The Stahl model is one of the most applied consumer search models, with many applications and an empirical background. The present paper explores an extension where sellers have asymmetries, which is mostly excluded by the literature. Sellers with heterogeneous numbers of stores are introduced, reflecting a typical market structure. As in the original Stahl model, a market consists of several sellers, and consumers, where some face a cost when sequentially searching. The paper shows that no symmetric Nash equilibrium exists in the extension. Additional results suggest that smallest sellers will be the ones offering the lowest prices, in line with several real world examples provided in the paper. However, profits remain in most cases fixed per store, making a larger firm more profitable, yet with lower quantity sold. The findings suggest that on some level price dispersion will still exist, together with some level of price stickiness, both observed in reality.
Sequential Consumer Search Oligopoly Asymmetric NE