Prices as Optimal Competitive Sales Mechanisms

We analyze the efficiency properties of price posting in a market where sellers compete for the buyers' business. They key feature of the approach is to investigate price posting as an equilibrium outcome even if sellers can compete with other mechanisms. When buyers are homogeneous, we show equivalence between price posting and a large class of competing mechanisms, including second price auctions. When buyers are heterogeneous, posted prices are able to perfectly screen ex-ante because different buyers endogenously choose to trade at different prices. As a result, search is non-random and buyers sort themselves by choosing different prices. Whether price posting is efficient depends on the matching technology. Prices are efficient and arise in equilibrium when meetings are bilateral, which is the case in competitive search models. When meetings are multilateral, as in directed search models, price posting is not an equilibrium. In that case, the efficient mechanism screens ex post amongst multiple buyers and necessarily involves random search. The conclusion for market design is that the prevalence of price posting over auctions depends crucially on the properties of the meeting technology.