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The hybrid solutions of an N-person game

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  • Zhao, Jingang

Abstract

We introduce a solution concept intermediate between the cooperative and noncooperative solutions of an n-person game in normal form. Consider a partition p of the players, with each s in p a coalition. A joint strategy x = {x_{s}|s in p} is a hybrid solution for the partition p if, for each s in p, x_{s} is a core solution of the corresponding parametric subgame, where this game is played by the players in s and is parameterized by x_{-s}, the strategies played by all outside players. This assumes that players behave cooperatively within each coalition and competitively across coalitions. Sufficient conditions are given for a general n-person game to have hybrid solutions for any partition.
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  • Zhao, Jingang, 1992. "The hybrid solutions of an N-person game," Games and Economic Behavior, Elsevier, vol. 4(1), pages 145-160, January.
  • Handle: RePEc:eee:gamebe:v:4:y:1992:i:1:p:145-160
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    1. Ichiishi, Tatsuro, 1981. "A Social Coalitional Equilibrium Existence Lemma," Econometrica, Econometric Society, vol. 49(2), pages 369-377, March.
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    Cited by:

    1. Diamantoudi, Effrosyni & Xue, Licun, 2007. "Coalitions, agreements and efficiency," Journal of Economic Theory, Elsevier, vol. 136(1), pages 105-125, September.
    2. Debraj Ray & Rajiv Vohra, 2013. "Coalition Formation," Working Papers 2013-1, Brown University, Department of Economics.
    3. Arribas, I. & Urbano, A., 2017. "Multiproduct trading with a common agent under complete information: Existence and characterization of Nash equilibrium," Journal of Economic Theory, Elsevier, vol. 167(C), pages 14-38.
    4. Kóczy Á., László, 2006. "A Neumann-féle játékelmélet
      [Neumanns game theory]
      ," Közgazdasági Szemle (Economic Review - monthly of the Hungarian Academy of Sciences), Közgazdasági Szemle Alapítvány (Economic Review Foundation), vol. 0(1), pages 31-45.
    5. Nessah, Rabia & Tazdaı¨t, Tarik, 2013. "Absolute optimal solution for a compact and convex game," European Journal of Operational Research, Elsevier, vol. 224(2), pages 353-361.
    6. McCain, Roger A., 2008. "Cooperative games and cooperative organizations," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 37(6), pages 2155-2167, December.
    7. Beth Allen, 2000. "The Future of Microeconomic Theory," Journal of Economic Perspectives, American Economic Association, vol. 14(1), pages 143-150, Winter.
    8. Zhao, Jingang, 1996. "The hybrid equilibria and core selection in exchange economies with externalities," Journal of Mathematical Economics, Elsevier, vol. 26(4), pages 387-407.
    9. Adam Brandenburger & Harborne Stuart, 2007. "Biform Games," Management Science, INFORMS, vol. 53(4), pages 537-549, April.
    10. Martinez, Emmanuel & Tazdaït, Tarik & Tovar, Elisabeth, 2008. "Participative democracy and local environmental issues," Ecological Economics, Elsevier, vol. 68(1-2), pages 68-79, December.
    11. Jingang Zhao, 1998. "Non-Empty Core as a Precondition for Horizontal Merger: Core Existence without Using Balancedness," Working Papers 98-07, Ohio State University, Department of Economics.
    12. repec:eee:poleco:v:49:y:2017:i:c:p:1-23 is not listed on IDEAS
    13. Eric Howe & Jingang Zhao, 2004. "Merger Incentives and Inverse Matrices from Bertrand Competition," Econometric Society 2004 North American Summer Meetings 586, Econometric Society.
    14. Brangewitz, Sonja & Brockhoff, Sarah, 2014. "Stability of coalitional equilibria within repeated tax competition," Center for Mathematical Economics Working Papers 461, Center for Mathematical Economics, Bielefeld University.
    15. Sonja Brangewitz & Sarah Brockhoff, 2012. "Stability of Coalitional Equilibria within Repeated Tax Competition," Working Papers CIE 48, Paderborn University, CIE Center for International Economics.
    16. Jingang Zhao, 2009. "Estimating Merging Costs by Merger Preconditions," Theory and Decision, Springer, vol. 66(4), pages 373-399, April.
    17. Ray, Debraj & Vohra, Rajiv, 2015. "Coalition Formation," Handbook of Game Theory with Economic Applications, Elsevier.
    18. Subhadip Chakrabarti & Robert Gilles & Emiliya Lazarova, 2011. "Strategic behavior under partial cooperation," Theory and Decision, Springer, vol. 71(2), pages 175-193, August.
    19. Marini, Marco A., 1998. "Earnings, Coalitions and the Stability of the Firm," MPRA Paper 70728, University Library of Munich, Germany, revised 2012.
    20. Hafalir, Isa E., 2007. "Efficiency in coalition games with externalities," Games and Economic Behavior, Elsevier, vol. 61(2), pages 242-258, November.
    21. Ferreira, Jose Luis, 1999. "Endogenous Formation of Coalitions in Noncooperative Games," Games and Economic Behavior, Elsevier, vol. 26(1), pages 40-58, January.

    More about this item

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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