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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

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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.

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Funding

(Information that explains whether and by whom the research was supported): Financial support from research programs “In-depth UDL 2018”, and “Mathématiques de la décision pour l’ingénierie physique et sociale” (MODMAD) is gratefully acknowledged.

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Authors and Affiliations

  1. CRESE EA3190, Université de Bourgogne Franche-Comté, 25000, Besançon, France

    Sylvain Béal

  2. CNRS, GATE L-SE UMR 5824, Université de Saint-Etienne, 42023, Saint-Etienne, France

    Eric Rémila & Philippe Solal

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  1. Sylvain Béal
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  2. Eric Rémila
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  3. Philippe Solal
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Correspondence to Sylvain Béal.

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We thank an associate editor and two anonymous reviewers for valuable comments. Financial support from research programs “In-depth UDL 2018”, and “Mathématiques de la décision pour l’ingénierie physique et sociale” (MODMAD) is gratefully acknowledged.

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Béal, S., Rémila, E. & Solal, P. Allocation rules for cooperative games with restricted communication and a priori unions based on the Myerson value and the average tree solution. J Comb Optim 43, 818–849 (2022). https://doi.org/10.1007/s10878-021-00811-4

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