Exploding offers and buy-now discounts

We consider a market with sequential consumer search in which firms can distinguish potential customers visiting for the first time from returning visitors. We show that firms often have an incentive to make it costly for its visitors to return after investigating rivals, either by making an "exploding offer" (which permits no return once the consumer leaves) or by offering a "buy-now discount" (which makes the price paid by first-time visitors lower than that for returning visitors). Prices often increase when return costs are artificially increased in this manner, and this harms consumers and market performance. If firms cannot commit to their buy-later price the outcome depends on whether there is an intrinsic cost of returning to a firm: if the intrinsic return cost is zero, it is often an equilibrium for firms not to offer any buy-now discount; if the return cost is positive, firms are forced to make exploding offers.