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Multicoalitional solutions

Author

Listed:
  • Stéphane Gonzalez

    (UJM - Université Jean Monnet - Saint-Étienne, GATE Lyon Saint-Étienne - Groupe d'Analyse et de Théorie Economique Lyon - Saint-Etienne - ENS de Lyon - École normale supérieure de Lyon - UL2 - Université Lumière - Lyon 2 - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon - UJM - Université Jean Monnet - Saint-Étienne - CNRS - Centre National de la Recherche Scientifique, CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

  • Michel Grabisch

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement)

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 equilibria of two strategic 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, 2016. "Multicoalitional solutions," Post-Print halshs-01293785, HAL.
    • Handle: RePEc:hal:journl:halshs-01293785
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-01293785
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    References listed on IDEAS

    as
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    3. Ferreira, João J.M. & Jalali, Marjan S. & Ferreira, Fernando A.F., 2018. "Enhancing the decision-making virtuous cycle of ethical banking practices using the Choquet integral," Journal of Business Research, Elsevier, vol. 88(C), pages 492-497.

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    More about this item

    Keywords

    Cooperative game; core; aspiration core; strong Nash equilibrium;
    All these keywords.

    JEL classification:

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

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