Sep 11, 2011 Filed in:
Working papersWith Heidi Gjertsen, Theodore Groves, Eduard Niesten, Dale Squires, and Joel Watson
Abstract: We model conservation agreements using contractual equilibrium, a concept introduced by Miller and Watson (2010) to model dynamic relationships with renegotiation. The setting takes the form of a repeated principal-agent problem, where the principal must pay to observe a noisy signal of the agent's effort. Lacking a strong external enforcement system, the parties rely on self-enforcement for their relational contract. 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. We argue that the model captures important features of real conservation agreements and reveals the ingredients required for successful agreements.
Working paper 9/23/2010 (stay tuned for an updated version in fall 2011)
PermalinkTags: Repeated games, Community enforcement, Conservation Agreements, Monitoring, Bargaining, Negotiation, Renegotiation, Principal-Agent, Cooperation, Forest Protection, Cambodia, Coral Reefs, Fiji, Sea Turtles, Solomon Islands, Grey Whales, Baja California
Feb 01, 2010 Filed in:
Work in progressWith Nageeb Ali
Abstract: We endogenize social network formation and collective enforcement using a model in which players interact bilaterally and repeatedly along costly links. Players observe only their own partners' actions, so collective punishments that support cooperation must spread endogenously through the network, as a contagion. Our model features asynchronous interaction, variable stakes in each relationship, and transferable utilities. With these properties, for any network there exists a contagion equilibrium in which incentive constraints bind along the equilibrium path. Among symmetric networks, the optimal network topology in a large society features many identical, independent cliques. We conjecture that such a network is also Pareto optimal among all (symmetric and asymmetric) networks. Our results formalize the notion that when collective enforcement is decentralized, the level of social cooperation, or "social capital," is maximized in tight-knit, highly clustered groups.
Working paper coming soon
PermalinkTags: Repeated games, Social Networks, Community enforcement, Network Formation, Cooperation, Contagion, Small Worlds, Cliques
Oct 13, 2011 Filed in:
Working papersWith Joel Watson
Abstract: This paper proposes a new approach to the problem of equilibrium selection in repeated games with transfers, by supposing that in each period the players bargain over how to play. Although the bargaining phase is cheap talk (which follows 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 satisfying these axioms exist for all discount factors and are simple to construct, and all equilibria attain the same joint value. Optimal play under agreement generally requires suboptimal play under disagreement. Whether patient players attain efficiency depends on both the stage game and the bargaining power that they derive from the details of 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.
Working paper 10/13/2011
PermalinkTags: Repeated games, Bargaining, Negotiation, Renegotiation, Relational contracts, Principal-Agent, Cooperation
May 20, 2011 Filed in:
PublicationsPublished in The Review of Economic Studies, 2011.
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.
Note: This is a major update of the paper formerly titled "Optimal ex post incentive compatible equilibria in repeated games of private information” and “The dynamic cost of ex post incentive compatibility in repeated games of private information."
Free-access link to published version
PermalinkTags: Collusion, Price wars, Repeated games, Private information, Mechanism design, Ex post incentive compatibility, Folk theorem
Jan 13, 2009 Filed in:
Working papersNote: Satoru Takahashi discovered an error in a previous version of this paper. I am working on figuring out how to correct it. For now, I am posting a shorter version that contains only the correct results. Please do not cite, circulate, or refer to any version of the paper dated prior to 2009.
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
PermalinkTags: Repeated games, Private information, Mechanism design, Folk theorem
Sep 01, 2007 Filed in:
PublicationsWith Susan Athey
Published in 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.
Published paper
PermalinkTags: Private information, Mechanism design, Budget balance, Repeated games, Ex post incentive compatibility, Trade
May 06, 2006 Filed in:
PublicationsWith Sameer Tilak and Tony Fountain
Published in the 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.
Working paper 5/22/2006 (newer and better than the StoDiS version)
PermalinkTags: Computer science, Private information, Repeated games, Cooperation, Sensor networks
