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In this paper we revisit the basic variant of the classical secretary problem. We propose a new approach in which we separate between an agent that evaluates the secretary performance and one that has to make the hiring decision. The…

Computer Science and Game Theory · Computer Science 2020-05-27 Niklas Hahn , Martin Hoefer , Rann Smorodinsky

An unknown positive number of items arrive at independent uniformly distributed times in the interval [0,1] to a selector, whose task is to pick online the last one. We show that under the assumption of an adversary determining the number…

Computer Science and Game Theory · Computer Science 2011-04-18 Johan Wästlund

We consider two variations of the classical secretary problem. * A variation of the returning secretary problem where each interviewee may appear a second time with a fixed probability p. The decision-maker observes interviewees…

Data Structures and Algorithms · Computer Science 2026-04-13 Sarthak Agrawal , Sanjeev Saxena

In the subject of optimal stopping, the classical secretary problem is concerned with optimally selecting the best of $n$ candidates when their relative ranks are observed sequentially. This problem has been extended to optimally selecting…

Probability · Mathematics 2017-12-06 Yi-Shen Lin , Shoou-Ren Hsiau , Yi-Ching Yao

The Secretary problem is a classical sequential decision-making question that can be succinctly described as follows: a set of rank-ordered applicants are interviewed sequentially for a single position. Once an applicant is interviewed, an…

Combinatorics · Mathematics 2023-03-07 Xujun Liu , Olgica Milenkovic , George V. Moustakides

The secretary problem is probably the purest model of decision making under uncertainty. In this paper we ask which advice can we give the algorithm to improve its success probability? We propose a general model that unifies a broad range…

Data Structures and Algorithms · Computer Science 2020-11-16 Paul Dütting , Silvio Lattanzi , Renato Paes Leme , Sergei Vassilvitskii

In this paper we consider two variants of the Secretary problem: The Best-or-Worst and the Postdoc problems. We extend previous work by considering that the number of objects is not known and follows either a discrete Uniform distribution…

Probability · Mathematics 2018-11-13 L. Bayon , P. Fortuny , J. M. Grau , M. M Ruiz , M. A. Oller-Marcen

In the secretary problem, a set of secretary candidates arrive in a uniformly random order and reveal their values one by one. A company, who can only hire one candidate and hopes to maximize the expected value of its hire, needs to make…

Data Structures and Algorithms · Computer Science 2026-02-16 Mohammad Mahdian , Jieming Mao , Enze Sun , Kangning Wang , Yifan Wang

We study a class of finite-action disclosure games in which the sender's preferences are state-independent and the receiver's optimal action depends only on the expected state. While receiver-preferred equilibria in these games involve full…

Theoretical Economics · Economics 2026-05-06 Denis Shishkin , Maria Titova , Kun Zhang

The secretary problem has been a focus of extensive study with a variety of extensions that offer useful insights into the theory of optimal stopping. The original solution is to set one stopping threshold that gives rise to an immediately…

Physics and Society · Physics 2023-02-08 Roberto Brera , Feng Fu

We study a generalization of the secretary problem, where decisions do not have to be made immediately upon candidates' arrivals. After arriving, each candidate stays in the system for some (random) amount of time and then leaves, whereupon…

Computer Science and Game Theory · Computer Science 2019-09-20 Thomas Kesselheim , Alexandros Psomas , Shai Vardi

We study a contest in which $N$ players sequentially draw from a distribution as many times as they want at a fixed cost per draw, with no recall, and the highest accepted value wins a prize. In the unique symmetric equilibrium, the…

Theoretical Economics · Economics 2026-04-28 Emre Ozdenoren , Murat Erkurt

We consider generalizations of the classical secretary problem, also known as the problem of optimal choice, to posets where the only information we have is the size of the poset and the number of maximal elements. We show that, given this…

Combinatorics · Mathematics 2012-06-29 Bryn Garrod , Robert Morris

In the Secretary Problem, one has to hire the best among n candidates. The candidates are interviewed, one at a time, at a random order, and one has to decide on the spot, whether to hire a candidate or continue interviewing. It is well…

Data Structures and Algorithms · Computer Science 2015-07-23 Moran Feldman , Rani Izsak

We extend the standard online worst-case model to accommodate past experience which is available to the online player in many practical scenarios. We do this by revealing a random sample of the adversarial input to the online player ahead…

Data Structures and Algorithms · Computer Science 2019-07-12 Haim Kaplan , David Naori , Danny Raz

Algorithms with predictions is a recent framework for decision-making under uncertainty that leverages the power of machine-learned predictions without making any assumption about their quality. The goal in this framework is for algorithms…

Machine Learning · Computer Science 2025-01-22 Eric Balkanski , Will Ma , Andreas Maggiori

Selective contests can impair participants' overall welfare in overcompetitive environments, such as school admissions. This paper models the situation as an optimal contest design problem with binary actions, treating effort costs as…

Theoretical Economics · Economics 2024-10-07 Penghuan Yan

A version of the classical secretary problem is studied, in which one is interested in selecting one of the b best out of a group of n differently ranked persons who are presented one by one in a random order. It is assumed that b is a…

Probability · Mathematics 2010-09-06 Chris Dietz , Dinard van der Laan , Ad Ridder

Suppose a customer is faced with a sequence of fluctuating prices, such as for airfare or a product sold by a large online retailer. Given distributional information about what price they might face each day, how should they choose when to…

Data Structures and Algorithms · Computer Science 2019-10-10 Hossein Esfandiari , MohammadTaghi HajiAghayi , Brendan Lucier , Michael Mitzenmacher

This paper studies a communication game between an uninformed decision maker and two perfectly informed senders with conflicting interests. Senders can misreport information at a cost that increases with the size of the misrepresentation.…

Theoretical Economics · Economics 2023-04-17 Federico Vaccari