Multi-layer network formation via a Colonel Blotto game

We introduce a two-player network formation game based on the classical Colonel Blotto game. We consider a scenario where there is a common set of nodes and each player in the game designs a network layer by purchasing a set of edges between these nodes. We assume that players have a limited budget with which to bid on each edge and the utility of a given set of edges to a player is a function of the resulting network layer. We characterize the ranges of player budgets for which the game admits pure Nash equilibria for utility functions that depend on the component sizes and diameter of the formed networks.