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This game has been studied in Hee-Kap Ahn, Siu-Wing Cheng, Otfried Cheong, Mordecai Golin, René van Oostrum: "Competitive facility location: the Voronoi game" Theoretical Computer Science 310, 2004, pp 457-467 There also are lots of follow-up works, as for instance Sayan Bandyapadhyay, Aritra Banik, Sandip Das, Hirak Sarkar: "Voronoi game on ...



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