This paper establishes a general form of the "payoff equivalence" result in mechanism design theory: under certain conditions, the utility of any type in an incentive-compatible mechanism is determined up to an additive constant by the allocation rule alone. When types are single-dimensional the result is well known (see, for instance, Myerson (1981)). When types are multi-dimensional the result follows from the Fundamental Theorem of Calculus once sufficient smoothness is assumed. We obtain a more general result by using an extension of the Fundamental Theorem to nonsmooth convex functions and more generally, to the class of regular Lipschitzian functions.

We study subgame perfect equilibria of finitely repeated games. We prove a limit "folk theorem" for these games. Under weak conditions, any feasible and individually rational payoff vector of the one-shot game can be approximated by the average payoff in a perfect equilibrium of a repeated game with a sufficiently long horizon.

We consider a decision maker who faces dynamic decision situations that involve intertemporal trade-offs, as in consumption–savings problems, and who experiences taste shocks that are transient contingent on the state of the world. We axiomatize a recursive representation of choice over state contingent infinite horizon consumption problems, where uncertainty about consumption utilities depends on the observable state and the state follows a subjective Markov process. The parameters of the representation are the subjective process that governs the evolution of beliefs over consumption utilities and the discount factor; they are uniquely identified from behavior. We characterize a natural notion of greater preference for flexibility in terms of a dilation of beliefs. An important special case of our representation is a recursive version of the Anscombe–Aumann model with parameters that include a subjective Markov process over states and state-dependent utilities, all of which are uniquely identified.

Perfect equilibria of finitely repeated games may be vulnerable to the possibility of renegotiation among players. We study the limiting properties of the set of payoffs from equilibria that are immune to renegotiation. Our main result is that the limit of the set of payoffs from renegotiation proof equilibria is either a singleton or a connected subset of the Pareto efficient frontier. A simple sufficient condition for the latter to occur is also provided.

We study the implications of optimal insurance provision for long‐run welfare and inequality in economies with persistent private information. A principal insures an agent whose private type follows an ergodic, finite‐state Markov chain. The optimal contract always induces immiseration : the agent's consumption and utility decrease without bound. Under positive serial correlation, it also backloads high‐powered incentives : the sensitivity of the agent's utility with respect to his reports increases without bound. These results extend—and help elucidate the limits of—the hallmark immiseration results for economies with i.i.d. private information. Numerically, we find that persistence yields faster immiseration, higher inequality, and novel short‐run distortions. Our analysis uses recursive methods for contracting with persistent types and allows for binding global incentive constraints.