitoring arises only off the equilibrium path after a failed renegotiation.

Working Paper October 2019

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.

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 7/31/2016

Community enforcement with imperfect monitoring

With David Yilin Yang

Abstract: Contagion equilibria enable communities to enforce cooperation in simple strategies, if the monitoring that occurs privately within bilateral relationships is perfect and partners can adjust the stakes of their relationships. But if monitoring within relationships is imperfect, then punishments arise on the equilibrium path, and players' private information about the spread of contagion makes it difficult for them to coordinate their continuation play. We introduce a novel approach to constructing equilibria in private strategies that are not "belief-free" but are nonetheless tractable. In equilibrium, players who are aware of contagion always shirk, whereas players who are unaware of contagion shirk only if they become very pessimistic due to lack of data. Thus contagion may start in two ways along the equilibrium path: an incorrect monitoring signal may make an innocent player appear to have shirked, or a pessimistic player may spontaneously shirk. The equilibria we construct converge to ordinary contagion equilibria as monitoring imperfections vanish.

Project in progress

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

Ostracism and forgiveness

With S. Nageeb Ali

Published in The American Economic Review, 8(106): 2329–2348, August 2016

Abstract: Many communities rely upon ostracism to enforce cooperation: if an individual shirks in one relationship, her innocent neighbors share information about her guilt in order to shun her, while continuing to cooperate among themselves. However, a strategic victim may herself prefer to shirk, rather than report others' deviations truthfully. If guilty players are to be permanently ostracized, then such deviations are so tempting that cooperation in any relationship is bounded by what the partners could obtain through bilateral enforcement. Ostracism can improve upon bilateral enforcement if tempered by forgiveness, through which guilty players are eventually readmitted to cooperative society.

Published article (restricted access)

Published article and Supplementary material (free access)

Wasteful sanctions, underperformance, and endogenous supervision

With Kareen Rozen

Published in The American Economic Journal: Microeconomics, 6(4):326–361, November 2014

Abstract: We study optimal contracting in team settings where agents have many opportunities to shirk, task-level monitoring is needed to provide useful incentives, and it is difficult to write individual performance into formal contracts. Incentives are provided informally, using wasteful sanctions like guilt and shame, or slowed promotion. These features give rise to optimal contracts with underperformance, forgiving sanctioning schemes, and endogenous supervision structures. Agents optimally take on more assigned tasks than they intend to complete, leading to the concentration of supervisory responsibility in the hands of one or two agents.

Published article (restricted access)

Published article and Supplementary Appendix (free access)

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

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

Robust collusion with private information

Published in The Review of Economic Studies, 79(2):778–811, April 2012.

Abstract: The game-theoretic literature on collusion has been hard pressed to explain why a cartel should engage in price wars, without resorting to either impatience, symmetry restrictions, inability to communicate, or failure to optimize. This paper introduces a new explanation that relies on none of these assumptions: if the cartel's member firms have private information about their costs, price wars can be optimal in the face of complexity. Specifically, equilibria that are robust to payoff-irrelevant disruptions of the information environment generically cannot attain or approximate efficiency. An optimal robust equilibrium must allocate market shares inefficiently, and may call for price wars under certain conditions. For a two-firm cartel, cost interdependence is a sufficient condition for price wars to arise in an optimal robust equilibrium. That optimal equilibria are inefficient generically applies not only to collusion games, but also to the entire separable payoff environment (Chung & Ely 2006)—a class that includes most typical economic models.

Published article (free access)

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