Existence theory for spatially competitive network facility location models
Annals of Operations Research
Maximizing a Voronoi Region: The Convex Case
ISAAC '02 Proceedings of the 13th International Symposium on Algorithms and Computation
Competitive facility location: the Voronoi game
Theoretical Computer Science
On finding a guard that sees most and a shop that sells most
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Maximum Neighbour Voronoi Games
WALCOM '09 Proceedings of the 3rd International Workshop on Algorithms and Computation
The isolation game: A game of distances
Theoretical Computer Science
Min-Max payoffs in a two-player location game
Operations Research Letters
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(MATH) In the one-round Voronoi game, the first player chooses an n-point set $\PFRST$ in a square $Q$, and then the second player places another n-point set $\PSCND$ into $Q$. The payoff for the second player is the fraction of the area of $Q$ occupied by the regions of the points of $\PSCND$ in the Voronoi diagram of $\PFRST\cup\PSCND$. We give a strategy for the second player that always guarantees him a payoff of at least $\frac12+\alpha$, for a constant $\alpha0$ independent of n. This contrasts with the one-dimensional situation, with $Q=[0,1]$, where the first player can always win more than 1/2.