Hotelling-Downs with Facility Synergy: The Mall Effect
2026-06-24 • Computer Science and Game Theory
Computer Science and Game Theory
AI summaryⓘ
The authors study a version of the Hotelling-Downs model where people like to be near many facilities, not just the closest one. They find that in this new model, stable situations (Nash equilibria) always exist, unlike the classic case. They also show that some stable setups can be just as good as the best possible facility placement. Finally, they prove that even the worst stable setup is not much less efficient than the best, which means adding facility synergy keeps the system relatively efficient.
Hotelling-Downs modelNash equilibriumfacility locationPrice of Anarchyclient behaviorgame theorysynergyoptimal solutioncost efficiencyequilibrium stability
Authors
Elliot Anshelevich, Jianan Lin, Noah Prisament
Abstract
We consider a variation of the classic Hotelling-Downs model with the addition of facility synergies. Unlike in the classic model, where clients always use the facility closest to them, we study clients who prefer locations with many facilities to those with few facilities while simultaneously attempting to minimize their distance as well. We show that, in contrast with the classic model, Nash equilibria for our setting always exist, and, in fact, there always exists a Nash equilibrium such that the sum of client costs equals the cost of the optimal solution. Our main result is a bound of $\frac{225}{64}\approx 3.516$ on the Price of Anarchy for our model, showing that, although the client behavior is more complex in our model (and often more realistic depending on the application), the cost of Nash equilibrium solutions still cannot be much worse than the cost of the optimal facility placement.