Prophet Secretary

Esfandiari, Hossein; Hajiaghayi, MohammadTaghi; Liaghat, Vahid; Monemizadeh, Morteza

doi:10.1137/15m1029394

Cited by 50 publications

(38 citation statements)

References 11 publications

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“…us, making it easier to extract revenue by o ering to good customers rst. Furthermore, this bound also matches the approximation guarantee obtained by Esfandiari et al [10], who also consider the random arrival model, but in their mechanism the sequence of prices depends on the arrival order of customers, and it is therefore adaptive (according to the de nition in this paper). Besides the natural application of our nonadaptive se ing, it is interesting to note that one can achieve this approximation factor in the random arrival model without using adaptivity.…”

Section: Introductionsupporting

confidence: 86%

Posted Price Mechanisms for a Random Stream of Customers

Correa

Foncea

Hoeksma

et al. 2017

Proceedings of the 2017 ACM Conference on Economics and Computation

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Section: Introductionsupporting

confidence: 86%

Posted Price Mechanisms for a Random Stream of Customers

Correa

Foncea

Hoeksma

et al. 2017

Proceedings of the 2017 ACM Conference on Economics and Computation

View full text Add to dashboard Cite

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“…Interestingly this bound matches the bound of Chawla et al [10] for the so called sequential posted price mechanisms (SPM) in which the arrival order of the random variables is chosen by the gambler rather than at random. Furthermore the bound also matches that of Esfandiari et al [17], however, Mathematics of Operations Research 00(0), pp. 000-000, ©0000 INFORMS their bound is obtained through a stopping rule that is adaptive.…”

Section: Related Worksupporting

confidence: 83%

“…We refer the reader to the survey of Hill and Kertz [24] for more results on prophet inequalities. More recently, Esfandiari et al [17] considered an interesting combination of the prophet inequality and the secretary problem, now known as the prophet secretary problem. This is basically a prophet inequality but the the random variables are presented in a random order to the gambler.…”

mentioning

confidence: 99%

Posted Price Mechanisms and Optimal Threshold Strategies for Random Arrivals

et al. 2021

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The classic prophet inequality states that, when faced with a finite sequence of nonnegative independent random variables, a gambler who knows the distribution and is allowed to stop the sequence at any time, can obtain, in expectation, at least half as much reward as a prophet who knows the values of each random variable and can choose the largest one. In this work, we consider the situation in which the sequence comes in random order. We look at both a nonadaptive and an adaptive version of the problem. In the former case, the gambler sets a threshold for every random variable a priori, whereas, in the latter case, the thresholds are set when a random variable arrives. For the nonadaptive case, we obtain an algorithm achieving an expected reward within at least a 0.632 fraction of the expected maximum and prove that this constant is optimal. For the adaptive case with independent and identically distributed random variables, we obtain a tight 0.745-approximation, solving a problem posed by Hill and Kertz in 1982. We also apply these prophet inequalities to posted price mechanisms, and we prove the same tight bounds for both a nonadaptive and an adaptive posted price mechanism when buyers arrive in random order.

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“…Surprisingly, Ehsani et al [2018] show that the same bound of 1−1/e can even be obtained with a single threshold. This may appear to contradict the upper bound bound of 1 2 of Esfandiari et al [2015], however, the subtle issue is that they allow to break ties at random. In particular, if in the previous example the gambler sets T = 1 and if there is a tie, she stops with probability 1/n.…”

Section: Prophet Secretarymentioning

confidence: 96%

“…In this version, the random variables are shown to the gambler in random order, as in the secretary problem. The problem was first studied by Esfandiari et al [2015] who found a bound of 1 − 1/e. Their algorithm defines a nonincreasing sequence of n thresholds that only depend on the expecta-• 63 tion of the maximum of the random variables, and the gambler stops whenever the currently sampled value surpasses the threshold corresponding to the current time.…”

Section: Introductionmentioning

confidence: 99%

Recent developments in prophet inequalities

et al. 2019

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The classic prophet inequality states that, when faced with a finite sequence of non-negative independent random variables, a gambler who knows their distribution and is allowed to stop the sequence at any time, can obtain, in expectation, at least half as much reward as a prophet who knows the values of each random variable and can choose the largest one. Following this classic theorem from the 70s, many results have been obtained for several related optimal stopping problems. Moreover, the recently uncovered connection between prophet inequalities and posted price mechanisms, has given the area a new surge. We survey some new developments and highlight some compelling open problems.

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Prophet Secretary

Cited by 50 publications

References 11 publications

Posted Price Mechanisms for a Random Stream of Customers

Posted Price Mechanisms for a Random Stream of Customers

Posted Price Mechanisms and Optimal Threshold Strategies for Random Arrivals

Recent developments in prophet inequalities

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