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

Banach Center Publications (2006)

- Volume: 71, Issue: 1, page 275-290
- ISSN: 0137-6934

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topTadeusz 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 -

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