Abstract
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 graphs with n nodes and k players. 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 ≥ n. Finally, we give exact bounds of \(\frac 94\) and 1 for the prices of anarchy and stability, respectively.
This work was partially supported by the IST Program of the European Union under contract number IST-15964 (AEOLUS).
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Mavronicolas, M., Monien, B., Papadopoulou, V.G., Schoppmann, F. (2008). Voronoi Games on Cycle Graphs. In: Ochmański, E., Tyszkiewicz, J. (eds) Mathematical Foundations of Computer Science 2008. MFCS 2008. Lecture Notes in Computer Science, vol 5162. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-85238-4_41
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DOI: https://doi.org/10.1007/978-3-540-85238-4_41
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