Time and Nash implementation

In this paper, we study the full implementation problem using mechanisms that allow a delay. The delay on the equilibrium path may be zero, an infinitesimally small number or a fixed positive number. In all these three cases, implementable rules are fully characterized by a monotonicity condition. We provide examples to show that some delayed implementable social choice rules are not implementable in Nash-equilibrium refinements without a delay. As an application of our approach, we characterize delayed implementable rules in environments where only the discounting changes between states.