Consumer Search with Chain Stores

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.