Heterogenous facility location games with entrance fees

Abstract

In recent decades, game theory and mechanism design have found applications across various domains of artificial intelligence. Among these applications, the facility location game has received significant attention within the field of mechanism design without money. In the classical model and its variants, the only concern of each agent is the distance between themselves and the facility. Consequently, agents receive the facility's services free of charge and only incur travel fees. However, a recent paper by Ma et al. (AAAI 2023) introduces a novel model that introduces an additional element: an entrance fee charged by each facility, determined by its location. As a result, the cost incurred by each agent comprises both the distance to the facility (travel fee) and the entrance fee levied by the facility. It should be noted that the facilities in the model proposed by Ma et al. are treated as homogeneous entities, meaning that the entrance fee solely depends on the facility's location and not its identity. However, an important characteristic of many practical facility location problems is that facilities possess inherent differences, even when they share the same location. In this paper, we extend the entrance fee model presented by Ma et al. by considering heterogeneous facilities. Our model considers not only the facility's location but also its unique identity when determining the entrance fee. Specifically, each facility is associated with a location-dependent entrance fee function, which may vary from facility to facility. We study the model from the perspective of mechanism design and propose new mechanisms for the two-facility games that are strategyproof and achieve approximation ratios that almost match the lower bounds.