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

Sylvain Béal, Eric Rémila () and Philippe Solal
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Eric Rémila: Université de Saint-Etienne

Journal of Combinatorial Optimization, 2022, vol. 43, issue 4, No 5, 818-849

Abstract: 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.

Keywords: Average tree solution; Coalition structure; Tree; Myerson value; Owen value; TU-game; 91A12; 91A43 (search for similar items in EconPapers)
JEL-codes: C71 (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (1)

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Working Paper: Allocation rules for cooperative games with restricted communication and a priori unions based on the Myerson value and the average tree solution (2022)
Working Paper: Allocation rules for cooperative games with restricted communication and a priori unions based on the Myerson value and the average tree solution (2021)
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DOI: 10.1007/s10878-021-00811-4

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