Multi-player Diffusion Games on Graph Classes

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 [8] for two players, we investigate the existence of pure Nash equilibria for 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 equilibrium for three players on m×n grids with min{m, n} ≥ 5. Further, extending results of Etesami and Basar [3] for two players, we prove the existence of pure Nash equilibria for four players on every d-dimensional hypercube.