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Multicoalitional solutions

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Abstract

The paper proposes a new concept of solution for TU games, called multicoalitional solution, which makes sense in the context of production games, that is, where v(S) is the production or income per unit of time. By contrast to classical solutions where elements of the solution are payoff vectors, multicoalitional solutions give in addition an allocation time to each coalition, which permits to realize the payoff vector. We give two instances of such solutions, called the d-multicoalitional core and the c-multicoalitional core, and both arise as the strong Nash equilibrium of two games, where in the first utility per active unit of time is maximized, while in the second it is the utility per total unit of time. We show that the d-core (or aspiration core) of Benett, and the c-core of Guesnerie and Oddou are strongly related to the d-multicoalitional and c-multicoalitional cores, respectively, and that the latter ones can be seen as an implementation of the former ones in a noncooperative framework

Suggested Citation

  • Stéphane Gonzalez & Michel Grabisch, 2013. "Multicoalitional solutions," Documents de travail du Centre d'Economie de la Sorbonne 13062, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
  • Handle: RePEc:mse:cesdoc:13062
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    File URL: ftp://mse.univ-paris1.fr/pub/mse/CES2013/13062.pdf
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    References listed on IDEAS

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    1. S. Flåm & L. Koutsougeras, 2010. "Private information, transferable utility, and the core," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 42(3), pages 591-609, March.
    2. Sun, Ning & Trockel, Walter & Yang, Zaifu, 2008. "Competitive outcomes and endogenous coalition formation in an n-person game," Journal of Mathematical Economics, Elsevier, vol. 44(7-8), pages 853-860, July.
    3. Camelia Bejan & Juan Gómez, 2012. "Axiomatizing core extensions," International Journal of Game Theory, Springer;Game Theory Society, vol. 41(4), pages 885-898, November.
    4. Stéphane Gonzalez & Michel Grabisch, 2015. "Preserving coalitional rationality for non-balanced games," International Journal of Game Theory, Springer;Game Theory Society, vol. 44(3), pages 733-760, August.
    5. Guesnerie, R. & Oddou, C., 1979. "On economic games which are not necessarily superadditive : Solution concepts and application to a local public good problem with few a agents," Economics Letters, Elsevier, vol. 3(4), pages 301-306.
    6. repec:wsi:igtrxx:v:14:y:2012:i:01:n:s0219198912500041 is not listed on IDEAS
    7. Benyamin Shitovitz, 1997. "A comparison between the core and the monopoly solutions in a mixed exchange economy," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 10(3), pages 559-563.
    8. Koczy, Laszlo A. & Lauwers, Luc, 2004. "The coalition structure core is accessible," Games and Economic Behavior, Elsevier, vol. 48(1), pages 86-93, July.
    9. repec:hal:journl:hal-00321625 is not listed on IDEAS
    10. John G. Cross, 1967. "Some theoretic characteristics of economic and political coalitions," Journal of Conflict Resolution, Peace Science Society (International), vol. 11(2), pages 184-195, June.
    11. Michel Grabisch & Pedro Miranda, 2008. "On the vertices of the k-additive core," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-00321625, HAL.
    12. Walter Trockel, 2005. "Core-equivalence for the Nash bargaining solution," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 25(1), pages 255-263, January.
    13. Garratt, Rod & Qin, Cheng-Zhong, 2000. "On Market Games When Agents Cannot Be in Two Places at Once," Games and Economic Behavior, Elsevier, vol. 31(2), pages 165-173, May.
    14. Martin J. Osborne & Ariel Rubinstein, 1994. "A Course in Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262650401, January.
    15. Kannai, Yakar, 1992. "The core and balancedness," Handbook of Game Theory with Economic Applications,in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 1, chapter 12, pages 355-395 Elsevier.
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    Cited by:

    1. Stéphane Gonzalez & Aymeric Lardon, 2016. "Optimal Deterrence of Cooperation," GREDEG Working Papers 2016-22, Groupe de REcherche en Droit, Economie, Gestion (GREDEG CNRS), University of Nice Sophia Antipolis, revised Jun 2017.
    2. repec:spr:jogath:v:47:y:2018:i:1:d:10.1007_s00182-017-0584-8 is not listed on IDEAS

    More about this item

    Keywords

    Cooperative game; core; aspiration core; strong Nash equilibrium;

    JEL classification:

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

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