The limits of ex post implementation

Abstract: The sensitivity of Bayesian implementation to agents be-liefs about others suggests the use of more robust notions of implementation such as ex-post implementation, which requires that each agents strategy be optimal for every possible realization of the types of other agents. We show that only constant social choice functions are ex-post implementable in generic mechanism design frameworks with multi-dimensional signals, in-terdependent valuations and transferable utilities. In other words, ex-post implementation requires that the same alternative must be chosen irrespec-tive of agents signals. The proof shows that ex-post implementability of a non-trivial 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\u85ed by generic valuation functions. 1The editor and three referees made many very helpful comments. We also wish t