With the increasing demand for wireless services, spectrum management agencies and service providers (SPs) are seeking more flexible mechanisms for spectrum sharing to accommodate this growth. Such mechanisms impact the market dynamics of competitive SPs. Prior market models of spectrum sharing largely focus on scenarios where competing SPs had identical coverage areas. We depart from this and consider a scenario in which two competing SPs have overlapping but distinct coverage areas. We study the resulting competition using a Cournot model. Our findings reveal that with limited shared bandwidth, SPs might avoid overlapping areas to prevent potential losses due to interference. Sometimes SPs can strategically cooperate by agreeing not to provide service in the overlapping areas and, surprisingly, customers might also benefit from such cooperation under certain circumstances. Overall, market outcomes exhibit complex behaviors that are influenced by the sizes of coverage areas and the bandwidth of the shared spectrum.