Posted price mechanisms for a random stream of customers

Abstract

Posted price mechanisms constitute a widely used way of selling items to strategic consumers. Although subop-timal, the a ractiveness of these mechanisms comes from their simplicity and easy implementation. In this pa-per, we investigate the performance of posted price mechanisms when customers arrive in an unknown randomorder. We compare the expected revenue of these mechanisms to the expected revenue of the optimal auction intwo di erent se ings. Namely, the nonadaptive se ing in which all o ers are sent to the customers beforehand,and the adaptive se ing in which an o er is made when a consumer arrives. For the nonadaptive case, weobtain a strategy achieving an expected revenue within at least a 1−1/efraction of that of the optimal auction.We also show that this bound is tight, even if the customers have i.i.d. valuations for the item. For the adaptivecase, we exhibit a posted price mechanism that achieves a factor 0.745 of the optimal revenue, when the custo-mers have i.i.d. valuations for the item. Furthermore, we prove that our results extend to the prophet inequalityse ing and in particular our result for i.i.d. random valuations resolves a problem posed by Hill and Kertz.