Pure-strategy Nash equilibria on competitive diffusion games

This paper treats two types of competitive facility location games on graphs: information diffusion games and discrete Voronoi games. Both of these games can be regarded as models of the rumor spreading processes on the networks, where each player of the game wants to select an influencer who can widely spread information throughout the network. For each game, given a graph and the number of players, we are interested in whether there exist pure Nash equilibria or not. In this paper, we discuss the existence of pure Nash equilibria on graphs with small diameter, path graphs, and cycle graphs. The results include the behavior of the discrete Voronoi games on graphs with diameter two, and the complete characterization of the existence of the pure Nash equilibria in the discrete Voronoi games and information diffusion games on path graphs.