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Non-cooperative Implementation of the Nucleolus: The 3-Player Case

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  • Serrano, Roberto

Abstract

I present a non-cooperative bargaining game, in which responders may exit at any time and have endogenous outside options. When the order of proposers corresponds to the power that players have in the underlying coalitional function, the unique Markov perfect equilibrium outcome of the game is the prenucleolus. The result holds for 3-player superadditive games. An example shows that it cannot be extended to the same class of games for n players. The mechanism is inspired by the consistency property of the prenucleolus.

Suggested Citation

  • Serrano, Roberto, 1993. "Non-cooperative Implementation of the Nucleolus: The 3-Player Case," International Journal of Game Theory, Springer;Game Theory Society, vol. 22(4), pages 345-357.
    • Handle: RePEc:spr:jogath:v:22:y:1993:i:4:p:345-57
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    Cited by:

    1. Michel Le Breton & Karine Van der Straeten, 2013. "Alliances électorales entre deux tours de scrutin. Le point de vue de la théorie des jeux coopératifs et une application aux élections régionales de mars 2010," Revue économique, Presses de Sciences-Po, vol. 64(2), pages 173-240.
    2. Schwarz Mordechai E., 2019. "From Jungle to Civilized Economy: The Power Foundation of Exchange Economy Equilibrium," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 19(2), pages 1-14, June.
    3. Elena Iñarra & Roberto Serrano & Ken-Ichi Shimomura, 2020. "The Nucleolus, the Kernel, and the Bargaining Set: An Update," Revue économique, Presses de Sciences-Po, vol. 71(2), pages 225-266.
    4. Roberto Serrano, 2004. "Fifty Years of the Nash Program, 1953-2003," Working Papers 2004-20, Brown University, Department of Economics.
    5. Juan D. Moreno-Ternero & Min-Hung Tsay & Chun-Hsien Yeh, 2020. "A strategic justification of the Talmud rule based on lower and upper bounds," International Journal of Game Theory, Springer;Game Theory Society, vol. 49(4), pages 1045-1057, December.
    6. Serrano, Roberto & Vohra, Rajiv, 2002. "Bargaining and Bargaining Sets," Games and Economic Behavior, Elsevier, vol. 39(2), pages 292-308, May.
    7. Matthew O. Jackson, 2001. "A crash course in implementation theory," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 18(4), pages 655-708.
    8. Sang-Chul Suh & Quan Wen, 2003. "Multi-Agent Bilateral Bargaining with Endogenous Protocol," Vanderbilt University Department of Economics Working Papers 0305, Vanderbilt University Department of Economics.
    9. Rebelo, S., 1997. "On the Determinant of Economic Growth," RCER Working Papers 443, University of Rochester - Center for Economic Research (RCER).
    10. 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.
    11. Serrano, Roberto, 1997. "Reinterpreting the Kernel," Journal of Economic Theory, Elsevier, vol. 77(1), pages 58-80, November.
    12. Gustavo Bergantiños & Luciano Méndez-Naya, 2000. "Implementation of the τ-value," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 8(1), pages 31-41, June.
    13. Hu, Cheng-Cheng & Tsay, Min-Hung & Yeh, Chun-Hsien, 2018. "A study of the nucleolus in the nested cost-sharing problem: Axiomatic and strategic perspectives," Games and Economic Behavior, Elsevier, vol. 109(C), pages 82-98.
    14. Kurz, Sascha & Napel, Stefan & Nohn, Andreas, 2014. "The nucleolus of large majority games," Economics Letters, Elsevier, vol. 123(2), pages 139-143.
    15. Sang-Chul Suh & Quan Wen, 2009. "A multi-agent bilateral bargaining model with endogenous protocol," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 40(2), pages 203-226, August.
    16. Serrano, Roberto, 1995. "Strategic bargaining, surplus sharing problems and the nucleolus," Journal of Mathematical Economics, Elsevier, vol. 24(4), pages 319-329.
    17. Joosung Lee, 2013. "Bargaining and Buyout," 2013 Papers ple701, Job Market Papers.
    18. Vidal-Puga, Juan, 2015. "A non-cooperative approach to the ordinal Shapley–Shubik rule," Journal of Mathematical Economics, Elsevier, vol. 61(C), pages 111-118.
    19. Roberto Serrano, 2005. "Fifty years of the Nash program, 1953-2003," Investigaciones Economicas, Fundación SEPI, vol. 29(2), pages 219-258, May.

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