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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

    (Université de Bourgogne Franche-Comté)

  • Eric Rémila

    (Université de Saint-Etienne)

  • Philippe Solal

    (Université de Saint-Etienne)

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.

Suggested Citation

  • Sylvain Béal & Eric Rémila & Philippe Solal, 2022. "Allocation rules for cooperative games with restricted communication and a priori unions based on the Myerson value and the average tree solution," Journal of Combinatorial Optimization, Springer, vol. 43(4), pages 818-849, May.
    • Handle: RePEc:spr:jcomop:v:43:y:2022:i:4:d:10.1007_s10878-021-00811-4
    DOI: 10.1007/s10878-021-00811-4
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    More about this item

    Keywords

    Average tree solution; Coalition structure; Tree; Myerson value; Owen value; TU-game;
    All these keywords.

    JEL classification:

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

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