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Multicoalitional solutions

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
Date of revision:
Handle: RePEc:mse:cesdoc:13062
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  1. Trockel, Walter, 2011. "Core-equivalence for the Nash bargaining solution," Center for Mathematical Economics Working Papers 355, Center for Mathematical Economics, Bielefeld University.
  2. Stéphane Gonzalez & Michel Grabisch, 2012. "Preserving coalitional rationality for non-balanced games," Documents de travail du Centre d'Economie de la Sorbonne 12022, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
  3. Sun, Ning & Trockel, Walter & Yang, Zaifu, 2011. "Competitive outcomes and endogenous coalition formation in an n-person game," Center for Mathematical Economics Working Papers 358, Center for Mathematical Economics, Bielefeld University.
  4. 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.
  5. 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.
  6. 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.
  7. Camelia Bejan & Juan Gómez, 2012. "Axiomatizing core extensions," International Journal of Game Theory, Springer, vol. 41(4), pages 885-898, November.
  8. S. Flåm & L. Koutsougeras, 2010. "Private information, transferable utility, and the core," Economic Theory, Springer, vol. 42(3), pages 591-609, March.
  9. 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.
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