A graph-theoretic characterization of the core in a homogeneous generalized assignment game

Tadeusz Sozański. "A graph-theoretic characterization of the core in a homogeneous generalized assignment game." Banach Center Publications 71.1 (2006): 275-290. <http://eudml.org/doc/282325>.

@article{TadeuszSozański2006,
abstract = {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.},
author = {Tadeusz Sozański},
journal = {Banach Center Publications},
language = {eng},
number = {1},
pages = {275-290},
title = {A graph-theoretic characterization of the core in a homogeneous generalized assignment game},
url = {http://eudml.org/doc/282325},
volume = {71},
year = {2006},
}

TY - JOUR
AU - Tadeusz Sozański
TI - A graph-theoretic characterization of the core in a homogeneous generalized assignment game
JO - Banach Center Publications
PY - 2006
VL - 71
IS - 1
SP - 275
EP - 290
AB - 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.
LA - eng
UR - http://eudml.org/doc/282325
ER -