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Integrating the Nash Program into Mechanism Theory

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  • Walter Trockel

    (UCLA)

Abstract

The present paper provides a method by which the Nash Program may be embedded into mechanism theory. It is shown that any result stating the support of any solution of a cooperative game in coalitional form by a Nash equilibrium of some suitable game in strategic form can be used to derive the mechanism theoretic Nash-implementation of that solution.

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File URL: http://www.econ.ucla.edu/workingpapers/wp787.pdf
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Bibliographic Info

Paper provided by UCLA Department of Economics in its series UCLA Economics Working Papers with number 787.

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Date of creation: 01 Feb 1999
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Handle: RePEc:cla:uclawp:787

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Web page: http://www.econ.ucla.edu/

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References

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  1. Matthew O. Jackson, 1990. "Undominated Nash Implementation in Bounded Mechanisms," Discussion Papers 966, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  2. Howard, J. V., 1992. "A social choice rule and its implementation in perfect equilibrium," Journal of Economic Theory, Elsevier, vol. 56(1), pages 142-159, February.
  3. Trockel,W., 1999. "A universal meta bargaining realization of the Nash solution," Working Papers 310, Bielefeld University, Center for Mathematical Economics.
  4. Jackson, Matthew O. & Palfrey, Thomas R., 1999. "Voluntary Implementation," Working Papers 1077, California Institute of Technology, Division of the Humanities and Social Sciences.
  5. Naeve, Jorg, 1999. "Nash implementation of the Nash bargaining solution using intuitive message spaces," Economics Letters, Elsevier, vol. 62(1), pages 23-28, January.
  6. Jackson, Matthew O, 1992. "Implementation in Undominated.Strategies: A Look at Bounded Mechanisms," Review of Economic Studies, Wiley Blackwell, vol. 59(4), pages 757-75, October.
  7. Martin J Osborne & Ariel Rubinstein, 2009. "A Course in Game Theory," Levine's Bibliography 814577000000000225, UCLA Department of Economics.
  8. Rubinstein, Ariel, 1982. "Perfect Equilibrium in a Bargaining Model," Econometrica, Econometric Society, vol. 50(1), pages 97-109, January.
  9. Walter Trockel, 2000. "Implementations of the Nash solution based on its Walrasian characterization," Economic Theory, Springer, vol. 16(2), pages 277-294.
  10. Trockel, Walter, 1996. "A Walrasian approach to bargaining games," Economics Letters, Elsevier, vol. 51(3), pages 295-301, June.
  11. Eric van Damme, 1984. "The Nash Bargaining Solution is Optimal," Discussion Papers 597, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  12. Nash, John, 1953. "Two-Person Cooperative Games," Econometrica, Econometric Society, vol. 21(1), pages 128-140, April.
  13. Claus-Jochen Haake, 1998. "Implementation of the Kalai-Smorodinsky Bargaining Solution in Dominant Strategies," Working Papers 301, Bielefeld University, Center for Mathematical Economics.
  14. Trockel, Walter, 1996. "An Exact Implementation of the Nash Bargaining Solution in Dominant Strategies," Economics Series 25, Institute for Advanced Studies.
  15. Krishna, Vijay & Serrano, Roberto, 1996. "Multilateral Bargaining," Review of Economic Studies, Wiley Blackwell, vol. 63(1), pages 61-80, January.
  16. Nir Dagan & Roberto Serrano, 1998. "Invariance and Randomness in the Nash Program for Coalitional Games," Economic theory and game theory 006, Nir Dagan.
  17. Eric Maskin, 1998. "Nash Equilibrium and Welfare Optimality," Harvard Institute of Economic Research Working Papers 1829, Harvard - Institute of Economic Research.
  18. Damme, E.E.C. van, 1986. "The Nash bargaining solution is optimal," Open Access publications from Tilburg University urn:nbn:nl:ui:12-154426, Tilburg University.
  19. Kim C. Border & Uzi Segal, 1997. "Preferences over Solutions to the Bargaining Problem," Econometrica, Econometric Society, vol. 65(1), pages 1-18, January.
  20. Martin J. Osborne & Ariel Rubinstein, 2005. "Bargaining and Markets," Levine's Bibliography 666156000000000515, UCLA Department of Economics.
  21. Damme, Eric van, 1986. "The Nash bargaining solution is optimal," Journal of Economic Theory, Elsevier, vol. 38(1), pages 78-100, February.
  22. Moulin, H., 1984. "Implementing the Kalai-Smorodinsky bargaining solution," Journal of Economic Theory, Elsevier, vol. 33(1), pages 32-45, June.
  23. Leonid Hurwicz, 1994. "Economic design, adjustment processes, mechanisms, and institutions," Review of Economic Design, Springer, vol. 1(1), pages 1-14, December.
  24. E. Maskin, 1983. "The Theory of Implementation in Nash Equilibrium: A Survey," Working papers 333, Massachusetts Institute of Technology (MIT), Department of Economics.
  25. Serrano, Roberto, 1997. "A comment on the Nash program and the theory of implementation," Economics Letters, Elsevier, vol. 55(2), pages 203-208, August.
  26. Bergin, James & Duggan, John, 1999. "An Implementation-Theoretic Approach to Non-cooperative Foundations," Journal of Economic Theory, Elsevier, vol. 86(1), pages 50-76, May.
  27. Trockel,W., 1999. "Unique Nash implementation for a class of bargaining solutions," Working Papers 308, Bielefeld University, Center for Mathematical Economics.
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Citations

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Cited by:
  1. Trockel, Walter, 2011. "An exact non-cooperative support for the sequential Raiffa solution," Journal of Mathematical Economics, Elsevier, vol. 47(1), pages 77-83, January.
  2. Hannu Vartiainen, 2007. "Nash implementation and the bargaining problem," Social Choice and Welfare, Springer, vol. 29(2), pages 333-351, September.
  3. Roberto Serrano, 2005. "Fifty years of the Nash program, 1953-2003," Investigaciones Economicas, FundaciĆ³n SEPI, vol. 29(2), pages 219-258, May.
  4. Sun,N. & Trockel,W. & Yang,Z., 2004. "Competitive outcomes and endogenous coalition formation in an n-person game," Working Papers 358, Bielefeld University, Center for Mathematical Economics.
  5. Claus-Jochen Haake & Walter Trockel, 2010. "On Maskin monotonicity of solution based social choice rules," Review of Economic Design, Springer, vol. 14(1), pages 17-25, March.
  6. Trockel,W., 2001. "Can and should the Nash program be looked at as a part of mechanism theory?," Working Papers 322, Bielefeld University, Center for Mathematical Economics.
  7. Ju, Yuan, 2012. "Reject and renegotiate: The Shapley value in multilateral bargaining," Journal of Mathematical Economics, Elsevier, vol. 48(6), pages 431-436.
  8. Trockel,W., 1999. "On the Nash program for the Nash bargaining solution," Working Papers 306, Bielefeld University, Center for Mathematical Economics.
  9. Trockel,W., 1999. "Unique Nash implementation for a class of bargaining solutions," Working Papers 308, Bielefeld University, Center for Mathematical Economics.
  10. Haake, Claus-Jochen, 2009. "Two support results for the Kalai-Smorodinsky solution in small object division markets," Mathematical Social Sciences, Elsevier, vol. 57(2), pages 177-187, March.

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