Advanced Search
MyIDEAS: Login to save this paper or follow this series

Implementation in Mixed Nash Equilibrium

Contents:

Author Info

  • Claudio Mezzetti
  • Ludovic Renou

    ()

Abstract

A mechanism implements a social choice correspondence f in mixed Nash equilibrium if at any preference profile, the set of all pure and mixed Nash equilibrium outcomes coincides with the set of f-optimal alternatives at that preference profile. This definition generalizes Maskin’s definition of Nash implementation in that it does not require each optimal alternative to be the outcome of a pure Nash equilibrium. We show that the condition of weak set-monotonicity, a weakening of Maskin’s monotonicity, is necessary for implementation. We provide sufficient conditions for implementation and show that important social choice correspondences that are not Maskin monotonic can be implemented in mixed Nash equilibrium.

Download Info

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
File URL: http://www.le.ac.uk/economics/research/repec/lec/leecon/dp09-10.pdf
Download Restriction: no

Bibliographic Info

Paper provided by Department of Economics, University of Leicester in its series Discussion Papers in Economics with number 09/10.

as in new window
Length:
Date of creation: Apr 2009
Date of revision: Jan 2010
Handle: RePEc:lec:leecon:09/10

Contact details of provider:
Postal: Department of Economics University of Leicester, University Road. Leicester. LE1 7RH. UK
Phone: +44 (0)116 252 2887
Fax: +44 (0)116 252 2908
Email:
Web page: http://www2.le.ac.uk/departments/economics
More information through EDIRC

Order Information:
Email:
Web: http://www2.le.ac.uk/departments/economics/research/discussion-papers

Related research

Keywords: implementation; Maskin monotonicity; pure and mixed Nash equilibrium; weak set-monotonicity; social choice correspondence;

Other versions of this item:

Find related papers by JEL classification:

This paper has been announced in the following NEP Reports:

References

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
as in new window
  1. Kim-Sau Chung & Jeffrey C. Ely, 2003. "Implementation with Near-Complete Information," Econometrica, Econometric Society, Econometric Society, vol. 71(3), pages 857-871, 05.
  2. Benoît, Jean-Pierre & Ok, Efe A., 2008. "Nash implementation without no-veto power," Games and Economic Behavior, Elsevier, Elsevier, vol. 64(1), pages 51-67, September.
  3. Dutta, Bhaskar & Sen, Arunava, 1991. "A Necessary and Sufficient Condition for Two-Person Nash Implementation," Review of Economic Studies, Wiley Blackwell, Wiley Blackwell, vol. 58(1), pages 121-28, January.
  4. Abreu, Dilip & Matsushima, Hitoshi, 1992. "A Response [Virtual Implementation in Iteratively Undominated Strategies I: Complete Information]," Econometrica, Econometric Society, Econometric Society, vol. 60(6), pages 1439-42, November.
  5. Danilov, Vladimir, 1992. "Implementation via Nash Equilibria," Econometrica, Econometric Society, Econometric Society, vol. 60(1), pages 43-56, January.
  6. Antonio Cabrales & Roberto Serrano, 2007. "Implementation in adaptive better-response dynamics," Working Papers, Instituto Madrileño de Estudios Avanzados (IMDEA) Ciencias Sociales 2007-16, Instituto Madrileño de Estudios Avanzados (IMDEA) Ciencias Sociales.
  7. Sjostrom, T., 1991. "Implementation in Undominated Nash Equilibria without Integer Games," Papers, Stockholm - International Economic Studies 491, Stockholm - International Economic Studies.
  8. Olivier, BOCHET & François, MANIQUET, 2006. "Virtual Nash implementation with admissible support," Discussion Papers (ECON - Département des Sciences Economiques), Université catholique de Louvain, Département des Sciences Economiques 2006043, Université catholique de Louvain, Département des Sciences Economiques.
  9. Saijo, Tatsuyoshi, 1987. "On constant maskin monotonic social choice functions," Journal of Economic Theory, Elsevier, Elsevier, vol. 42(2), pages 382-386, August.
  10. Roberto Serrano & Rajiv Vohra, 2009. "Multiplicity of mixed equilibria in mechanisms: A unified approach to exact and approximate implementation," Working Papers, Instituto Madrileño de Estudios Avanzados (IMDEA) Ciencias Sociales 2009-08, Instituto Madrileño de Estudios Avanzados (IMDEA) Ciencias Sociales.
  11. Gibbard, Allan, 1977. "Manipulation of Schemes That Mix Voting with Chance," Econometrica, Econometric Society, Econometric Society, vol. 45(3), pages 665-81, April.
  12. Hannu Vartiainen, 2007. "Subgame perfect implementation of voting rules via randomized mechanisms," Social Choice and Welfare, Springer, Springer, vol. 29(3), pages 353-367, October.
  13. Matthew O. Jackson, 2001. "A crash course in implementation theory," Social Choice and Welfare, Springer, Springer, vol. 18(4), pages 655-708.
  14. Maskin, Eric & Sjostrom, Tomas, 2002. "Implementation theory," Handbook of Social Choice and Welfare, Elsevier, in: K. J. Arrow & A. K. Sen & K. Suzumura (ed.), Handbook of Social Choice and Welfare, edition 1, volume 1, chapter 5, pages 237-288 Elsevier.
  15. Marion Oury & Olivier Tercieux, 2012. "Continuous Implementation," Econometrica, Econometric Society, Econometric Society, vol. 80(4), pages 1605-1637, 07.
  16. Barbera, Salvador & Bogomolnaia, Anna & van der Stel, Hans, 1998. "Strategy-proof probabilistic rules for expected utility maximizers," Mathematical Social Sciences, Elsevier, Elsevier, vol. 35(2), pages 89-103, March.
  17. Palfrey, Thomas R & Srivastava, Sanjay, 1991. "Nash Implementation Using Undominated Strategies," Econometrica, Econometric Society, Econometric Society, vol. 59(2), pages 479-501, March.
  18. Dirk Bergemann & Stephen Morris & Olivier Tercieux, 2010. "Rationalizable Implementation," Levine's Working Paper Archive 661465000000000022, David K. Levine.
  19. Aumann, Robert & Brandenburger, Adam, 1995. "Epistemic Conditions for Nash Equilibrium," Econometrica, Econometric Society, Econometric Society, vol. 63(5), pages 1161-80, September.
  20. Olivier Bochet, 2007. "Nash Implementation with Lottery Mechanisms," Social Choice and Welfare, Springer, Springer, vol. 28(1), pages 111-125, January.
  21. Eric Maskin, 1998. "Nash Equilibrium and Welfare Optimality," Harvard Institute of Economic Research Working Papers, Harvard - Institute of Economic Research 1829, Harvard - Institute of Economic Research.
  22. Matsushima, Hitoshi, 1988. "A new approach to the implementation problem," Journal of Economic Theory, Elsevier, Elsevier, vol. 45(1), pages 128-144, June.
  23. Abreu, Dilip & Matsushima, Hitoshi, 1992. "Virtual Implementation in Iteratively Undominated Strategies: Complete Information," Econometrica, Econometric Society, Econometric Society, vol. 60(5), pages 993-1008, September.
  24. Moore, John & Repullo, Rafael, 1990. "Nash Implementation: A Full Characterization," Econometrica, Econometric Society, Econometric Society, vol. 58(5), pages 1083-99, September.
  25. Eichberger, Jurgen & Kelsey, David, 2000. "Non-Additive Beliefs and Strategic Equilibria," Games and Economic Behavior, Elsevier, Elsevier, vol. 30(2), pages 183-215, February.
  26. Abreu, Dilip & Sen, Arunava, 1991. "Virtual Implementation in Nash Equilibrium," Econometrica, Econometric Society, Econometric Society, vol. 59(4), pages 997-1021, July.
  27. M. Sanver, 2006. "Nash implementing non-monotonic social choice rules by awards," Economic Theory, Springer, Springer, vol. 28(2), pages 453-460, 06.
  28. Jackson, Matthew O, 1991. "Bayesian Implementation," Econometrica, Econometric Society, Econometric Society, vol. 59(2), pages 461-77, March.
  29. Cabrales, Antonio & Serrano, Roberto, 2011. "Implementation in adaptive better-response dynamics: Towards a general theory of bounded rationality in mechanisms," Games and Economic Behavior, Elsevier, Elsevier, vol. 73(2), pages 360-374.
Full references (including those not matched with items on IDEAS)

Citations

Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
as in new window

Cited by:
  1. Ludovic Renou & Karl H. Schlag, 2009. "Implementation in Minimax Regret Equilibrium," Discussion Papers in Economics, Department of Economics, University of Leicester 09/24, Department of Economics, University of Leicester.
  2. Bergemann, Dirk & Morris, Stephen & Tercieux, Olivier, 2011. "Rationalizable implementation," Journal of Economic Theory, Elsevier, Elsevier, vol. 146(3), pages 1253-1274, May.
  3. Roberto Serrano & Rajiv Vohra, 2009. "Multiplicity of Mixed Equilibria in Mechanisms: a Unified Approach ot Exact and Approximate Implementation," Working Papers 2009-11, Brown University, Department of Economics.

Lists

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

Statistics

Access and download statistics

Corrections

When requesting a correction, please mention this item's handle: RePEc:lec:leecon:09/10. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Mrs. Alexandra Mazzuoccolo).

If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

If references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

Please note that corrections may take a couple of weeks to filter through the various RePEc services.