Two-step values for games with two-level communication structure

Sylvain Béal, Anna Khmelnitskaya () and Philippe Solal
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Anna Khmelnitskaya: Saint-Petersburg State University, Faculty of Applied Mathematics

Journal of Combinatorial Optimization, 2018, vol. 35, issue 2, No 18, 563-587

Abstract: Abstract TU games with two-level communication structure, in which a two-level communication structure relates fundamentally to the given coalition structure and consists of a communication graph on the collection of the a priori unions in the coalition structure, as well as a collection of communication graphs within each union, are considered. For such games we introduce two families of two-step values inspired by the two-step procedures staying behind the Owen value (Owen, in: Henn, Moeschlin (eds) Essays in mathematical economics and game theory, Springer, Berlin, pp 76–88, 1977) and the two-step Shapley value (Kamijo in Int Game Theory Rev 11:207–214, 2009) for games with coalition structure. Our approach is based on the unified treatment of several component efficient values for games with communication structure and it generates two-stage solution concepts that apply component efficient values for games with communication structure on both distribution levels. Comparable axiomatic characterizations are provided.

Keywords: TU game with two-level communication structure; Owen value; Two-step Shapley value; Component efficiency; Deletion link property; 91A12; 91A43 (search for similar items in EconPapers)
JEL-codes: C71 (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (2)

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Working Paper: Two-step values for games with two-level communication structure (2018)
Working Paper: Two-step values for games with two-level communication structure (2015)
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DOI: 10.1007/s10878-017-0194-1

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