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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 with single crossing preferences, we identify a strict contraction property on the preferences which together with strict ex post incentive compatibility is suﬀicient to guarantee robust implementation in the direct mechanism. Strict EPIC and the contraction property are also necessary for robust implementation in any 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.
Bergemann, Dirk and Morris, Stephen, "Robust Implementation: The Case of Direct Mechanisms" (2006). Cowles Foundation Discussion Papers. 1850.