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Multicoalitional solutions

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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.

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Paper provided by Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne in its series Documents de travail du Centre d'Economie de la Sorbonne with number 13062.

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Length: 19 pages
Date of creation: Aug 2013
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Handle: RePEc:mse:cesdoc:13062

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Keywords: Cooperative game; core; aspiration core; strong Nash equilibrium.;

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  1. Stéphane Gonzalez & Michel Grabisch, 2012. "Preserving coalitional rationality for non-balanced games," Documents de travail du Centre d'Economie de la Sorbonne 12022r, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne, revised Apr 2013.
  2. Camelia Bejan & Juan Gómez, 2012. "Axiomatizing core extensions," International Journal of Game Theory, Springer, vol. 41(4), pages 885-898, November.
  3. Camelia Bejan & Juan Camilo Gómez, 2012. "Using The Aspiration Core To Predict Coalition Formation," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 14(01), pages 1250004-1-1.
  4. Walter Trockel, . "Core-Equivalence for the Nash Bargaining Solution," Discussion Papers 03-21, University of Copenhagen. Department of Economics.
  5. Sun, N. & Trockel, W. & Yang, Z.F., 2004. "Competitive Outcomes and Endogenous Coalition Formation in an n-Person Game," Discussion Paper 2004-93, Tilburg University, Center for Economic Research.
  6. 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.
  7. Juan C. Cesco, 2012. "Nonempty Core-Type Solutions Over Balanced Coalitions In Tu-Games," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 14(03), pages 1250018-1-1.
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