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Proportional Fairness in Obnoxious Facility Location

Author

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  • Haris Aziz
  • Alexander Lam
  • Bo Li
  • Fahimeh Ramezani
  • Toby Walsh

Abstract

We consider the obnoxious facility location problem (in which agents prefer the facility location to be far from them) and propose a hierarchy of distance-based proportional fairness concepts for the problem. These fairness axioms ensure that groups of agents at the same location are guaranteed to be a distance from the facility proportional to their group size. We consider deterministic and randomized mechanisms, and compute tight bounds on the price of proportional fairness. In the deterministic setting, not only are our proportional fairness axioms incompatible with strategyproofness, the Nash equilibria may not guarantee welfare within a constant factor of the optimal welfare. On the other hand, in the randomized setting, we identify proportionally fair and strategyproof mechanisms that give an expected welfare within a constant factor of the optimal welfare.

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  • Haris Aziz & Alexander Lam & Bo Li & Fahimeh Ramezani & Toby Walsh, 2023. "Proportional Fairness in Obnoxious Facility Location," Papers 2301.04340, arXiv.org.
    • Handle: RePEc:arx:papers:2301.04340
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    References listed on IDEAS

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    1. Chien, Steve & Sinclair, Alistair, 2011. "Convergence to approximate Nash equilibria in congestion games," Games and Economic Behavior, Elsevier, vol. 71(2), pages 315-327, March.
    2. Dimitris Bertsimas & Vivek F. Farias & Nikolaos Trichakis, 2011. "The Price of Fairness," Operations Research, INFORMS, vol. 59(1), pages 17-31, February.
    3. Melo, M.T. & Nickel, S. & Saldanha-da-Gama, F., 2009. "Facility location and supply chain management - A review," European Journal of Operational Research, Elsevier, vol. 196(2), pages 401-412, July.
    4. Haris Aziz & Alexander Lam & Mashbat Suzuki & Toby Walsh, 2022. "Random Rank: The One and Only Strategyproof and Proportionally Fair Randomized Facility Location Mechanism," Papers 2205.14798, arXiv.org, revised Jun 2022.
    5. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
    6. Ľuboš Buzna & Michal Koháni & Jaroslav Janáček, 2014. "An Approximation Algorithm for the Facility Location Problem with Lexicographic Minimax Objective," Journal of Applied Mathematics, Hindawi, vol. 2014, pages 1-12, June.
    7. Yukun Cheng & Qiaoming Han & Wei Yu & Guochuan Zhang, 2019. "Strategy-proof mechanisms for obnoxious facility game with bounded service range," Journal of Combinatorial Optimization, Springer, vol. 37(2), pages 737-755, February.
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