Abstract
In the fair cost facility location game, players control terminals and must open and connect each terminal to a facility, while paying connection costs and equally sharing the opening costs associated with the facilities it connects to. In most of the literature, it is assumed that each player control a single terminal. We explore a more general version of the game where each player may control multiple terminals. We prove that this game does not always possess pure Nash equilibria, and deciding whether an instance has equilibria is NP-Hard, even in metric instances. Furthermore, we present results regarding the efficiency of equilibria, showing that the price of stability of this game is equal to the price of anarchy, in both uncapacitated and capacitated settings.
Highlights
Facility location problems covers a broad range of optimization problems, with practical applications in many different areas such as public policy, urban planning, telecommunications and computer networking
In this paper we have studied a general version of the fair cost facility location game
We provide a negative partial answer to an open question whether weighted fair cost facility location games always posses pure Nash equilibrium (PNE), by showing the connections of these weighted games to scenarios where players control multiple terminals
Summary
Facility location problems covers a broad range of optimization problems, with practical applications in many different areas such as public policy, urban planning, telecommunications and computer networking. Each store would share the costs associated with storing the goods in the warehouse they are connected to, as well as individually paying for the connection to such warehouse This scenario exemplifies the singleton fair cost facility location game, where each store is controlled by a single player. This scenario fails to accommodate the common case when multiple supermarket or stores are part of the same chain. In the fair cost facility location games we analyze, each player controls multiple terminals, and can move them simultaneously to minimize their own costs. We extend our results to weighted and capacitated versions of these games
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