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

Silvain Béal; Anna Borisovna Khmelnitskaya; Philippe Solal

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

Silvain Béal, Anna Borisovna Khmelnitskaya, Philippe Solal

Discrete Mathematics and Mathematical Programming

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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, 1977) and the two-step Shapley value (Kamijo, 2009) for games with coalition structures. Our approach is based on the unied 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.

Original language	English
Place of Publication	Enschede
Publisher	University of Twente
Number of pages	21
Publication status	Published - Mar 2015

Publication series

Name	Memorandum of the Department of Applied Mathematics
No.	2043
ISSN (Print)	1874-4850

Keywords

Deletion link property
C71
Two-step Shapley value
Component eciency
Owen value
TU game with two-level communication structure

Cite this

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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, 1977) and the two-step Shapley value (Kamijo, 2009) for games with coalition structures. Our approach is based on the unied 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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N2 - 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, 1977) and the two-step Shapley value (Kamijo, 2009) for games with coalition structures. Our approach is based on the unied 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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KW - Two-step Shapley value

KW - Component eciency

KW - Owen value

KW - TU game with two-level communication structure

M3 - Report

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

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ER -

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

Abstract

Publication series

Keywords

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Cite this