Conditioning prices on search behaviour

We consider a market in which firms can partially observe each consumer's search behavior in the market. In our main model, a firm knows whether a consumer is visiting it for the first time or whether she is returning after a previous visit. Firms have an incentive to offer a lower price on a first visit than a return visit, so that new consumers are offered a "buy-now" discount. The ability to offer such discounts acts to raise all prices in the market. If firms cannot commit to their buy-later price, in many cases firms make "exploding" offers, and consumers never return to a previously sampled firm. Likewise, if firms must charge the same price to all consumers, regardless of search history, we show that they sometimes have the incentive to make exploding offers. We also consider other ways in which firms could use information about search behaviour to determine their prices.