Robust Implementation: the Case of Direct Mechanisms

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 at every type profile. In an interdependent value environment, we identify a strict contraction property on the preferences which together with strict ex post incentive compatibility and the strict single crossing property is sufficient to guarantee robust implementation in the direct mechanism. The contraction property essentially requires that the interdependence is not too large. In a linear signal model, the contraction property is equivalent to an interdependence matrix having an eigenvalue less than one. The contraction property is also necessary for robust implementation in any mechanism.