The existing theoretical and empirical literature to investigate the existence of local market power is typically based on spatial competition models in the tradition of Hotelling's (1929) linear city and Salop's (1979) circular city. In models of this kind, strong assumptions are made that lead to a spatial homogeneity (symmetry) of firms in a highly stylized one-dimensional market space. However, some of these assumptions are hardly satisfied in many (retail) markets. The present thesis builds on a recent model by Chen and Riordan (2007), in which the market is characterized by a star-shaped graph with a central intersection. In an extension of Chen and Riordan, I distinguish between firms close to the center and firms in the periphery of a spatial market. This spatial heterogeneity leads to an asymmetric competition between firms. A central firm directly competes with a larger number of firms than remote firms do. The implications of the theoretical model are tested in two empirical applications to the retail gasoline market of Vienna and Austria. Using station level data on diesel prices, I estimate price reaction functions for gasoline stations in two different approaches. In the first approach the Austrian retail gasoline market is divided into numerous highly localized and delimited markets. The second approach analyzes the metropolitan area of Vienna and treats the whole market as one big network of gasoline stations, which are connected through the road network. In both approaches I apply econometric spatial autoregressive (SAR) models. The estimated parameters of the slopes of the reaction functions are used to evaluate the impact of individual gasoline stations on equilibrium market prices depending on their location within the market (network). All results obtained provide evidence for (more) central suppliers serving as a stronger reference in pricing than (rather) remote suppliers. Thus, the assumption of a symmetry in spatial competition which is usually implied by spatial competition models in theoretical and applied research, is rejected. (author's abstract)