Bounding quality of pure Nash equilibria in dual-role facility location games

Abstract

We study a dual-role game setting of locating facilities in a metric space where each agent can open a facility at her location or be a customer to receive the service, and an opening cost function is given to represent the cost of opening a facility at some specific location. We first show the existence of pure Nash equilibria (PNE) in such games by a polynomial-time algorithm, then use the price of anarchy (PoA) to measure the quality of PNE under social objectives of minimizing the maximum/social cost. For dual-role facility location games with general opening cost functions, we show the PoA under maximum/social cost can tend to be infinite. However, for games with L-Lipschitz conditioned opening cost functions where $L\ge 0$ is a given parameter, the PoA under maximum cost is exactly $L+1$ and the PoA under social cost is bounded by the interval $\left[ (n+L)/3, n+\max \{L-1,0\}\right]$.