Abstract
We study the two-opposite-facility location game on a line segment, where a mechanism determines the locations of a popular facility and an obnoxious facility for finitely many agents. The agents report their private locations, and try to maximize their own utilities depending on their distances to the facilities. We prove tight bounds on the inapproximability of both randomized and deterministic strategy-proof mechanisms for maximizing the total agent utility minus a penalty determined by the distance between the two facilities.
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