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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. Krishna, Vijay & Serrano, Roberto, 1996. "Multilateral Bargaining," Review of Economic Studies, Wiley Blackwell, vol. 63(1), pages 61-80, January.
  2. Abreu, Dilip & Matsushima, Hitoshi, 1992. "Virtual Implementation in Iteratively Undominated Strategies: Complete Information," Econometrica, Econometric Society, vol. 60(5), pages 993-1008, September.
  3. 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.
  4. Thomson, William, 1994. "Cooperative models of bargaining," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 2, chapter 35, pages 1237-1284 Elsevier.
  5. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
  6. Rubinstein, Ariel, 1982. "Perfect Equilibrium in a Bargaining Model," Econometrica, Econometric Society, vol. 50(1), pages 97-109, January.
  7. Hart, Sergiu & Mas-Colell, Andreu, 1996. "Bargaining and Value," Econometrica, Econometric Society, vol. 64(2), pages 357-80, March.
  8. Gul, Faruk, 1989. "Bargaining Foundations of Shapley Value," Econometrica, Econometric Society, vol. 57(1), pages 81-95, January.
  9. 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.
  10. Nash, John, 1953. "Two-Person Cooperative Games," Econometrica, Econometric Society, vol. 21(1), pages 128-140, April.
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Citations

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Cited by:
  1. Naeve, Jorg, 1999. "Nash implementation of the Nash bargaining solution using intuitive message spaces," Economics Letters, Elsevier, vol. 62(1), pages 23-28, January.
  2. Trockel,W., 1999. "Unique Nash implementation for a class of bargaining solutions," Working Papers 308, Bielefeld University, Center for Mathematical Economics.
  3. 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.
  4. Güth, W. & Ritzberger, K. & Damme, E.E.C. van, 2002. "On the Nash Bargaining Solution with Noise," Discussion Paper 2002-79, Tilburg University, Center for Economic Research.
  5. David Pérez-Castrillo & David Wettstein, . "Bidding For The Surplus: A Non-Cooperative Approach To The Shapley Value," UFAE and IAE Working Papers 461.00, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
  6. Walter Trockel, 1999. "On the Nash Program for the Nash Bargaining Solution," UCLA Economics Working Papers 788, UCLA Department of Economics.
  7. Luis Corchón & Matteo Triossi, 2008. "Implementation with renegotiation when preferences and feasible sets are state dependent," Documentos de Trabajo 255, Centro de Economía Aplicada, Universidad de Chile.
  8. Walter Trockel, 2002. "Integrating the Nash program into mechanism theory," Review of Economic Design, Springer, vol. 7(1), pages 27-43.
  9. Roberto Serrano, 2004. "Fifty Years of the Nash Program, 1953-2003," Working Papers 2004-20, Brown University, Department of Economics.
  10. Matteo Triossi & Luis Corchón, 2006. "Implementation with State Dependent Feasible Sets and Preferences: A Renegotiation Approach," Carlo Alberto Notebooks 24, Collegio Carlo Alberto.
  11. 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.
  12. 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.
  13. Claus-Jochen Haake & Walter Trockel, 2007. "On Maskin monotonicity of solution based social choice rules," Working Papers 393, Bielefeld University, Center for Mathematical Economics.

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