Statistical network models allow us to study the co-evolution between the products and the social aspects of a market system, by modeling these components and their interactions as graphs. In this paper, we study competition between different car models using network theory, with a focus on how product attributes (like fuel economy and price) affect which cars are considered together and which cars are finally bought by customers. Unlike past work, where most systems have been studied with the assumption that relationships between competitors are binary (i.e., whether a relationship exists or not), we allow relationships to take strengths (i.e., how strong a relationship is). Specifically, we use valued Exponential Random Graph Models and show that our approach provides a significant improvement over the baselines in predicting product co-considerations as well as in the validation of market share. This is also the first attempt to study aggregated purchase preference and car competition using valued directed networks.