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

Communication and cooperation in markets

With S. Nageeb Ali

American Economic Journal: Microeconomics, 14(4):200–217, November 2022

Abstract: Many markets rely on traders truthfully communicating who has cheated in the past and ostracizing those traders from future trade. This paper investigates when truthful communication is incentive compatible. We find that if each side has a myopic incentive to deviate, then communication incentives are satisfied only when the volume of trade is low. By contrast, if only one side has a myopic incentive to deviate, then communication incentives do not constrain the volume of supportable trade. Accordingly, there are strong gains from structuring trade so that one side either moves first or has its cooperation guaranteed by external enforcement.

Free access: Published article

Conservation agreements: Relational contracts with endogenous monitoring

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

Journal of Law, Economics, and Organization, 37(1):1–40, March 2021

Abstract: This paper examines the structure and performance of conservation agreements, which are relational contracts 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. A repeated-game model is developed and utilized to organize an evaluation of real conservation agreements, using three case studies as representative examples.

Free access: Published article

Relational contracting, negotiation, and external enforcement

With Joel Watson and Trond E. Olsen

American Economic Review 110(7): 2153–2197, July 2020

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 renegotiate in each new period, intense monitoring arises only off the equilibrium path after a failed renegotiation.

Free access: Published article and Supplementary material

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

Ostracism and forgiveness

With S. Nageeb Ali

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.

Free access: Published article and Supplementary material

Wasteful sanctions, underperformance, and endogenous supervision

With Kareen Rozen

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.

Free access: Published article and Supplementary Appendix

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

A theory of disagreement in repeated games with bargaining

With Joel Watson

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.

Free access: Published article and Supplemental material

Robust collusion with private information

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.

Free access: Author’s manuscript May 2011

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

Invention under uncertainty and the threat of ex post entry

European Economic Review, 52(3):387–412, April 2008

Abstract: This paper proposes a theoretical framework for studying the invention of new products when demand is uncertain. In this framework, under general conditions, the threat of ex post entry by a competitor can deter invention ex ante. Asymmetric market power in the ex post market exacerbates the problem. The implications of these general results are examined in a series of examples that represent important markets in the computer industry. The first is a model that shows how an operating system monopolist, by its mere presence, can deter the invention of complements, to its own detriment as well as that of society. The implications of policies such as patent protection, price regulation, and mandatory divestiture are considered. Three additional examples consider the ability of a monopolist in one market to commit to bundling an unrelated product, a pair of horizontally differentiated firms that can add a new feature to their products, and a platform leader that can be challenged in its base market by the supplier of a complementary product.

Free Access: Author’s Manuscript April 2007

Was there too little entry during the Dot Com Era?

With Brent Goldfarb and David Kirsch

Journal of Financial Economics, 86(1):100-144, October 2007

Abstract: We present four stylized facts about the Dot Com Era: (1) there was a widespread belief in a "Get Big Fast" business strategy; (2) the increase and decrease in public and private equity investment was most prominent in the internet and information technology sectors; (3) the survival rate of dot com firms is on par or higher than other emerging industries; and (4) firm survival is independent of private equity funding. To connect these findings we offer a herding model that accommodates a divergence between the information and incentives of venture capitalists and their investors. A Get Big Fast belief cascade may have led to overly focused investment in too few internet startups and, as a result, too little entry.

Free Access: Authors’ manuscript April 2006

Press coverage:

• The New York Times (Leslie Berlin): "Lessons of survival from the Dot-Com attic," p. BU4, 11/23/2008

• The Wall Street Journal (Lee Gomes): "The Dot-Com Bubble is reconsidered—and maybe relived," p. B1, 11/8/2006

• Inc.com (Leslie Taylor): "The dot-com bust? Not as bad as you think," 12/4/2006

Efficiency in repeated trade with hidden valuations

With Susan Athey

Theoretical Economics, 2(3):299-354, September 2007

Abstract: We analyze the extent to which efficient trade is possible in an ongoing relationship between impatient agents with hidden valuations (i.i.d. over time), restricting attention to equilibria that satisfy ex post incentive constraints in each period. With ex ante budget balance, efficient trade can be supported in each period if the discount factor is at least one half. In contrast, when the budget must balance ex post, efficiency is not attainable, and furthermore for a wide range of probability distributions over their valuations, the traders can do no better than employing a posted price mechanism in each period. Between these extremes, we consider a "bank" that allows the traders to accumulate budget imbalances over time, but only within a bounded range. We construct non-stationary equilibria that allow traders to receive payoffs that approach efficiency as their discount factor approaches one, while the bank earns exactly zero expected profits. For some probability distributions there exist equilibria that yield exactly efficient payoffs for the players and zero profits for the bank, but such equilibria require high discount factors.

“Token” equilibria in sensor networks with multiple sponsors

With Sameer Tilak and Tony Fountain

Proceedings of the Workshop on Stochasticity in Distributed Systems (StoDiS'05), San Jose, CA, December 19, 2005

Abstract: When two sponsoring organizations, working towards separate goals, employ wireless sensor networks for a finite period of time, it can be efficiency-enhancing for the sponsors to program their sensors to cooperate. But if each sensor privately knows whether it can provide a favor in any particular period, and the sponsors cannot contract on ex post payments, then no favors are performed in any Nash equilibrium. Allowing the sponsors to contract on ex post payments, we construct equilibria based on the exchange of "tokens" that yield significant cooperation and increase expected sponsor payoffs. Increasing the sponsors' liability is beneficial because it enables them to use more tokens.

Newer version: Working paper May 2006