Multi-Player Diffusion Games on Graph Classes

Laurent Bulteau (1, 2) , Vincent Froese (1) , Nimrod Talmon (1)

1 SWT - TUB - Department of Software Engineering and Theoretical Computer Science
2 LIGM - Laboratoire d'Informatique Gaspard-Monge

We study competitive diffusion games on graphs introduced by Alon et al. to model the spread of influence in social networks. Extending results of Roshanbin for two players, we investigate the existence of pure Nash equilibriafor at least three players on different classes of graphs including paths, cycles, grid graphs and hypercubes; as a main contribution, we answer an open question proving that there is no Nash equilibriumfor three players on m × n grids with min {m, n} ≥ 5. Further, extending results of Etesami and Basar for two players, we prove the existence of pure Nash equilibriafor four players on every d-dimensional hypercube.

Domaines: Algorithme et structure de données [cs.DS]

Laurent Bulteau, Vincent Froese, Nimrod Talmon. Multi-Player Diffusion Games on Graph Classes. Internet Mathematics, 2016, 12 (6), pp.363 - 380. ⟨10.1080/15427951.2016.1197167⟩. ⟨hal-01494989⟩