The Price of Stability for Network Design with Fair Cost Allocation
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Nash equilibria in Voronoi games on graphs
ESA'07 Proceedings of the 15th annual European conference on Algorithms
On the Performances of Nash Equilibria in Isolation Games
COCOON '09 Proceedings of the 15th Annual International Conference on Computing and Combinatorics
Nash Equilibria for Voronoi Games on Transitive Graphs
WINE '09 Proceedings of the 5th International Workshop on Internet and Network Economics
On the performances of Nash equilibria in isolation games
Journal of Combinatorial Optimization
The competitive facility location problem in a duopoly: connections to the 1-median problem
WINE'12 Proceedings of the 8th international conference on Internet and Network Economics
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In a Voronoi game, each of a finite number of players chooses a point in some metric space. The utility of a player is the total measure of all points that are closer to him than to any other player, where points equidistant to several players are split up evenly among the closest players. In a recent paper, Dürr and Thang (2007) considered discrete Voronoi games on graphs, with a particular focus on pure Nash equilibria. They also looked at Voronoi games on cycle graphswith nnodes and kplayers. In this paper, we prove a new characterization of all Nash equilibria for these games. We then use this result to establish that Nash equilibria exist if and only if $k \leq \frac{2n}3$ or k茂戮驴 n. Finally, we give exact bounds of $\frac 94$ and 1 for the prices of anarchy and stability, respectively.