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Single NTU-value solutions

Author

Listed:
  • Emililo Calvo

    (Dep. of Economic Analysis. University of Valencia)

Abstract

We propose a variation of the Hart and Mas-Colell non-cooperative bargaining model for n-person games in coalitional form. This strategic game implements, in the limit, a new NTU-value for the class of monotonic games. This value coincides with the Maschler and Owen value for hyperplane games, and with the Shapley value for TU games. The main characteristic of this proposal is that always select a unique payoff allocation. This value can also be considered as an extension of the Nash bargaining solution. Variations of this model yield extensions of the Discrete Raiffa solution, and the Kalai-Smorodinsky solution.

Suggested Citation

  • Emililo Calvo, 2004. "Single NTU-value solutions," Game Theory and Information 0405004, University Library of Munich, Germany, revised 10 Jun 2004.
  • Handle: RePEc:wpa:wuwpga:0405004
    Note: Type of Document - pdf; pages: 31
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    References listed on IDEAS

    as
    1. Thomson,William & Lensberg,Terje, 2006. "Axiomatic Theory of Bargaining with a Variable Number of Agents," Cambridge Books, Cambridge University Press, number 9780521027038.
    2. Gomes, Armando & Hart, Sergiu & Mas-Colell, Andreu, 1999. "Finite Horizon Bargaining and the Consistent Field," Games and Economic Behavior, Elsevier, vol. 27(2), pages 204-228, May.
    3. Roth, Alvin E., 1977. "Independence of irrelevant alternatives, and solutions to Nash's bargaining problem," Journal of Economic Theory, Elsevier, vol. 16(2), pages 247-251, December.
    4. Hart, Sergiu, 1985. "An Axiomatization of Harsanyi's Nontransferable Utility Solution," Econometrica, Econometric Society, vol. 53(6), pages 1295-1313, November.
    5. 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.
    6. Moulin, H., 1984. "Implementing the Kalai-Smorodinsky bargaining solution," Journal of Economic Theory, Elsevier, vol. 33(1), pages 32-45, June.
    7. Hart, Sergiu & Mas-Colell, Andreu, 1996. "Bargaining and Value," Econometrica, Econometric Society, vol. 64(2), pages 357-380, March.
    8. Kalai, Ehud & Smorodinsky, Meir, 1975. "Other Solutions to Nash's Bargaining Problem," Econometrica, Econometric Society, vol. 43(3), pages 513-518, May.
    9. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
    10. Aumann, Robert J, 1985. "An Axiomatization of the Non-transferable Utility Value," Econometrica, Econometric Society, vol. 53(3), pages 599-612, May.
    11. Sergiu Hart, 2005. "An axiomatization of the consistent non-transferable utility value," International Journal of Game Theory, Springer;Game Theory Society, vol. 33(3), pages 355-366, September.
    12. Sjostrom, Tomas, 1991. "Stahl's bargaining model," Economics Letters, Elsevier, vol. 36(2), pages 153-157, June.
    13. Hart, Oliver & Moore, John, 1990. "Property Rights and the Nature of the Firm," Journal of Political Economy, University of Chicago Press, vol. 98(6), pages 1119-1158, December.
    14. Ken Binmore & Ariel Rubinstein & Asher Wolinsky, 1986. "The Nash Bargaining Solution in Economic Modelling," RAND Journal of Economics, The RAND Corporation, vol. 17(2), pages 176-188, Summer.
    15. Emilio Calvo & Iñaki Garci´a & José M. Zarzuelo, 2001. "Replication invariance on NTU games," International Journal of Game Theory, Springer;Game Theory Society, vol. 29(4), pages 473-486.
    16. Winter, Eyal, 1994. "The Demand Commitment Bargaining and Snowballing Cooperation," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 4(2), pages 255-273, March.
    17. Maschler, M & Owen, G, 1989. "The Consistent Shapley Value for Hyperplane Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 18(4), pages 389-407.
    18. Roger B. Myerson, 1978. "Conference Structures and Fair Allocation Rules," Discussion Papers 363, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    19. Ehud Kalai & Dov Samet, 1983. "On Weighted Shapley Values," Discussion Papers 602, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
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    More about this item

    Keywords

    Shapley value; NTU-value solutions; Nash Bargaining; Raiffa solution; Kali-Smorodinsky solution.;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games

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