Posted price mechanisms for a random stream of customers

Posted price mechanisms constitute a widely used way of selling items to strategic consumers. Although suboptimal, the affractiveness of these mechanisms comes from their simplicity and easy implementation. In this paper, we investigate the performance of posted price mechanisms when customers arrive in an unknown random order. We compare the expected revenue of these mechanisms to the expected revenue of the optimal auction in two different settings. 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, we obtain a strategy achieving an expected revenue within at least a 11e fraction 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 adaptive case, we exhibit a posted price mechanism that achieves a factor 0:745 of the optimal revenue, when the customers have i.i.d. valuations for the item. Furthermore, we prove that our results extend to the prophet inequality se.ing and in particular our result for i.i.d. random valuations resolves a problem posed by Hill and Kertz [13].