EX POST IMPLEMENTATION BY DIRK BERGEMANN and STEPHEN MORRIS COWLES FOUNDATION PAPER NO. 1226 COWLES FOUNDATION FOR RESEARCH IN ECONOMICS

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—sufficient for full implementation in ex post equilibrium. We also identify an ex post monotonicity no veto condition that is sufficient. Ex post monotonicity is satisfied 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 satisfies Maskin monotonicity. © 2006 Elsevier Inc. All rights reserved. JEL classification: C79; D82