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Invariance and Randomness in the Nash Program for Coalitional Games

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Abstract

By introducing physical outcomes in coalitional games we note that coalitional games and social choice problems are equivalent (implying that so are the theory of implementation and the Nash program). This clarifies some misunderstandings (in regrad to invariance and randomness), sometimes found in the Nash program.

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Bibliographic Info

Paper provided by Nir Dagan in its series Economic theory and game theory with number 006.

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Length: 7 pages
Date of creation: 1998
Date of revision:
Publication status: Published in Economics Letters 58:43-49 (1998)
Handle: RePEc:nid:ndagan:006

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Postal: Nir Dagan, Dept. of Economics and Management, Tel-Hai Academic College, Upper Galilee, Israel.
Web page: http://www.nirdagan.com/research/

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Keywords: Nash program; implementation; scale invariance; ordinal invariance; randomness;

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References

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  1. Sergiu Hart & Andreu Mas-Colell, 1994. "Bargaining and value," Economics Working Papers 114, Department of Economics and Business, Universitat Pompeu Fabra, revised Feb 1995.
  2. Gul, Faruk, 1989. "Bargaining Foundations of Shapley Value," Econometrica, Econometric Society, vol. 57(1), pages 81-95, January.
  3. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
  4. Thomson, W., 1989. "Cooperative Models Of Bargaining," RCER Working Papers 177, University of Rochester - Center for Economic Research (RCER).
  5. Ariel Rubinstein, 2010. "Perfect Equilibrium in a Bargaining Model," Levine's Working Paper Archive 252, David K. Levine.
  6. Abreu, Dilip & Matsushima, Hitoshi, 1992. "A Response [Virtual Implementation in Iteratively Undominated Strategies I: Complete Information]," Econometrica, Econometric Society, vol. 60(6), pages 1439-42, November.
  7. Nash, John, 1953. "Two-Person Cooperative Games," Econometrica, Econometric Society, vol. 21(1), pages 128-140, April.
  8. Roberto Serrano, 1996. "A comment on the Nash program and the theory of implementation," Economics Working Papers 161, Department of Economics and Business, Universitat Pompeu Fabra.
  9. Krishna, Vijay & Serrano, Roberto, 1996. "Multilateral Bargaining," Review of Economic Studies, Wiley Blackwell, vol. 63(1), pages 61-80, January.
  10. Abreu, Dilip & Matsushima, Hitoshi, 1992. "Virtual Implementation in Iteratively Undominated Strategies: Complete Information," Econometrica, Econometric Society, vol. 60(5), pages 993-1008, September.
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Citations

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Cited by:
  1. Luis Corchón & Matteo Triossi, 2011. "Implementation with renegotiation when preferences and feasible sets are state dependent," Social Choice and Welfare, Springer, vol. 36(2), pages 179-198, February.
  2. Walter Trockel, 1999. "On the Nash Program for the Nash Bargaining Solution," UCLA Economics Working Papers 788, UCLA Department of Economics.
  3. Claus-Jochen Haake & Walter Trockel, 2007. "On Maskin monotonicity of solution based social choice rules," Working Papers 393, Bielefeld University, Center for Mathematical Economics.
  4. Roberto Serrano, 2005. "Fifty years of the Nash program, 1953-2003," Investigaciones Economicas, Fundación SEPI, vol. 29(2), pages 219-258, May.
  5. Güth, W. & Ritzberger, K. & Damme, E.E.C. van, 2004. "On the Nash Bargaining Solution with noise," Open Access publications from Tilburg University urn:nbn:nl:ui:12-129218, Tilburg University.
  6. Trockel,W., 1999. "Integrating the Nash program into mechanism theory," Working Papers 305, Bielefeld University, Center for Mathematical Economics.
  7. Luis C. Corchon & Matteo Triosi, 2005. "Implementation With State Dependent Feasible Sets And Preferences: A Renegotiation Approach," Economics Working Papers we057136, Universidad Carlos III, Departamento de Economía.
  8. 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.
  9. Trockel,W., 1999. "Unique Nash implementation for a class of bargaining solutions," Working Papers 308, Bielefeld University, Center for Mathematical Economics.
  10. Claus-Jochen Haake, 2005. "Two support results for the Kalai-Smorodinsky solution in small object division markets," Working Papers 366, Bielefeld University, Center for Mathematical Economics.
  11. 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.
  12. Perez-Castrillo, David & Wettstein, David, 2001. "Bidding for the Surplus : A Non-cooperative Approach to the Shapley Value," Journal of Economic Theory, Elsevier, vol. 100(2), pages 274-294, October.
  13. Naeve, Jorg, 1999. "Nash implementation of the Nash bargaining solution using intuitive message spaces," Economics Letters, Elsevier, vol. 62(1), pages 23-28, January.

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