In graph games, Myerson assumed that only connected coalitions achieve fully the worth, but the structures of coalitions are ignored. In 1996, Jackson and Wolinsky generalized the Myerson’s model to “network situation”. The characteristic function is replaced by the value function to reflect the influence of the structures on benefits of feasible coalitions. In this paper we consider hypernetwork situations, which is a natural extension on network situations. It consists of a triple (N, H, v) where (N, H) is a hypernetwork and v is the value function to describe the possible gains from TU-games, whose cooperation is restricted by a hypernetwork. In 2012, van den Nouweland and Slikker characterized the position value axiomatically for network situations by using four axioms. By introducing a new axiom, called partial balanced conference contributions, and combining component efficiency, we propose an axiomatic characterization of the position value for hypernetwork situations. As an immediate corollary, we give a new characterization of the position value for network situations.
LI Siwen, ZHAO Jiagui, SHAN Erfang
. A characterization of the position value for hypernetwork situations[J]. Operations Research Transactions, 2019
, 23(4)
: 165
-174
.
DOI: 10.15960/j.cnki.issn.1007-6093.2019.04.015
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