The Sorting Effect of Price Competition

It is well known that a monopolist selling a single good, say a painting, can extract higher rents running an auction-type mechanism rather than posting a fixed price. In competitive markets, for example selling used books on line, price posting is often more prevalent than auctions. While auctions dominate price posting even in a competitive market, we show in this paper that price posting is remarkably effective because under competition buyers sort into differently priced markets ex ante. In auctions, buyers are screened ex post. We find that the gains from auctions relative to price posting vanish as the dispersion of valuations of the buyers decreases. We show that in the presence of frictions in auctions markets, for example the presence of shill bidders or the opportunity cost of time for bidding, the auction equilibrium unravels and price posting arises as the unique equilibrium mechanism.