Rochet’s Theorem characterizes implementable allocations in a mechanism design environment in terms of cyclic monotonicity, a concept from convex analysis. In this paper, I offer an alternative approach to both the proof and interpretation of this result, based on linear duality. This duality reveals a formal relationship between incentives and detection, much like that between prices and quantities. Moreover, it allows me to extend Rochet’s Theorem and present a subdifferential characterization of implementing payments, revenue equivalence as differentiability of a value function, as well as budget-balanced implementation in terms of attributing innocence after unilateral deviations, together with other ancillary results.

This paper provides the first systematic experimental analysis of delay, communication, and reaction lags in a repeated prisoners’ dilemma with frequent actions and imperfect monitoring. We independently manipulate delay of information and the ability of subjects to engage in limited communication and find that subjects earn significantly more without delay, a result that cannot be explained by standard repeated games models. We also find that communication always improves welfare and that average payoffs in one of our treatments (with communication and no delay) are significantly greater than the upper bound on public Nash equilibrium payoffs. We explore the possibility that this is driven by bounded rationality in the form of reaction lags and find that slowing down the experiment has no significant effect on behavior. ∗We thank Drew Fudenberg, Thomas Holmes, Antonio Penta, John Quah, Itai Sher, Jan Werner and seminar participants at the University of Minnesota Applied Microeconomics and Mathematical Economics Workshops for helpful discussions. Please send any comments to pevdokim@gmail.com. Financial support from the National Science Foundation Grant No. SES 09-22253 and from the Heller-Hurwicz Economics Institute is gratefully acknowledged.

I study repeated games with mediated communication and frequent actions. I derive Folk Theorems with imperfect public and private monitoring under minimal detectability assumptions. Even in the limit, when noise is driven by Brownian motion and actions are arbitrarily frequent, as long as players are suciently patient they can attain virtually ecient equilibrium outcomes, in two ways: secret monitoring and infrequent coordination. Players follow private strategies over discrete blocks of time. A mediator constructs latent Brownian motions to score players on the basis of others’ secret monitoring, and gives incentives with these variables at the end of each block to economize on the cost of providing incentives. This brings together the work on repeated games in discrete and continuous time in that, despite actions being continuous, strategic coordination is endogenously discrete. As an application, I show how individual full rank is necessary and sucient for the Folk Theorem in the Prisoners’ Dilemma regardless of whether monitoring is public or private.

In this paper, I offer two ways in which firms can collude: secret monitoring and infrequent coordination. Such collusion is enforceable with intuitive communication protocols. I make my case in the context of a repeated Cournot oligopoly with flexible production, prices that follow a Brownian motion and no monetary side payments, an environment where it has previously been argued that any collusion is impossible. Trade associations can easily facilitate collusion by mediating communication amongst firms.

I study repeated games with frequent actions and obtain a Folk Theorem in strongly symmetric strategies for the Prisoners’ Dilemma if public information can be delayed. I allow for both Brownian motions and Poisson processes.

I study repeated games with mediated communication and frequent actions. I derive a Folk Theorem under imperfect monitoring assuming a conditional form of individual identiability. Even in the limit, when noise is driven by Brownian motion and actions are arbitrarily frequent, as long as players are suciently

In this paper I prove a Folk theorem with T -private communication equilibria with an imperfect monitoring structure that may be public, private, and conditionally dependent or independent. I show that an efficient outcome is approachable as players become patient if every disobedience from efficiency is detectable by some player and some not necessarily efficient action profile. I also show that efficiency is approachable if and only if every profitable deviation from efficiency is uniformly and credibly detectable. JEL Classification: D21, D23, D82.

This paper studies partnerships that employ a mediator to improve their contractual ability. Intuitively, profitable deviations must be attributable, that is, there must be some group behavior such that an individual can be statistically identified as innocent, to provide incentives in partnerships. Mediated partnerships add value by effectively using different behavior to attribute different deviations. As a result, mediated partnerships are necessary to provide the right incentives in a wide range of economic environments.

This paper studies partnerships that employ a mediator to improve their

In this paper I study the possibility of full surplus extraction on arbitrary type spaces using direct mechanisms, with three main results: (i) I characterize full surplus extraction, (ii) I characterize full surplus extraction assuming incentive compatibility, and (iii) I show that virtually full surplus extraction implies full surplus extraction. The characterizing condition in (ii) above is equivalent to McAfee and Reny’s (1992a) condition in their restricted environment. Since they only characterized virtually full surplus extraction, it follows that their proposed mechanisms incur a loss relative to the direct mechanisms studied here, with which full surplus extraction is possible.

In this paper I study the possibility of full surplus extraction on arbitrary type spaces, with three main results: (i) I characterize full surplus extraction, (ii) I characterize full surplus extraction assuming that the surplus-extracting allocation is implementable, and (iii) I show that virtually full surplus extraction implies full surplus extraction. The characterizing condition in (ii) above is equivalent to McAfee and Reny’s (1992a) condition in their restricted environment. Since they only characterized virtually full surplus extraction, it follows that their proposed mechanisms incur a loss relative to the direct mechanisms studied here, with which full surplus extraction is possible. JEL Classification: C62, D71, D82.

Consider a strategic environment subject to moral hazard and adverse selection across multiple stages, with rich communication protocols. In this paper, we prove that for any allocation, there exist linear transfers to make it incentive compatible if and only if every undetectable deviation from honesty and obedience is unprofitable when the transfers equal zero, where ‘undetectable’ means that the distributions of actual and reported types coincide. The set of transfers that implement a given implementable allocation is also characterized. These results extend Rochet’s (1987) characterization of implementability to a dynamic context. The paper also characterizes optimal allocations, profitmaximizing mechanisms, virtual implementation, implementation subject to dynamic budget balance, and dynamic revenue equivalence. JEL Classification: D82, D83, D86.

Consider a group of individuals whose behavior is subject to moral hazard, and suppose that providing them with incentives requires a monitor to detect deviations. What about the monitor's deviations? I study mediated contracts and find that the monitor's deviations are effectively irrelevant. Hence, nobody needs to monitor the monitor. I also characterize exactly when such contracts can provide the right incentives for everyone. In doing so, several new characterizations of virtual implementation are derived.

We analyze collective action by citizens to protest an autocrat with private information about foreign threats. High expected threats prevent protest and allow the ruler to exploit citizen fears for rent expropriation. When expected threats are low, citizen protest undermines national security. To establish greater credibility and thus improve defense capacity, the ruler can undertake political reform that empowers citizens and reduces expropriation. Reform harms the ruler when threats are high, while for low threats the benefit of reform increases with the likelihood of attack. Overall, we show that the ruler's incentive to undertake reform is non-monotonic. We also analyze foreign policy, which can help explain why citizens may not protest. The ruler provokes international tensions when minimal protest scale is the hurdle, but not when citizens are trapped in coordination failure. Finally, we analyze international sanctions, which may have a commitment value similar to political reform.

This paper establishes and interprets a necessary and sucient condition for existence of (countably additive) correlated equilibrium in n-person games, assuming only that utility functions are bounded, measurable. A sequence of deviation profiles is consistent if there exists a correlated strategy that makes every profile in the sequence unprofitable with respect to the sum of utilities. An equilibrium exists if and only if every sequence of deviation profiles has a consistent subsequence. This condition fails to characterize Nash equilibrium. As a direct corollary, existence of (communication) equilibrium is characterized in games with incomplete information on type spaces large enough to include the universal one. Exact conditions for existence of approximate correlated equilibrium are also obtained, as well as a value for two-person zero-sum games.

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. JEL Classification: D21, D23, D82.

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

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. JEL Classification: D21, D23, D82.