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

Note: 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 Please do not cite, circulate, or refer to any version of the paper dated prior to 2009.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

Efficiency in repeated trade with hidden valuations

With 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 article (free access)

“Token” equilibria in sensor networks with multiple sponsors

With 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)