Time and Nash Implementation

Abstract

In this paper, we study full implementation problem by mechanisms that allow delay. The delay on the equilibrium path may be zero, infinitesimally small or a fixed positive number. In all these three cases, implementable rules are characterized by a monotonicity-like condition alone, including the case of two agents. We specialize this condition to an environment where only the patience of the agents changes. In this environment, zero-delayed implementable rules are characterized by a simple yet restrictive condition; however, it is possible to find a delay such that almost any rule is implementable. To compare our notion of implementation to the existing ones, we provide examples of rules that are not implementable in Nash equilibrium refinements, but are implementable with infinitesimally small delay (imminently). We also establish a link between imminent and virtual implementation.

Keywords: Implementation, delay, time, lotteries, social choice rules, Nash equilibrium

JEL Classification: D78, C72, D60, D71, D72