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Journal of Combinatorial Optimization

Erschienen in:

21.09.2016

Two efficient values of cooperative games with graph structure based on \(\tau \)-values

verfasst von: Guang Zhang, Erfang Shan, Liying Kang, Yanxia Dong

Erschienen in: Journal of Combinatorial Optimization | Ausgabe 2/2017

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Abstract

The paper is devoted to value concepts for cooperative games with a communication structure represented by a graph. Under assumptions that the players partition themselves into ‘components’ before realizing cooperation and the worth of the grand coalition not less than the sum of the worths of all components, the fair distribution of surplus solution and the two-step \(\tau \)-value are introduced as two efficient values for such games, each of which is an extension of the graph \(\tau \)-value. For the two efficient values, we discuss their special properties and we provide their axiomatic characterizations in views of those properties. By analysing an example applied to the two values, we conclude that the fair distribution of surplus solution allocates more surplus to the bigger coalitions and favors the powerful players, while the two-step \(\tau \)-value benefits the vulnerable groups and inspires to form small coalitions.

Vorheriger Artikel On the online multi-agent O–D k-Canadian Traveler Problem

Nächster Artikel Online scheduling to minimize the total weighted completion time plus the rejection cost

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Note that the minimal right property is weaker than the relative invariance under S-equivalence.

We could also consider such game as a graph game with no links, however, to keep the parameter \(\delta ^{v,L}\) is meaningful, we do not choose this way.

This property is an extension of restricted proportionality, because if \(b^w=0\), then it immediately reduces to the restricted proportionality.

This property is also an extension of the restricted proportionality, because if \(r^{v,L}=0\), then \(\delta ^{v,L}=\lambda ^{v,L}\), and so it reduced to the restricted proportionality.

Béal S, Rémila E, Solal P (2012) Fairness and fairness for neighbors: the difference between the Myerson value and component-wise egalitarian solutions. Econ Lett 117(1):263–267MathSciNetCrossRefMATH

Béal S, Casajus A, Huettner F (2015a) Efficient extension of communication values. Working paper CRESE 2015-04

Béal S, Casajus A, Huettner F (2015b) Efficient extension of the Myerson values. Soc Choice Welf 45:819–827MathSciNetCrossRefMATH

Casajus A (2007) An efficient value for TU games with a cooperation structure. Working paper, Universität Leipzig, Germany

Casas-Méndez B, García-Jurado I, van den Nouweland A, Vázquez-Brage M (2003) An extension of the \(\tau \)-value to games with coalition structures. Eur J Oper Res 148:494–513MathSciNetCrossRefMATH

Driessen T, Tijs SH (1983) The \(\tau \)-value, the nucleolus and the core for a subclass of games. Methods Oper Res 46:395–406MathSciNetMATH

Driessen T, Tijs SH (1992) The core and the \(\tau \)-value for cooperative games with coalition structures. In: Dutta B, Mookherjee D, Parthasarathy T, Raghavan TES, Ray D, Tijs SH (eds) Game theory and economic applications. Springer, Berlin, pp 146–169

Herings PJJ, van der Laan G, Talman AJJ (2008) The average tree solution for cycle-free graph games. Games Econ Behav 62:77–92MathSciNetCrossRefMATH

Kamijo Y (2009) A two-step Shapley value for cooperative games with coalition structures. Int Game Theory Rev 11(02):207–214MathSciNetCrossRefMATH

Khmelnitskaya A (2014) Values for games with two-level communication structures. Discrete Appl Math 166:34–50MathSciNetCrossRefMATH

Myerson RB (1977) Graphs and cooperation in games. Math Oper Res 2(3):225–229MathSciNetCrossRefMATH

Owen G (1977) Values of games with a priori unions. In: Henn R, Moeschlin O (eds) Mathematical economics and game theory. Springer, Berlin

Tijs SH (1981) Bounds for the core and the \(\tau \)-value. In: Moeschlin O, Pallaschke D (eds) Game theory and mathematical economics. North-Holland, New York

Tijs SH (1987) An axiomatization of the \(\tau \)-value. Math Soc Sci 13(2):177–181MathSciNetCrossRefMATH

van den Brink R, Khmelnitskaya A, van der Laan G (2012) An efficient and fair solution for communication graph games. Econ Lett 117(3):786–789MathSciNetCrossRefMATH

van den Brink R, Khmelnitskaya A, van der Laan G (2016) An Owen-type value for games with two-level communication structure. Ann Oper Res 243(1):179–198MathSciNetCrossRefMATH

Wang W, Sun H, Han W (2011) The \(\tau \)-value of cooperative games restricted by graph (in Chinese). Oper Res Trans 15(4):75–84MathSciNet

Titel: Two efficient values of cooperative games with graph structure based on -values
verfasst von: Guang Zhang
Erfang Shan
Liying Kang
Yanxia Dong
Publikationsdatum: 21.09.2016
Verlag: Springer US
Erschienen in: Journal of Combinatorial Optimization / Ausgabe 2/2017
Print ISSN: 1382-6905
Elektronische ISSN: 1573-2886
DOI: https://doi.org/10.1007/s10878-016-0081-1

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