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Invariance and randomness in the Nash program for coalitional games

Author

Listed:
  • Nir Dagan
  • Roberto Serrano

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 facilitates the understanding of the role of invariance and randomness in the Nash program. Also, the extent to which mechanisms in the Nash program perform ``real implementation'' is examined.

Suggested Citation

  • Nir Dagan & Roberto Serrano, 1997. "Invariance and randomness in the Nash program for coalitional games," Economics Working Papers 217, Department of Economics and Business, Universitat Pompeu Fabra.
  • Handle: RePEc:upf:upfgen:217
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    References listed on IDEAS

    as
    1. Rubinstein, Ariel, 1982. "Perfect Equilibrium in a Bargaining Model," Econometrica, Econometric Society, vol. 50(1), pages 97-109, January.
    2. Nash, John, 1953. "Two-Person Cooperative Games," Econometrica, Econometric Society, vol. 21(1), pages 128-140, April.
    3. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
    4. Serrano, Roberto, 1997. "A comment on the Nash program and the theory of implementation," Economics Letters, Elsevier, vol. 55(2), pages 203-208, August.
    5. 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.
    6. Gul, Faruk, 1989. "Bargaining Foundations of Shapley Value," Econometrica, Econometric Society, vol. 57(1), pages 81-95, January.
    7. Abreu, Dilip & Matsushima, Hitoshi, 1992. "A Response [Virtual Implementation in Iteratively Undominated Strategies I: Complete Information]," Econometrica, Econometric Society, vol. 60(6), pages 1439-1442, November.
    8. Hart, Sergiu & Mas-Colell, Andreu, 1996. "Bargaining and Value," Econometrica, Econometric Society, vol. 64(2), pages 357-380, March.
    9. Vijay Krishna & Roberto Serrano, 1996. "Multilateral Bargaining," Review of Economic Studies, Oxford University Press, vol. 63(1), pages 61-80.
    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. 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.
    2. Guth, Werner & Ritzberger, Klaus & van Damme, Eric, 2004. "On the Nash bargaining solution with noise," European Economic Review, Elsevier, vol. 48(3), pages 697-713, June.
    3. Roberto Serrano, 2005. "Fifty years of the Nash program, 1953-2003," Investigaciones Economicas, Fundación SEPI, vol. 29(2), pages 219-258, May.
    4. Trockel,W., 2001. "Can and should the Nash program be looked at as a part of mechanism theory?," Center for Mathematical Economics Working Papers 322, Center for Mathematical Economics, Bielefeld University.
    5. Luis Corchón & Matteo Triossi, 2011. "Implementation with renegotiation when preferences and feasible sets are state dependent," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 36(2), pages 179-198, February.
    6. 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.
    7. Trockel,W., 1999. "Integrating the Nash program into mechanism theory," Center for Mathematical Economics Working Papers 305, Center for Mathematical Economics, Bielefeld University.
    8. Triossi, Matteo & Corchón Díaz, Luis Carlos, 2005. "Implementation with state dependent feasible sets and preferences: a renegotiation approach," UC3M Working papers. Economics we057136, Universidad Carlos III de Madrid. Departamento de Economía.
    9. Claus-Jochen Haake & Walter Trockel, 2010. "On Maskin monotonicity of solution based social choice rules," Review of Economic Design, Springer;Society for Economic Design, vol. 14(1), pages 17-25, March.
    10. Walter Trockel, 1999. "Integrating the Nash Program into Mechanism Theory," UCLA Economics Working Papers 787, UCLA Department of Economics.
    11. Naeve, Jorg, 1999. "Nash implementation of the Nash bargaining solution using intuitive message spaces," Economics Letters, Elsevier, vol. 62(1), pages 23-28, January.
    12. Haake, Claus-Jochen, 2011. "Two support results for the Kalai-Smorodinsky solution in small object division markets," Center for Mathematical Economics Working Papers 366, Center for Mathematical Economics, Bielefeld University.
    13. repec:jmi:articl:jmi-v1i1a3 is not listed on IDEAS
    14. Walter Trockel, 1999. "On the Nash Program for the Nash Bargaining Solution," UCLA Economics Working Papers 788, UCLA Department of Economics.
    15. Trockel,W., 1999. "Unique Nash implementation for a class of bargaining solutions," Center for Mathematical Economics Working Papers 308, Center for Mathematical Economics, Bielefeld University.
    16. Duman, Papatya & Trockel, Walter, 2016. "On non-cooperative foundation and implementation of the Nash Solution in subgame perfect equilibrium via Rubinstein’s game," Center for Mathematical Economics Working Papers 550, Center for Mathematical Economics, Bielefeld University.

    More about this item

    Keywords

    Coalitional games; social choice; Nash program; implementation; scale invariance; ordinal invariance; randomness;

    JEL classification:

    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General

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