Strategic Facility Location with Clients that Minimize Total Waiting Time

TL;DR

This paper models a strategic two-sided facility location game where facilities and clients behave strategically, analyzing equilibrium existence, computational complexity, and providing an efficient approximation algorithm.

Contribution

It introduces a novel two-sided game model with strategic clients and facilities, proving equilibrium properties and computational complexity, and offers an efficient approximation method.

Findings

Client equilibrium exists, is unique, and can be computed efficiently.

Subgame perfect equilibria may not exist and are NP-hard to determine.

An efficient algorithm computes 3-approximate subgame perfect equilibria.

Abstract

We study a non-cooperative two-sided facility location game in which facilities and clients behave strategically. This is in contrast to many other facility location games in which clients simply visit their closest facility. Facility agents select a location on a graph to open a facility to attract as much purchasing power as possible, while client agents choose which facilities to patronize by strategically distributing their purchasing power in order to minimize their total waiting time. Here, the waiting time of a facility depends on its received total purchasing power. We show that our client stage is an atomic splittable congestion game, which implies existence, uniqueness and efficient computation of a client equilibrium. Therefore, facility agents can efficiently predict client behavior and make strategic decisions accordingly. Despite that, we prove that subgame perfect equilibria do not exist in all instances of this game and that their existence is NP-hard to decide. On the positive side, we provide a simple and efficient algorithm to compute 3-approximate subgame perfect equilibria.