Competitive facility location: the Voronoi game

Authors:
Hee-Kap Ahn;Siu-Wing Cheng;Otfried Cheong;Mordecai Golin;René van Oostrum
Affiliations:
Image Media Research Center, Korea Institute of Science & Technology, P.O. Box 131, CheongRyang, Seoul, South Korea;Department of Computer Science, HKUST, Clear Water Bay, Kowloon, Hong Kong;Institute of Information & Computing Sciences, Utrecht University, Netherlands;Department of Computer Science, HKUST, Clear Water Bay, Kowloon, Hong Kong;Institute of Information & Computing Sciences, Utrecht University, Netherlands
Venue:
Theoretical Computer Science
Year:
2004

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Abstract

We consider a competitive facility location problem with two players. Players alternate placing points, one at a time, into the playing arena, until each of them has placed n points. The arena is then subdivided according to the nearest-neighbor rule, and the player whose points control the larger area wins. We present a winning strategy for the second player, where the arena is a circle or a line segment. We permit variations where players can play more than one point at a time, and show that the first player can ensure that the second player wins by an arbitrarily small margin.