Abstract
We study competitive diffusion games on graphs introduced by Alon et al. [1] to model the spread of influence in social networks. Extending results of Roshanbin [7] for two players, we investigate the existence of pure Nash equilibria for at least three players on different classes of graphs including paths, cycles, and grid graphs. As a main result, we answer an open question proving that there is no Nash equilibrium for three players on \(m\times n\) grids with \(\min \{m,n\}\ge 5\).
A full version is available at http://arxiv.org/abs/1412.2544.
L. Bulteau—Supported by the Alexander von Humboldt Foundation, Bonn, Germany.
V. Froese—Supported by the DFG, project DAMM (NI 369/13).
N. Talmon—Supported by DFG Research Training Group MDS (GRK 1408).
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Bulteau, L., Froese, V., Talmon, N. (2015). Multi-player Diffusion Games on Graph Classes. In: Jain, R., Jain, S., Stephan, F. (eds) Theory and Applications of Models of Computation. TAMC 2015. Lecture Notes in Computer Science(), vol 9076. Springer, Cham. https://doi.org/10.1007/978-3-319-17142-5_18
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DOI: https://doi.org/10.1007/978-3-319-17142-5_18
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