Working Paper: CEPR ID: DP14521
Authors: Stephen Morris; Dirk Bergemann; Benjamin A. Brooks
Abstract: Consider a market with many identical firms offering a homogeneous good. Aconsumer obtains price quotes from a subset of firms and buys from the firm offeringthe lowest price. The \price count" is the number of firms from which the consumerobtains a quote. For any given ex ante distribution of the price count, we obtain a tightupper bound (under first-order stochastic dominance) on the equilibrium distributionof sale prices. The bound holds across all models of firms' common-prior higher-orderbeliefs about the price count, including the extreme cases of complete information(firms know the price count exactly) and no information (firms only know the ex antedistribution of the price count). A qualitative implication of our results is that even asmall ex ante probability that the price count is one can lead to dramatic increases inthe expected price. The bound also applies in a wide class of models where the pricecount distribution is endogenized, including models of simultaneous and sequentialconsumer search.
Keywords: search; price competition; bertrand competition; law of one price; price count; price quote; information structure; bayes; correlated equilibrium
JEL Codes: D41; D42; D43; D83
Edges that are evidenced by causal inference methods are in orange, and the rest are in light blue.
| Cause | Effect |
|---|---|
| price count distribution (D39) | equilibrium sale price distribution (D39) |
| price count distribution indicates higher likelihood of monopoly (D42) | expected sale prices (P22) |
| incomplete information (D89) | expected sale price (D44) |