Cooperative Game Theoretic Solutions to Facility Location Problems in Continuous Setting

Abstract

The facility location game in continuous setting usually has two distinct sections: the location problem, where the facility position is found by cost minimization; the cost allocation, where the distribution of total cost is studied with cooperative game theoretic solution concepts, such as the Core or the Shapley Value. This paper shows how the cost allocation rules can also provide solutions for the location part. In particular, after having defined a generalized game (which avoids attaching a minimization problem for the location part), we study the concept of the “set of Core locations” (or location-Core), i.e. the set of feasible locations satisfying the Core conditions, a concept that was first introduced under a narrower setting by the author in [3]. Thanks to a more formal problem definition, the location-Core is here generalized and further investigated.