An exchange network is a socioeconomic system in which any two actors are allowed to negotiate and conclude a transaction if and only if their positions-mathematically represented by the points of a connected graph-are joined by a line of this graph. A transaction consists in a bilaterally agreed-on division of a profit pool assigned to a given line. Under the one-exchange rule, every actor is permitted to make no more than one transaction in each negotiation round. Bienenstock and Bonacich ([1]) proposed to represent a one-exchange network with an n-person game in characteristic function form. A special case, known as a two-sided assignment game, was studied earlier by Shapley and Shubik ([10]) who proved that the game representing any one-exchange network has a nonempty core if the underlying graph is bipartite. This paper offers a graph-theoretic criterion for the existence of a nonempty core in the game associated with an arbitrary not necessarily bipartite homogeneous one-exchange network where network homogeneity means that every line of the transaction opportunity graph is assigned a profit pool of the same size.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc71-0-23,
author = {Tadeusz Soza\'nski},
title = {A graph-theoretic characterization of the core in a homogeneous generalized assignment game},
journal = {Banach Center Publications},
volume = {72},
year = {2006},
pages = {275-290},
zbl = {1255.91011},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc71-0-23}
}
Tadeusz Sozański. A graph-theoretic characterization of the core in a homogeneous generalized assignment game. Banach Center Publications, Tome 72 (2006) pp. 275-290. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc71-0-23/