Identifying the most relevant competitors in a geographical market is crucial for businesses with a significant offline presence, such as hotels, restaurants, and retail stores. The specific location of a business and the geographical density of potential competitors are critical factors in determining the competitive structure. However, this task can be challenging when the potential number of competitors is large and the competition is asymmetric. In this study, we apply the Conditional Sure Independence Screening (CSIS) method to a system of demand functions for competitor identification. This method offers significant computational efficiency by estimating a marginal regression for each potential competitor, rather than a full model consisting of all potential competitors. To validate the effectiveness of the CSIS method and explore the boundary conditions of its performance, we conduct extensive simulation analyses under different spatial data-generating processes. Our findings demonstrate that the CSIS method outperforms multiple other variable selection methods and remains robust under spatial misspecifications. Then we apply the CSIS method to hotel competition in two U.S. geographical regions, illustrating how the competitive structure varies across geographical densities and market segments. Finally, we highlight how managers can strategically use the results and outline the potential of the method for other non-geographical applications.