Facility Location Games with Optional Preference

Abstract

The classic facility location game models the scenario where the government plans to build some public facilities like supermarkets, movie theaters and base stations on a street where some self-interested residents are situated. The residents are required to report their information like locations and preferences to the government, which will then be mapped to the building locations of the facilities by some mechanisms. In this research, a new model of the facility location game, the optional preference model is proposed and studied. Unlike the classic preference model, agents in this model are allowed to have optional preference, which gives them more flexibility when reporting. The creativity in the optional preference model is that if an agent only cares one of the several similar facilities, e.g. the closest one (The Min variant), or the most far away one (The Max variant), she can report her preference precisely and this will be taken into consideration, which is not possible in the classic preference models studied before. With the objective of minimizing the highest(maximum) or the sum(social) of all agents' cost, corresponding strategyproof mechanisms are proposed, which means no agents can benefit, e.g. reducing her cost, by lying to these mechanisms. For the Min variant, a 2-approximation mechanism as well as a lower bound of 4/3 are proposed for the maximum cost objective. And a (1+n/2)-approximation mechanism as well as a lower bound of 2 are proposed for the social cost objective. Lower bound means that no strategyproof mechanism can have a better approximation ratio than this bound. For the Max variant, an optimal mechanism is proposed for the maximum cost objective and a 2-approximation mechanism for the social cost objective. The significance of this new preference model, apart from its real life applications, is that it enriched the types of preference and the cost functions of agents and opened up a new direction for researchers to work along. Also, with the results obtained for the two variants, it can serve as the potential building blocks for more general functions.