THE CORE OF SOME LOCATION GAMES

An important problem in Location Theory is that of assigning plants to locations in an optimal manner. In the context of this problem, recognizing interplant transportation costs, Koopmans and Beckmann (1957) introduced the Quadratic Assignment Problem (QAP). It is shown in this paper that when the QAP is formulated as a cooperative location game, its core may be empty. By contrast, the core of the game corresponding to the linear assignment problem (where transportation costs are disregarded) is assured to be non-empty. Some conditions under which the core is non-empty are discussed.