Robust Implementation in Direct Mechanisms

40 Pages Posted: 21 Jan 2009

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: January 20, 2009

Abstract

A social choice function is robustly implementable if there is a mechanism under which the process of iteratively eliminating strictly dominated messages leads to outcomes that agree with the social choice function for all beliefs at every type profile. In an interdependent value environment with single crossing preferences, we identify a contraction property on the preferences which together with strict ex post incentive compatibility is sufficient to guarantee robust implementation in the direct mechanism. Strict ex post incentive compatibility and the contraction property are also necessary for robust implementation in any mechanism, including indirect ones.

The contraction property requires that the interdependence is not too large. In a linear signal model, the contraction property is equivalent to an interdependence matrix having all eigenvalues smaller than one.

Keywords: Mechanism design, Implementation, Robustness, Common knowledge, Interim equilibrium, Iterative deletion, Direct mechanism

JEL Classification: C79, D82

Suggested Citation

Bergemann, Dirk and Morris, Stephen Edward, Robust Implementation in Direct Mechanisms (January 20, 2009). Cowles Foundation Discussion Paper No. 1561RR. Available at SSRN: https://ssrn.com/abstract=1330469

Dirk Bergemann (Contact Author)

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

Princeton University - Department of Economics ( email )

Princeton, NJ 08544-1021
United States

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