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Strategyproof Facility Location Mechanisms with Richer Action Spaces

We study facility location problems where agents control multiple locations and when reporting their locations can choose to hide some locations (hiding), report some locations more than once (replication) and lie about their locations (manipulation). We fully characterize all facility location mechanisms that are anonymous, efficient, and strategyproof with respect to the richer strategic behavior for this setting. We also provide a characterization with respect to manipulation only. This is the first, to the best of our knowledge, characterization result for the strategyproof facility location mechanisms where each agent controls multiple locations.