A cooperative location game based on the 1-center location problem

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 the service radius of the coalition. We study the existence of core allocations and the existence of polynomial representations of the cores of these games, focusing on network spaces, i.e., finite metric spaces induced by undirected graphs and positive edge lengths, and on the ℓp metric spaces defined over Rd.