This paper investigates a scenario where multiple network service providers (NSPs) compete to provide wireless connectivity to a set of users. The users could either be a single mobile device, a set of localized Internet-of-Things (IoT) devices, or even a campus-wide network requiring wireless backhaul. The NSPs compete with one another to provide wireless service to the users by strategically allocating the available bandwidth so as to maximize their total payoff. The NSPs present each user with an offer to provide wireless connectivity using a certain amount of bandwidth. Users then decide to connect to that NSP whose offered bandwidth maximizes their utility function. Under such an architecture, this paper focuses on the optimal bandwidth allocation strategies for the NSPs. Such a problem is best modeled using a classical problem in game theory called the Colonel Blotto game-a multidimensional strategic resource allocation game. We show that the problem of spectrum allocation can be reframed as a Colonel Blotto game and analyze the mixed strategies that achieve Nash equilibrium. Depending on whether spectrum is treated a discrete or a continuous resource, we take recourse to either existing theoretical results or rely on numerical techniques to establish the equilibrium-achieving mixed strategies. We finally discuss interesting aspects about these mixed strategies, including an intrinsic user-association mechanism that emerges when spectral efficiency is taken into consideration.