Two-step values for games with two-level communication structure |
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Authors: | Sylvain Béal Anna Khmelnitskaya Philippe Solal |
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Affiliation: | 1.CRESE EA3190,Univ. Bourgogne Franche-Comté,Besan?on,France;2.Saint-Petersburg State University, Faculty of Applied Mathematics,Saint Petersburg,Russia;3.Université Jean Monnet,Saint-étienne,France |
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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. |
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