Ex Post Implementation

63 Pages Posted: 12 Apr 2005

See all articles by Dirk Bergemann

Dirk Bergemann

Yale University - Cowles Foundation - Department of Economics; Yale University - Cowles Foundation

Stephen Morris

Princeton University - Department of Economics

Date Written: March 2005

Abstract

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. 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.

Keywords: Ex Post Equilibrium, Implementation, Single Crossing, Interdependent Values

JEL Classification: C79, D82

Suggested Citation

Bergemann, Dirk and Morris, Stephen Edward, Ex Post Implementation (March 2005). Cowles Foundation Discussion Paper No. 1502. Available at SSRN: https://ssrn.com/abstract=703042

Dirk Bergemann

Yale University - Cowles Foundation - Department of Economics ( email )

28 Hillhouse Ave
New Haven, CT 06520-8268
United States
203-432-3592 (Phone)
203-432-2128 (Fax)

HOME PAGE: http://www.econ.yale.edu/~dirk/

Yale University - Cowles Foundation

Box 208281
New Haven, CT 06520-8281
United States

Stephen Edward Morris (Contact Author)

Princeton University - Department of Economics ( email )

Princeton, NJ 08544-1021
United States

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