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Bounding quality of pure Nash equilibria in dual-role facility location games

Author

Listed:
  • Xin Chen

    (Ocean University of China)

  • Wenjing Liu

    (Ocean University of China)

  • Qingqin Nong

    (Ocean University of China)

  • Qizhi Fang

    (Ocean University of China)

Abstract

We study a dual-role game setting of locating facilities in a metric space where each agent can open a facility at her location or be a customer to receive the service, and an opening cost function is given to represent the cost of opening a facility at some specific location. We first show the existence of pure Nash equilibria (PNE) in such games by a polynomial-time algorithm, then use the price of anarchy (PoA) to measure the quality of PNE under social objectives of minimizing the maximum/social cost. For dual-role facility location games with general opening cost functions, we show the PoA under maximum/social cost can tend to be infinite. However, for games with L-Lipschitz conditioned opening cost functions where $$L\ge 0$$ L ≥ 0 is a given parameter, the PoA under maximum cost is exactly $$L+1$$ L + 1 and the PoA under social cost is bounded by the interval $$\left[ (n+L)/3, n+\max \{L-1,0\}\right] $$ ( n + L ) / 3 , n + max { L - 1 , 0 } .

Suggested Citation

  • Xin Chen & Wenjing Liu & Qingqin Nong & Qizhi Fang, 2022. "Bounding quality of pure Nash equilibria in dual-role facility location games," Journal of Combinatorial Optimization, Springer, vol. 44(5), pages 3520-3534, December.
    • Handle: RePEc:spr:jcomop:v:44:y:2022:i:5:d:10.1007_s10878-022-00905-7
    DOI: 10.1007/s10878-022-00905-7
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    References listed on IDEAS

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    1. Osborne Martin J., 1993. "Candidate Positioning and Entry in a Political Competition," Games and Economic Behavior, Elsevier, vol. 5(1), pages 133-151, January.
    2. Anthony Downs, 1957. "An Economic Theory of Political Action in a Democracy," Journal of Political Economy, University of Chicago Press, vol. 65(2), pages 135-135.
    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. Omer Ben-Porat & Moshe Tennenholtz, 2019. "Multiunit Facility Location Games," Mathematics of Operations Research, INFORMS, vol. 44(3), pages 865-889, August.
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