Math Meth Oper Res (2017) 85:407–423
Decomposition of network communication games
· Peter Borm
Received: 9 December 2015 / Accepted: 28 January 2017 / Published online: 15 February 2017
© The Author(s) 2017. This article is published with open access at Springerlink.com
Abstract Using network control structures, this paper introduces a general class of
network communication games and studies their decomposition into unanimity games.
We obtain a relation between the dividends in any network communication game
and its underlying transferable utility game, which depends on the structure of the
communication network. Moreover, we introduce a new class of network control values
which contains both the Myerson value and the position value. The decomposition
results are used to explicitly express these values in terms of dividends.
Keywords Network control structures · Network communication games · Decompo-
sition theory · Network control values · Myerson value · Position value
Mathematics Subject Classiﬁcation 05C57 · 91A12 · 91A43
Cooperative game theory analyzes allocations of joint revenues among cooperating
players, taking the economic possibilities of subcoalitions into account. To describe
an allocation problem for a set of players, Von Neumann and Morgenstern (1944)
introduced the model of a transferable utility game, in which a characteristic function
assigns to each subgroup of the cooperating players its worth, a number reﬂecting the
The authors thank two anonymous referees and the associate editor for useful comments and suggestions.
CentER and Department of Econometrics and Operations Research, Tilburg University,
P.O. Box 90153, 5000 LE Tilburg, The Netherlands