Dynamic Incentives in Incompletely Specified Environments

Abstract

Consider a repeated interaction where it is unknown which of various stage games will be played each period. This framework separates the basic logic of intertemporal incentives from the requirement that any given strategy profile yields a well‐defined payoff vector. A natural solution concept is ex post perfect equilibrium: strategies must form a subgame‐perfect equilibrium for any realization of the sequence of stage games. When there is one long‐run player and others are short‐run, and public randomization is available, we can adapt the standard recursive approach to determine the maximum feasible gap between reward and punishment for the long‐run player. This allows us to identify which actions can be played in equilibrium and, assuming perfect monitoring, to fully characterize what outcome paths can arise. With multiple long‐run players or no public randomization, the approach fails; a diagnostic of this failure is that optimal penal codes may no longer exist.