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

Xin Chen (), Wenjing Liu (), Qingqin Nong () and Qizhi Fang ()
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Xin Chen: Ocean University of China
Wenjing Liu: Ocean University of China
Qingqin Nong: Ocean University of China
Qizhi Fang: Ocean University of China

Journal of Combinatorial Optimization, 2022, vol. 44, issue 5, No 16, 3520-3534

Abstract: 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 } .

Keywords: Facility location game; Nash equilibrium; Price of anarchy; Dual role; Lipschitz function (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s10878-022-00905-7

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