Multiunit Facility Location Games

Facility location games have been a topic of major interest in economics, operations research, and computer science, starting from the seminal work by Hotelling [Hotelling H (1929) Stability in competition. Econom. J. 39(153):41–57]. In the classical pure location Hotelling game, businesses compete for maximizing customer attraction by strategically locating their facilities, assuming no price competition, and customers are attracted to their closest facilities. Surprisingly, very little rigorous work has been presented on multiunit facility location games, where the classical pure location Hotelling games are extended to contexts where each player is to locate several facilities. In this paper, we present two major contributions to the study of multiunit pure location Hotelling games. In the first part of this paper, we deal with the two-player multiunit setting and fully characterize its equilibria. In the second part of this paper, we deal with multiunit facility location games, with $N\ge 3$ players; our main result in this part is the full characterization of the settings where pure strategy equilibria exist. Our results also extend classical results on necessary and sufficient conditions for a strategy profile to be in equilibrium in a pure location (single-unit) Hotelling game to multiunit pure location games.