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Allocation Rules for Multi-choice Games with a Permission Tree Structure

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  • David Lowing

    (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 - UJM - Université Jean Monnet - Saint-Étienne - CNRS - Centre National de la Recherche Scientifique)

Abstract

We consider multi-choice cooperative games with a permission tree structure. Multi-choice games are a generalization of a cooperative transferable utility games in which each player has several activity levels. In addition, a permission tree structure models a situation in which a player needs permission from another player to cooperate. In this framework, the influence of a permission structure on the possibility of cooperation may have several interpretations depending on the context. In this paper, we investigate several of these interpretations and introduce for each of them a new allocation rule that we axiomatically characterize.

Suggested Citation

  • David Lowing, 2021. "Allocation Rules for Multi-choice Games with a Permission Tree Structure," Working Papers halshs-03121514, HAL.
    • Handle: RePEc:hal:wpaper:halshs-03121514
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-03121514
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    References listed on IDEAS

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    1. René Brink & P. Herings & Gerard Laan & A. Talman, 2015. "The Average Tree permission value for games with a permission tree," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 58(1), pages 99-123, January.
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    3. David Lowing & Kevin Techer, 2022. "Marginalism, egalitarianism and efficiency in multi-choice games," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 59(4), pages 815-861, November.
    4. René van den Brink, 2017. "Games with a Permission Structure: a survey on generalizations and applications," Tinbergen Institute Discussion Papers 17-016/II, Tinbergen Institute.
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    7. S. Béal & A. Lardon & E. Rémila & P. Solal, 2012. "The average tree solution for multi-choice forest games," Annals of Operations Research, Springer, vol. 196(1), pages 27-51, July.
    8. Lowing, David & Techer, Kevin, 2022. "Priority relations and cooperation with multiple activity levels," Journal of Mathematical Economics, Elsevier, vol. 102(C).
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    12. Sylvain Béal & Sylvain Ferrières & Philippe Solal, 2022. "The priority value for cooperative games with a priority structure," International Journal of Game Theory, Springer;Game Theory Society, vol. 51(2), pages 431-450, June.
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    15. René Brink, 2017. "Games with a permission structure - A survey on generalizations and applications," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(1), pages 1-33, April.
    16. Herings, P. Jean Jacques & van der Laan, Gerard & Talman, Dolf, 2008. "The average tree solution for cycle-free graph games," Games and Economic Behavior, Elsevier, vol. 62(1), pages 77-92, January.
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    23. René Brink, 2017. "Rejoinder on: Games with a permission structure - A survey on generalizations and applications," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(1), pages 45-48, April.
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    Cited by:

    1. David Lowing & Kevin Techer, 2022. "Marginalism, egalitarianism and efficiency in multi-choice games," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 59(4), pages 815-861, November.
    2. David Lowing & Kevin Techer, 2021. "Marginalism, Egalitarianism and E ciency in Multi-Choice Games," Working Papers halshs-03334056, HAL.
    3. Lowing, David & Techer, Kevin, 2022. "Priority relations and cooperation with multiple activity levels," Journal of Mathematical Economics, Elsevier, vol. 102(C).

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    More about this item

    Keywords

    Multi-choice games; Multi-choice Permission value; Permission (tree) structures Multi-choice games; Permission (tree) structures;
    All these keywords.

    JEL classification:

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

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