COWLES FOUNDATION FOR RESEARCH IN ECONOMICS
AT YALE UNIVERSITY

Box 208281
New Haven, CT 06520-8281

COWLES FOUNDATION DISCUSSION PAPER NO. 1561RR

Robust Implementation in Direct Mechanisms

Dirk Bergemann and Stephen Morris

May 2006
Revised January 2009

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