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Optimality of the coordinate-wise median mechanism for strategyproof facility location in two dimensions

Goel, Sumit and Hann-Caruthers, Wade (2022) Optimality of the coordinate-wise median mechanism for strategyproof facility location in two dimensions. Social Choice and Welfare . ISSN 0176-1714. doi:10.1007/s00355-022-01435-1. (In Press)

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We consider the facility location problem in two dimensions. In particular, we consider a setting where agents have Euclidean preferences, defined by their ideal points, for a facility to be located in ℝ². We show that for the p-norm (p ≥ 1) objective, the coordinate-wise median mechanism (CM) has the lowest worst-case approximation ratio in the class of deterministic, anonymous, and strategyproof mechanisms. For the minisum objective and an odd number of agents n, we show that CM has a worst-case approximation ratio (AR) of √2[(√(n² + 1))/(n + 1)]. For the p-norm social cost objective (p ≥ 2), we find that the AR for CM is bounded above by 2^(3/2 − 2/p. We conjecture that the AR of CM actually equals the lower bound 2^(1 − (1/p)) (as is the case for p = 2 and p = ∞) for any p ≥ 2.

Item Type:Article
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URLURL TypeDescription ReadCube access
Goel, Sumit0000-0003-3266-9035
Hann-Caruthers, Wade0000-0002-4273-6249
Additional Information:We are grateful to Arunava Sen, Federico Echenique, Tom Palfrey, Omer Tamuz, Debasis Mishra, the Editor Clemens Puppe, and referees for this journal, as well as referees and participants at the Winter School of the Econometric Society at the Delhi School of Economics (2019), the Meeting of the Society for Social Choice and Welfare (2022), and the Symposium on Algorithmic Game Theory (2022) for helpful comments and suggestions. An earlier version of this paper circulated under the title “Coordinate-wise median: Not bad, Not bad, Pretty good”.
Record Number:CaltechAUTHORS:20221103-652750400.29
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ID Code:117706
Deposited By: Research Services Depository
Deposited On:16 Nov 2022 22:47
Last Modified:16 Nov 2022 22:47

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