Non-cooperative capacitated facility location games

We study capacitated facility location games, where players control terminals and need to connect each one to a facility from a set of possible locations. There are opening costs and capacity restrictions for each facility. Also, there are connection costs for each pair of facility and terminal if such facility attends this terminal. This problem has several applications, especially in distributed scenarios where a central authority is too expensive or even infeasible to exist. In this paper, we analyze and present new results concerning the existence of equilibria, Price of Anarchy (PoA), and Stability (PoS) for metric and non-metric versions of this game. We prove unbounded PoA and PoS for some versions of the game, even when sequential versions are considered. For metric variants, we prove that sequentiality leads to bounded PoA and PoS.