Weak implementation

  • Kym PramEmail author
Research Article


I define Weak Implementation under incomplete information. A social choice set is weakly implementable if the set of equilibrium outcomes of some mechanism is a non-empty subset of the social choice set. Weak implementation is a more natural objective than either full or partial implementation in many cases. I show that there are social choice sets where every subset can be weakly implemented, yet the set cannot be fully implemented. I give a complete characterization of the weakly implementable social choice sets under a weak restriction on preferences. As a corollary, I show that in independent private values environments the set of interim efficient social choice functions is weakly implementable whenever it is partially implementable.


Implementation theory Mechanism design Game theory Full implementation 

JEL Classification

C72 D71 D80 D82 



I would like to thank Eddie Dekel, Jeff Ely, Alessandro Pavan and Asher Wolinsky for their invaluable support and feedback. I would also like to thank Chris Li, Matteo Foschi, and a seminar audience at Northwestern for their helpful comments.


  1. Bergemann, D., Morris, S.: Robust mechanism design. Econometrica 73, 1771–1813 (2005)CrossRefGoogle Scholar
  2. Brusco, S.: Perfect Bayesian implementation. Econ. Theory 5, 419–444 (1995). CrossRefGoogle Scholar
  3. Duggan, J.: Virtual Bayesian implementation. Econometrica 65, 1775–1199 (1997)CrossRefGoogle Scholar
  4. Dutta, B., Sen, A.: 2-person Bayesian implementation. Econ. Des. 1, 41–54 (1994)Google Scholar
  5. Hahn, G., Yannelis, N.C.: Coalitional Bayesian Nash equilibrium in differential information economies. Econ. Theory 18, 485–509 (2001). CrossRefGoogle Scholar
  6. Jackson, M.: Bayesian implementation. Econometrica 59, 461–477 (1991)CrossRefGoogle Scholar
  7. Kara, T., Sonmez, T.: Implementation of college admission rules. Econ. Theory 9, 197–218 (1997). CrossRefGoogle Scholar
  8. Kunimoto T (2018) Interim equilibrium implementation. MimeoGoogle Scholar
  9. Maskin, E.S.: The theory of implementation in Nash equilibrium: a survey. In: Hurwicz, L., Schmeidler, D., Sonnenschein, H. (eds.) Social Goals and Social Organization, pp. 173–204. Cambridge University Press, Cambridge (1985)Google Scholar
  10. Maskin, E.S.: Nash equilibrium and welfare optimality. Rev. Econ. Stud. 66, 23–38 (1999)CrossRefGoogle Scholar
  11. Palfrey, T., Srivastava, S.: On Bayesian implementable allocations. Rev. Econ. Stud. 54, 193–208 (1987)CrossRefGoogle Scholar
  12. Palfrey, T., Srivastava, S.: Mechanism design with incomplete information: a solution to the implementation problem. J. Polit. Econ. 97, 668–691 (1989)CrossRefGoogle Scholar
  13. Postlewaite, A., Schmeidler, D.: Implementation of differential information economies. J. Econ. Theory 39, 14–33 (1986)CrossRefGoogle Scholar
  14. Serrano R, Vohra R (2010) Multiplicity of mixed equilibria in mechanisms: a unified approach to exact and approximate implementation. J. Math. Econ. 774–785Google Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.University of Nevada, RenoRenoUSA

Personalised recommendations