  The paper explores a consumer search setting where the sellers have
asymmetries. The model is an extension of the popular Stahl Model, which is
widely used in the literature. The extension introduces sellers with
heterogeneous stores number, reflecting the typical market structure. The
market consists of several sellers heterogeneous in size consumers, some of
which face a cost when sequentially searching. The paper shows that no
symmetric model exist in the extension and asymmetric NE of the Stahl model are
found for comparison. Additional results suggest that smallest sellers will be
the ones offering 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 sold quantity. The
findings suggest that on some level price dispersion will still exist, together
with some level of price stickiness, both observed in reality.
