The Limits of Ex-Post Implementation

The sensitivity of Bayesian implementation to agents’beliefs about others suggests the use of more robust notions of implementation such as ex-post implementation, which requires that each agent’s strategy be optimal for every possible realization of the types of other agents. We show that the only deterministic social choice functions that are ex-post implementable in generic mechanism design frameworks with multi-dimensional signals, interdependent valuations and transferable utilities, are constant functions. In other words, deterministic ex-post implementation requires that the same alternative must be chosen irrespective of agents’signals. The proof shows that ex-post implementability of a non-trivial deterministic social choice function implies that certain rates of information substitution coincide for all agents. This condition amounts to a system of di¤erential equations that are not satis…ed by generic valuation functions. 1The editor and three referees made many very helpful comments. We also wish to thank Dilip Abreu, Dirk Bergemann, Jerry Green, Oliver Hart, Martin Hellwig, Thomas Kittsteiner, Paul Milgrom, Steve Morris, Georg Noeldeke, Andy Postlewaite and Chris Shannon for stimulating remarks. Financial support provided by the Max Planck Research Prize and the German Science Foundation, SFB 15TR (Moldovanu) and by the John Simon Guggenheim Foundation, the National Science Foundation (under grants SES-0079299 and SES-0317752) and the UCLA Academic Senate Committee on Research (Zame). Jehiel: UCL London and PSE, Paris; [email protected]; Meyer-ter-Vehn : [email protected]; Moldovanu: University of Bonn; [email protected]; Zame: UCLA & Caltech; [email protected]