Publication Date: March 2020
Revision Date: May 2020November 2020
Consider a market with identical ﬁrms oﬀering a homogeneous good. A consumer obtains price quotes from a subset of ﬁrms and buys from the ﬁrm oﬀering the lowest price. The “price count” is the number of ﬁrms from which the consumer obtains a quote. For any given ex ante distribution of the price count, we derive a tight upper bound (under ﬁrst-order stochastic dominance) on the equilibrium distribution of sales prices. The bound holds across all models of ﬁrms’ common-prior higher-order beliefs about the price count, including the extreme cases of full information (ﬁrms know the price count) and no information (ﬁrms only know the ex ante distribution of the price count). A qualitative implication of our results is that a small ex ante probability that the price count is equal to one can lead to a large increase in the expected price. The bound also applies in a large class of models where the price count distribution is endogenously determined, including models of simultaneous and sequential consumer search.
Keywords: Search, Price Competition, Bertrand Competition, "Law of One Price", Price Count, Price Quote, Information Structure
JEL Classification Codes: D41, D42, D43, D83CFDP 2224CFDP 2224R