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Efficient extensions of communication values

Sylvain Béal (), André Casajus () and Frank Huettner ()
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André Casajus: HHL Leipzig Graduate School of Management
Frank Huettner: ESMT European School of Management and Technology

Annals of Operations Research, 2018, vol. 264, issue 1, 41-56

Abstract: Abstract 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 deletion link 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. (Soc Choice Welf 45:819–827, 2015) prove that the Myerson value (Myerson in Math Oper Res 2:225–229, 1977) admits a unique efficient extension, which has been introduced by van den Brink et al. (Econ Lett 117:786–789, 2012). We pursue this line of research by showing that the average tree solution (Herings et al. in Games Econ Behav 62:77–92, 2008) and the compensation solution (Béal et al. in Int J Game Theory 41:157–178, 2012b) admit similar unique efficient extensions, and that there exists no efficient extension of the position value (Meessen in Communication games, 1988; Borm et al. in SIAM J Discrete Math 5:305–320, 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; 91A12 (search for similar items in EconPapers)
JEL-codes: C71 (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s10479-017-2661-6

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