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Allocation rules for cooperative games with restricted communication and a priori unions based on the Myerson value and the average tree solution

Author

Listed:
  • Sylvain Béal
  • Eric Rémila
  • Philippe Solal

    (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 cooperatives games (TU-games) enriched by a system of a priori unions and a communication forest graph which are independent from each other. These two structures reflect the limitations of cooperation possibilities. In this framework, we introduce four Owen-type allocation rules, which are defined by a two-step application of an allocation rule à la Owen (in: Henn R, Moeschlin O (eds) Essays in mathematical economics and game theory, Springer, Berlin, 1977) to TU-games with a priori unions where the TU-game is replaced by Myerson’s (Math Oper Res 2:225–229, 1977) graph-restricted TU-game. The four possibilities arise by applying, at each step, either the Myerson value (Myerson 1977) or the average tree solution (Herings et al. in Games Econ Behav 62:77–92, 2008). Our main result offers comparable axiomatizations of these four allocation rules.
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Sylvain Béal & Eric Rémila & Philippe Solal, 2021. "Allocation rules for cooperative games with restricted communication and a priori unions based on the Myerson value and the average tree solution," Post-Print hal-03422939, HAL.
    • Handle: RePEc:hal:journl:hal-03422939
    DOI: 10.1007/s10878-021-00811-4
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    References listed on IDEAS

    as
    1. Guang Zhang & Erfang Shan & Liying Kang & Yanxia Dong, 2017. "Two efficient values of cooperative games with graph structure based on $$\tau $$ τ -values," Journal of Combinatorial Optimization, Springer, vol. 34(2), pages 462-482, August.
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    3. Sylvain Béal & Eric Rémila & Philippe Solal, 2012. "Compensations in the Shapley value and the compensation solutions for graph games," International Journal of Game Theory, Springer;Game Theory Society, vol. 41(1), pages 157-178, February.
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    JEL classification:

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

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