Multi-player Diffusion Games on Graph Classes

Laurent Bulteau, Vincent Froese, Nimrod Talmon

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 $$\min \{m,n\}\ge 5$$ .