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The Average Covering Tree Value for Directed Graph Games

CentER Discussion Paper Series No. 2012-037

19 Pages Posted: 11 May 2012  

Anna Khmelnitskaya

St.-Petersburg State University

Özer Selcuk

Tilburg University - Center for Economic Research (CentER)

Dolf Talman

Tilburg University - Department of Econometrics & Operations Research

Date Written: May 9, 2012

Abstract

We introduce a single-valued solution concept, the so-called average covering tree value, for the class of transferable utility games with limited communication structure represented by a directed graph. The solution is the average of the marginal contribution vectors corresponding to all covering trees of the directed graph. The covering trees of a directed graph are those (rooted) trees on the set of players that preserve the dominance relations between the players prescribed by the directed graph. The average covering tree value is component efficient and under a particular convexity-type condition is stable. For transferable utility games with complete communication structure the average covering tree value equals to the Shapley value of the game. If the graph is the directed analog of an undirected graph the average covering tree value coincides with the gravity center solution.

Keywords: TU game, directed communication structure, marginal contribution vector, Myerson value, average tree solution, stability

JEL Classification: C71

Suggested Citation

Khmelnitskaya, Anna and Selcuk, Özer and Talman, Dolf, The Average Covering Tree Value for Directed Graph Games (May 9, 2012). CentER Discussion Paper Series No. 2012-037. Available at SSRN: https://ssrn.com/abstract=2055092 or http://dx.doi.org/10.2139/ssrn.2055092

Anna Khmelnitskaya (Contact Author)

St.-Petersburg State University ( email )

Universitetskii prospekt 35, Petergof
Saint-Petersburg, 198504
Russia

HOME PAGE: http://wwwhome.math.utwente.nl/~khmelnitskayaab/

Özer Selcuk

Tilburg University - Center for Economic Research (CentER) ( email )

P.O. Box 90153
Tilburg, 5000 LE
Netherlands

Dolf J. J. Talman

Tilburg University - Department of Econometrics & Operations Research ( email )

Tilburg, 5000 LE
Netherlands
+31 13 466 2346 (Phone)

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