In 3G wireless technologies, competitive operators are assigned a fixed part of the spectrum from long-term auctions. This is known to lead to utilization inefficiencies because some providers can be congested while others are lightly used. Moreover it forbids the entrance of new candidate providers. There is now a stream of work dealing with spectrum sharing among providers to lead to a better utilization. In this paper, we study an intermediate model of price competition between two providers having a fixed (licensed) part of the spectrum, but where a remaining part (an unlicensed band) can be used in case of congestion, and is therefore shared. We discuss the existence and uniqueness of the Nash equilibrium in the pricing game when demand is distributed among providers according to Wardrop’s principle so that users choose the least expensive perceived price (when congestion pricing is used), and investigate the influence of the shared band on social and user welfare.