Multi-Unit Facility Location Games

TL;DR

This paper extends classical Hotelling facility location models to multi-unit settings, fully characterizing equilibria for two-player cases and conditions for existence of pure strategy equilibria for three or more players.

Contribution

It provides the first comprehensive analysis of multi-unit pure location Hotelling games, including equilibrium characterization and existence conditions for multiple players.

Findings

Complete equilibrium characterization for two-player multi-unit games.

Conditions for pure strategy equilibrium existence with three or more players.

Extension of classical Hotelling results to multi-unit contexts.

Abstract

Facility location games have been a topic of major interest in economics, operations research and computer science, starting from the seminal work by Hotelling. In the classical pure location Hotelling game businesses compete for maximizing customer attraction by strategically locating their facilities, assuming no price competition, while customers are attracted to their closest facilities. Surprisingly, very little rigorous work has been presented on multi-unit 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 multi-unit pure location Hotelling games. In the first part of this paper we deal with the two-player multi-unit setting, and fully characterize its equilibria. In the second part of this paper we deal with multi-unit facility location games, with $N\geq 3$ 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 multi-unit pure location games.