Facility Location Games With Dual Preference

Abstract

In this project, we focus on the facility location games with the property of dual preference. The origin of it, the facility location game, deals with the problem faced by the government when it plans to build a facility in a line segment but has to decide the facility location based on information reported by some self-interested agents who intend to benefit from misreporting. Dual preference property indicates that both two preferences of agents, staying close to and staying away from the facility(s), exist in the facility location game. We will explore two types of facility location games with this property, the dual character facility location game and the two-opposite-facility location game with limited distance which model the scenarios in real life. In both models, we wish to design strategy-proof mechanisms, which ensure that no single agent can get more utility by misreporting, and group strategy-proof mechanisms, which prevent a group of agents having their utility increased together after simultaneous misreporting. Also, for randomized mechanisms which output a set of possible schemes for building with possibilities, we try to find truthful-in-expectation mechanisms and group truthful-in-expectation mechanisms which discourage any single agent or group of agents from getting more expected utilities by misreporting. For the dual character facility location game, with the objective of optimizing the social utility, we propose a strategy-proof optimal deterministic mechanism when misreporting is restricted to agents' preferences, and give a 1/3-approximation deterministic group strategy-proof mechanism when both location and preference are considered as private information. For the two-opposite-facility location game with limited distance, with the objective of social utility, when the number of agents is even (denoted as 2k), we give a 1/k-approximation deterministic group strategy-proof mechanism, and when the number of agents is odd (denoted as 2k-1), we propose a 1/2k-1 -approximation deterministic group strategy-proof mechanism. The approximation ratios for both mechanisms are proved to be the best a deterministic strategy-proof mechanism can achieve. In addition, we give two group truthful-in-expectation randomized mechanisms for even and odd case respectively and each of them has an approximation ratio of 1/2. We also consider the objective of maximizing the minimum agent utility among all agents in the second model, and propose a strategy-proof optimal deterministic mechanism for it.