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Efficient extensions of communication values

  • We study values for transferable utility games enriched by a communication graph. The most well-known such values are component-efficient and characterized by some link-deletion property. We study efficient extensions of such values: for a given component-efficient value, we look for a value that (i) satisfies efficiency, (ii) satisfies the link-deletion property underlying the original component-efficient value, and (iii) coincides with the original component-efficient value whenever the underlying graph is connected. Béal et al. (2015) prove that the Myerson value (Myerson, 1977) admits a unique efficient extension, which has been introduced by van den Brink et al. (2012). We pursue this line of research by showing that the average tree solution (Herings et al., 2008) and the compensation solution (Béal et al., 2012b) admit similar unique efficient extensions, and that there exists no efficient extension of the position value (Meessen, 1988; Borm et al., 1992). As byproducts, we obtain new characterizations of the average tree solution and the compensation solution, and of their efficient extensions. Keywords: Efficient extension, average tree solution, compensation solution, position value, component fairness, relative fairness, balanced link contributions, Myerson value, component-wise egalitarian solution

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Document Type:Article
Author:Sylvain Béal, André CasajusORCiD, Frank HuettnerORCiD
Chairs and Professorships:Chair of Economics and Information Systems
Parent Title (English):Annals of operations research
Year of Completion:2018
First Page:41
Last Page:56
Tag:Average tree solution; Balanced link contributions; Compensation solution; Component fairness; Component-wise egalitarian solution; Efficient extension; Myerson value; Position value; Relative fairness
Content Focus:Academic Audience
Peer Reviewed:Yes
Rankings:AJG Ranking / 3
VHB Ranking / B
SJR Ranking / Q1
Licence (German):License LogoUrheberrechtlich geschützt