@MISC{Esfandiari15prophetsecretary, author = {Hossein Esfandiari and Morteza Monemizadeh and et al.}, title = {Prophet Secretary}, year = {2015} }

Share

OpenURL

Abstract

Optimal stopping theory is a powerful tool for analyzing scenarios such as online auctions in which we generally require optimizing an objective function over the space of stopping rules for an allocation process under uncertainty. Perhaps the most classic problems of stopping theory are the prophet inequal-ity problem and the secretary problem. The classical prophet inequality states that by choosing the same threshold OPT/2 for every step, one can achieve the tight competitive ratio of 0.5. On the other hand, for the basic secretary problem, the optimal strategy achieves the tight competitive ratio of 1/e ≈ 0.36 In this paper, we introduce prophet secretary, a natural combination of the prophet inequality and the secretary problems. An example motivation for our problem is as follows. Consider a seller that has an item to sell on the market to a set of arriving customers. The seller knows the types of customers that may be interested in the item and he has a price distribution for each type: the price offered by a customer of a type is anticipated to be drawn from the corresponding distribution. However, the customers arrive in a random order. Upon the arrival of a customer, the seller makes an irrevocable decision whether to sell the item at the offered price. We address the question of finding a strategy for selling the item at a high price. In particular, we show that by using a single uniform threshold one cannot break the 0.5 barrier of