Manipulation-resistant facility location mechanisms for ZV-line graphs
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In many real-life scenarios, a group of agents needs to agree on a common action, e.g., on the location for a public facility, while there is some consistency between their preferences, e.g., all preferences are derived from a common metric space. The Facility location problem models such scenarios and it is a well-studied problem in social choice. We study mechanisms for facility location on graphs, which are resistant to manipulations (strategy-proof, abstention-proof, and false-name-proof) by both individuals and coalitions and are efficient (Pareto optimal). We present a family of graphs, ZV-line graphs, which we claim includes many of the basic graphs and graph families that were studied for this problem. We show a general facility location mechanism for this family which satisfies all these desired properties. Moreover, we show that this mechanism can be computed in polynomial time, it is anonymous, and it can be equivalently defined as the first Pareto optimal location, according to some pre-defined order. Finally, we discuss some generalizations and limitations of the characterization.
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