Abstract
This paper examines the mechanism design for a two-facility-location game involving two types of agents. Type I agents only prioritize the facility closer to their location, while type II agents are concerned with the overall distance to both facilities. The objective is to minimize the total cost of all agents. In a game setting, agents have the option to strategically report their locations or types. Therefore, a mechanism which ensures that agents do not have any incentive to misreport their private information is considered strategy-proof. We design strategy-proof mechanisms with approximation ratios for both continuous and discrete facility locations, which are designed with respect to various restrictions on misreporting. Furthermore, we establish lower bounds on approximation ratios.
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