Imminent Nash Implementation∗

We introduce delay in simultaneous-move mechanisms. Delay is infinitesimal in equilibrium, hence the name: imminent implementation. We show that mechanisms with delay implement rules that are not implementable without delay in Nash equilibrium and its refinements. We obtain a version of the monotonicity condition that is necessary and sufficient for imminent implementability. If the domain includes all possible preferences, we find that the only unanimous functions that are implementable are dictatorial, as in Nash implementation. This result stands in sharp contrast to the result of a lottery-based “virtual implementation” that nearly all SCRs can be virtually implemented. Suppose that a virtual environment is restricted to the lotteries between an outcome that is fixed in advance and an arbitrary pure outcome. With this restriction, virtual and imminent environments are isomorphic. Furthermore, mechanisms with delay exist in practice. As an example, we consider legislative procedures, which allow the obstruction of bills. We conjecture that these procedures persist because they are particular instances of mechanisms that use delay. JEL classification: D78, C72, D60, D71, D72