Jun 12, 2016 Filed in: Projects in progress
With Trond Olsen and Joel Watson
Abstract: We examine the interplay among incomplete external enforcement, self enforcement, and renegotiation in ongoing contractual relationships. In each period, contracting parties negotiate over both their long-term externally enforced "formal" contract and their self-enforced “informal" contract that coordinates their continuation strategies. Players reach an agreement in accordance with the Nash bargaining solution, sharing the surplus in accordance with their bargaining power, relative to the disagreement outcome in which their previously-agreed contract remains in force. We show that contractual settings with externally enforced monetary transfers or with no verifiable information, an optimal contract is semi-stationary: the players always renegotiate to the same formal contract, which specifies particular terms for the current period and then distinct stationary terms for all future periods. Current-period terms are designed to support optimal behavior; future-period terms are designed to maximize the power of incentives, while anticipating that they will be renegotiated.
Working paper coming in Summer 2016
Slides available on request
Jun 08, 2016 Filed in: Projects in progress
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.
Working paper coming in Summer 2016
Apr 21, 2016 Filed in: Working papers
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
Feb 22, 2016 Filed in: Publications
With S. Nageeb Ali
Forthcoming August 2016 in The American Economic Review
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.
Working paper version 2/8/2016
Jan 20, 2016 Filed in: Working papers
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 July 2016)
Nov 01, 2014 Filed in: Publications
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)
Nov 01, 2013 Filed in: Publications
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.
Apr 01, 2012 Filed in: Publications
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)
Apr 01, 2008 Filed in: Publications
Published in the 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.
Published article (ScienceDirect subscribers only)
Working paper 8/24/2006 (older version but freely distributable)