Ex Post Implementation

We analyze the problem of fully implementing a social choice set in ex post equilibrium. We identify an ex post monotonicity condition that is necessary and- in economic environments-su ¢ cient for full implementation in ex post equilibrium. We also identify an ex post monotonicity no veto condition that is su ¢ cient. Ex post monotonicity is satis\u85ed in all single crossing environments with strict ex post incentive constraints. We show by means of two classic examples that ex post monotonicity does not imply nor is it implied by Maskin monotonicity. The single unit auction with interdependent valuations is shown to satisfy ex post monotonicity but not Maskin monotonicity. We further describe a Pareto correspondence that fails ex post monotonicity but satis\u85es Maskin monotonicity