Recent trends in wireless networking such as small cells and network function virtualization, strongly suggest that the future cellular network will consist of many sub-networks controlled by self-interest operators competing for a share of the revenues associated with the high demand for service. This paper attempts to analyze the future network performance under these new market conditions, taking into account not only engineering properties of the sub-networks, e.g., spectral efficiency, but economic properties as well, i.e., service pricing. Going beyond previous related works, large scale infrastructure deployments over wide geographical areas, targeting a large number of users, are explicitly considered. The focus of the analysis is on the effects of different deployment densities (in units of average number of small cells per unit area) among competing operators as well as random placement of small cells. A game-theoretic system analysis is employed with market equilibrium characterization obtained analytically for the practical cases of two competing operators with arbitrary network characteristics and multiple competing operators with similar network characteristics. Closed form expressions for user and operator utilities at equilibrium are provided, revealing, among others, that extreme infrastructure densification, even though desirable from a purely engineering perspective, may not lead to stable market conditions under the considered competition model.