Ex Post Implementation

We analyze the problem of fully implementing a social choice set in ex post equilibrium. Weidentify an ex post monotonicity condition that is necessary and -- in economic environments -- sufficient for full implementation in ex post equilibrium. We also identify an ex post monotonicityno veto condition that is sufficient. Ex post monotonicity is satisfied in all single crossing environments with strict ex post incentive constraints. In many economically significant environments, ex post implementation can be achieved in the direct mechanism. We show by means of two classic examples that ex post monotonicity does not imply nor is it implied by Maskin monotonicity (necessary and almost sufficient for complete information implementation). The single unit auction with interdependent valuations is shown to satisfy ex post monotonicity but not Maskin monotonicity. Ex post implementation in the direct mechanism is also possible in this case. We describe an example where the Pareto correspondence fails ex post monotonicity but Maskin monotonicity is satisfied.