last updated on April, 2010

Working Papers

Toward a Belief-Based Approach to Repeated Games with Private Monitoring (joint with M. Kandori)
abstract, A draft will be available soon.

Informational Smallness and Private Monitoring (joint with R. McLean and A. Postlewaite)
abstract, A new version is coming soon.

Approximate Implementability with Ex Post Budget Balance (joint with D. Rahman)
abstract, pdf [April, 2006]
(This is now incorporated into "Mediated Partnerships")

Endogenous Monitoring (joint with M. Kandori)
abstract, pdf [December, 2004]

Private Strategy and Efficiency: Repeated Partnership Games Revisited pdf [May, 2000]
This paper is now merged with a part of "Check Your Partner's Behavior by Randomization: New Efficiency Results on Repeated Games with Imperfect Monitoring " by Michihiro Kandori and contained in the paper "Efficiency in Repeated Games Revisited: the Role of Private strategy"

Repeated Prisoner's Dilemma with Private Monitoring: a N-player case pdf [May, 2000]
Most of this paper is now contained in the paper above, "Belief-Based Equilibria in the Prisoners' Dilemma with Private Monitoring". However, this old version contains some examples which are not in the revised version.

Published and Forthcoming Papers

Mediated Partnerships (joint with D. Rahman)
Econometrica 78 (2010), 285-308.
abstract, pdf [June, 2008]

Firm Reputation and Horizontanl Integration (joint with H. Cai)
RAND Journal of Economics 40 (2009), 340-363.
abstract, pdf [March, 2008]

Folk Theorem with Communication
Journal of Economic Theory 144 (2009), 122-134.
abstract, pdf [February, 2008]

The Full Surplus Extraction Theorem with Hidden Actions
The B.E. Journal of Theoretical Economics : Vol. 8 : Iss. 1 (Advances), (2008).
abstract, pdf [January, 2008]

Less is more: An Observability Paradox in Repeated Games (joint with M. Kandori)
International Journal of Game Theory, 34 (2006), 475-493.
abstract, pdf [August, 2006]

Efficiency in Repeated Games Revisited: the Role of Private Strategies (joint with M. Kandori)
Econometrica, 74 (2006), 499-519.
abstract, UCLA Woking Paper [January, 2003], pdf [January, 2004]

The Maximum Efficient Equilibrium Payoff in the Repeated Prisoners' Dilemma (joint with G. Mailath and T. Sekiguchi)
Games and Economic Behavior 40 (2002), 99-122.
abstract, pdf [June, 2001]

Belief-Based Equilibria in the Repeated Prisoners' Dilemma with Private Monitoring (joint with V. Bhaskar)
Journal of Economic Theory 102 (2002), 40-69.
abstract, pdf [May, 2001]

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Abstracts of the Papers

Secret Contracts for Efficient Partnerships
(joint with D. Rahman)

Abstract

By allocating different information to team members, secret contracts can provide better incentives to perform with an intuitive organizational design. For instance, they may help to monitor monitors, and attain approximately efficient partnerships by appointing a secret principal. More generally, secret contracts highlight a rich duality between enforceability and identifiability. It naturally yields necessary and sufficient conditions on a monitoring technology for any team using linear transfers to approximate efficiency (with and without budget balance). The duality is far-reaching: it is robust to complications in the basic model such as environments with infinitely many actions and signals. Thus, we obtain a subdifferential characterization of equilibrium payoffs as well as a tight folk theorem in discounted repeated games with imperfect private monitoring and mediated communication.

Approximate Implementability with Ex Post Budget Balance
(joint with D. Rahman)

Abstract

This paper characterizes public and private monitoring technologies with respect to which the efficient outcome is approximately implementable in team production by way of ex post budget-balanced linear transfers.

Folk Theorem with Communication

Abstract

This paper proves a new folk theorem for repeated games with private monitoring and communication, extending the idea of delaying communication in Compte (1998) to the case where private signals are correlated. The proposed sufficient condition is generic when the number of the players is more than two and the number of actions and signals are similar for every player. This folk theorem also applies to some two-players repeated games.

Less is more: An Observability Paradox in Repeated Games
(joint with M. Kandori)

Abstract

We present a repeated prisoners' dilemma game with imperfect public monitoring, which exhibits the following paradoxical feature: the (limit) equilibrium payoff set achieves full efficiency asymptotically as the public signal becomes insensitive to the hidden actions of the players. The basic logic behind this result also provides an example where the Folk theorem is obtained, while Fudenberg-Levine-Maskin's sufficient conditions (Econometrica 1994) for Folk theorem are violated.

Firm Reputation and Horizontanl Integration
(joint with H. Cai)

Abstract

We study effects of horizontal integration on firm reputation. In an environment where customers observe only imperfect signals about firms' effort/quality choices, firms cannot maintain high reputation and earn quality premium forever. Even when firms choose high quality, there is always a possibility that a bad signal is observed, in which case firms must give up their quality premium (at least temporarily) as punishment. A firm's integration decision is based on the extent to which integration attenuates this necessary cost of maintaining a good reputation. Since the merged firm has a larger market base, horizontal integration leads to more effective punishment and better monitoring (by reducing idiosyncratic market shocks), which helps reputation-building. On the other hand, it allows the merged firm to deviate in a more sophisticated way: the merged firm may deviate only in a subset of markets and pretend that a bad outcome is observed by accident, which hinders reputation-building. When there is systematic firm-level noise in the signal, this negative effect becomes more severe as the firm size grows larger. These effects give rise to a reputation-based theory of the optimal firm size. We characterize the optimal degree of integration and show that the optimal size of a firm is smaller when (1) trades are more frequent and information is disseminated more rapidly; or (2) the deviation gain is smaller compared to the quality premium; or (3) customer information about firm choices is more precise.

The Full Surplus Extraction Theorem with Hidden Actions

Abstract

Consider a situation in which a principal commits to a mechanism first and then agents choose unobservable actions before their types are realized. The agents' actions may affect not only their payoffs directly but also the distribution of their types as well. This paper extends Crémer and McLean's full surplus extraction theorem to such a setting. In this environment, the principal may not extract may not be able to extract all the surplus from the agents generically when there are many actions to which the agents can deviate. However, the principal can extract full surplus given any completely mixed approximately efficient action profile for a generic information structure. This result is based on a general mechanism in which the agents announce both their types and their realized actions. Therefore there is a big gap between exact full surplus extraction and approximate full surplus extraction.

Efficiency in Repeated Games Revisited: the Role of Private Strategies
(joint with M. Kandori)

Abstract

Most theoretical or applied research on repeated games with imperfect monitoring has focused mostly on public strategies: strategies that depend solely on the history of publicly observable signals. This paper sheds light on the role of private strategies: strategies that depend not only on public signals but also on players' own actions in the past. Our main finding is that players can sometimes make better use of information by using private strategies and that efficiency in repeated games can be improved. Our equilibrium private strategy for repeated prisoners' dilemma games consists of two states and has the property that each player's optimal strategy is independent of the other player's state.

Informational Smallness and Private Monitoring
(joint with R. McLean and A. Postlewaite)

Abstract

We examine robustness of perfect public equilibrium/subgame perfect equilibrium with public monitoring when monitoring is private, but "close" to the public monitoring. Private monitoring is "close" to public monitoring if the private signals can generate approximately the same public signal once they are aggregated through communication. Two key notions on private monitoring are introduced: Informational Smallness and Distributional Variability. A player is informationally small if she believes that her signal is likely to have a small impact on the public signal when the private signals are aggregated. Distributional variability measures the variation in a player's conditional beliefs over the generated public signal as her private signal varies. When each player's informational size is small relative to her distributional variability (and private monitoring is sufficiently close to public monitoring), a uniformly strict equilibrium with public monitoring remains an equilibrium with private monitoring and communication. To demonstrate that uniform strictness is not overly restrictive, we prove a uniform folk theorem with public monitoring. Then we derive a new folk theorem for repeated games with private monitoring and communication by showing that all such equilibria are robust.

The Maximum Efficient Equilibrium Payoff in the Repeated Prisoners' Dilemma
(joint with G. Mailath and T. Sekiguchi)

Abstract

We describe the maximum efficient subgame perfect equilibrium payoff for a player in the repeated Prisoner's Dilemma, as a function of the discounting factor. For discount factors above a critical level, every efficient, feasible, and individually rational payoff profile can be sustained. For an open and dense set of discount factors below a critical value, the maximum efficient payoff is not an equilibrium payoff. When a player cannot achieve this payoff, the unique equilibrium outcome achieving the best efficient payoff is eventually cyclic. There are an uncountable number of discount factors below the critical level such that the maximum efficient payoff is an equilibrium payoff.

Belief-Based Equilibria in the Repeated Prisoners' Dilemma with Private Monitoring
(joint with V. Bhaskar)

Abstract

We analyze infinitely repeated prisoners' dilemma games with imperfect private monitoring, and construct sequential equilibria where strategies are measurable with respect to players' beliefs regarding their opponents' continuation strategies. We show that, when monitoring is almost perfect, the symmetric efficient outcome can be approximated in any prisoners' dilemma game, while every individually rational feasible payoff can be approximated in a class of prisoner dilemma games. We also extend the approximate efficiency result to n-player prisoners' dilemma games and to prisoner's dilemma games with more general information structure. Our results require that monitoring be sufficiently accurate but do not require very low discounting.