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The One-Round Multi-player Discrete Voronoi Game on Grids and Trees

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Computing and Combinatorics (COCOON 2019)

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Abstract

Basing on the two-player Voronoi game introduced by Ahn et al. [1] and the multi-player diffusion game introduced by Alon et al. [2] on grids, we investigate the following one-round multi-player discrete Voronoi game on grids and trees. There are n players playing this game on a graph \(G=(V,E)\). Each player chooses an initial vertex from the vertex set of the graph and tries to maximize the size of the nearest vertex set. As the main result, we give sufficient conditions for the existence/non-existence of pure Nash equilibrium in 4-player Voronoi game on grids and only a constant gap leaves unknown. We further consider this game with more than 4 players and construct a family of strategy profiles, which are pure Nash equilibrium on sufficiently narrow graphs. Besides, we investigate the game with 3 players on trees and design a linear time/space algorithm to decide the existence of a pure Nash equilibrium.

This work was supported in part by the National Natural Science Foundation of China Grants No. 61433014, 61832003, 61761136014, 61872334, 61502449, the 973 Program of China Grant No. 2016YFB1000201, and K.C. Wong Education Foundation.

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Authors and Affiliations

  1. CAS Key Lab of Network Data Science and Technology, Institute of Computing Technology, Chinese Academy of Sciences, Beijing, China

    Xiaoming Sun, Yuan Sun, Zhiyu Xia & Jialin Zhang

  2. University of Chinese Academy of Sciences, Beijing, China

    Xiaoming Sun, Yuan Sun, Zhiyu Xia & Jialin Zhang

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  1. Xiaoming Sun
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  2. Yuan Sun
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  3. Zhiyu Xia
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  4. Jialin Zhang
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Correspondence to Zhiyu Xia .

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Editors and Affiliations

  1. The University of Texas at Dallas, Richardson, TX, USA

    Ding-Zhu Du

  2. Xidian University, Xi'an, China

    Zhenhua Duan

  3. Xidian University, Xi'an, China

    Cong Tian

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Sun, X., Sun, Y., Xia, Z., Zhang, J. (2019). The One-Round Multi-player Discrete Voronoi Game on Grids and Trees. In: Du, DZ., Duan, Z., Tian, C. (eds) Computing and Combinatorics. COCOON 2019. Lecture Notes in Computer Science(), vol 11653. Springer, Cham. https://doi.org/10.1007/978-3-030-26176-4_44

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  • DOI: https://doi.org/10.1007/978-3-030-26176-4_44

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-26175-7

  • Online ISBN: 978-3-030-26176-4

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