The 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 Grant SFB 15TR (Moldovanu), and by the John Simon Guggenheim Foundation, the National Science Foundation (under Grants SES-00-79299 and SES-03-17752) and the UCLA Academic Senate Committee on Research (Zame).
The Limits of ex post Implementation
Article first published online: 27 APR 2006
Volume 74, Issue 3, pages 585–610, May 2006
How to Cite
Jehiel, P., Meyer-ter-Vehn, M., Moldovanu, B. and Zame, W. R. (2006), The Limits of ex post Implementation. Econometrica, 74: 585–610. doi: 10.1111/j.1468-0262.2006.00675.x
- Issue published online: 27 APR 2006
- Article first published online: 27 APR 2006
- Manuscript received January, 2004; final revision received January, 2006.
- Ex post equilibrium;
- interdependent values
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 multidimensional 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 nontrivial deterministic social choice function implies that certain rates of information substitution coincide for all agents. This condition amounts to a system of differential equations that are not satisfied by generic valuation functions.