Centrality Rewarding Shapley and Myerson Values for Undirected Graph Games

CentER Discussion Paper Series No. 2016-035

31 Pages Posted: 6 Sep 2016  

Anna Khmelnitskaya

St.-Petersburg State University

Gerard van der Laan

VU University Amsterdam - Faculty of Economics and Business Administration

Dolf Talman

Tilburg University - Department of Econometrics & Operations Research

Multiple version iconThere are 2 versions of this paper

Date Written: September 5, 2016

Abstract

In this paper we introduce two values for cooperative games with communication graph structure. For cooperative games the shapley value distributes the worth of the grand coalition amongst the players by taking into account the worths that can be obtained by any coalition of players, but does not take into account the role of the players when communication between players is restricted. Existing values for communication graph games as the Myerson value and the average tree solution only consider the worths of connected coalitions and respect only in this way the communication restrictions. The two values take into account the position of a player in the graph. The first one respects centrality, but not the communication abilities of any player. The second value reflects both centrality and the communication ability of each player. That implies that in unanimity games players that do not generate worth but are needed to connect worth generating players are treated as those latter players, and simultaneously players that are more central in the graph get bigger shares in the worth than players that are less central. For both values an axiomatic characterization is given on the class of connected cycle-
free graph games.

Keywords: cooperative game; Shapley value; communication graph; restricted

JEL Classification: C71

Suggested Citation

Khmelnitskaya, Anna and van der Laan, Gerard and Talman, Dolf, Centrality Rewarding Shapley and Myerson Values for Undirected Graph Games (September 5, 2016). CentER Discussion Paper Series No. 2016-035. Available at SSRN: https://ssrn.com/abstract=2834806 or http://dx.doi.org/10.2139/ssrn.2834806

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/

Gerard Van der Laan

VU University Amsterdam - Faculty of Economics and Business Administration ( email )

De Boelelaan 1105
Amsterdam, 1081HV
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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