Some new cooperative coverage facility location games

Abstract

In this paper we introduce and analyze new classes of cooperative games related to facility location models defined on general metric spaces. The players are the customers (demand points) in the location problem and the characteristic value of a coalition is the cost of serving its members. Specifically, the cost in our games is either the service radius or the diameter of the coalition. We study the existence of core allocations for these games, focusing on network spaces, i.e., finite metric spaces induced by undirected graphs and positive edge lengths, and on finite dimension vector spaces endowed with a norm (Rd).