FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
Competitive facility location: the Voronoi game
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FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
The one-round Voronoi game replayed
Computational Geometry: Theory and Applications - Special issue on the 19th European workshop on computational geometry - EuroCG 03
STACS'99 Proceedings of the 16th annual conference on Theoretical aspects of computer science
MFCS '08 Proceedings of the 33rd international symposium on Mathematical Foundations of Computer Science
$\mathcal{NP}$-Hardness of Pure Nash Equilibrium in Scheduling and Connection Games
SOFSEM '09 Proceedings of the 35th Conference on Current Trends in Theory and Practice of Computer Science
On the Performances of Nash Equilibria in Isolation Games
COCOON '09 Proceedings of the 15th Annual International Conference on Computing and Combinatorics
The isolation game: A game of distances
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Nash Equilibria for Voronoi Games on Transitive Graphs
WINE '09 Proceedings of the 5th International Workshop on Internet and Network Economics
A note on competitive diffusion through social networks
Information Processing Letters
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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
Nash Equilibria for competitive information diffusion on trees
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Information diffusion on the iterated local transitivity model of online social networks
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NP-hardness of pure Nash equilibrium in Scheduling and Network Design Games
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In this paper we study a game where every player is to choose a vertex (facility) in a given undirected graph. All vertices (customers) are then assigned to closest facilities and a player's payoff is the number of customers assigned to it. We show that deciding the existence of a Nash equilibrium for a given graph is NP-hard. We also introduce a new measure, the social cost discrepancy, defined as the ratio of the costs between the worst and the best Nash equilibria. We show that the social cost discrepancy in our game is Ω(&radicn/k) and O(√kn), where n is the number of vertices and k the number of players.