Abstract
Generalized location problems withn agents are considered, who each report a point inm-dimensional Euclidean space. A solution assigns a compromise point to thesen points, and the individual utilities for this compromise point are equal to the negatives of the distances to the individual positions. These distances are measured by a given strictly convex norm, common to all agents. Form=2, it is shown that if a Pareto optimal, strategy-proof and anonymous solution exists, thenn must be odd, and the solution is obtained by taking the median coordinatewise, where the coordinates refer to a basis that is orthogonal with respect to the given norm. Furthermore, in that case (m=2) such a solution always exists. Form > 2, existence of a solution depends on the norm.
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Supported by a grant from the Cooperation Centre Tilburg and Eindhoven University.
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Peters, H., van der Stel, H. & Storcken, T. Generalized median solutions, strategy-proofness and strictly convex norms. ZOR Zeitschrift für Operations Research Methods and Models of Operations Research 38, 19–53 (1993). https://doi.org/10.1007/BF01416005
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DOI: https://doi.org/10.1007/BF01416005