Recent Developments in Prophet Inequalities

Jose Correa*, Patricio Foncea, Ruben Hoeksma, Tim Oosterwijk, Tjark Vredeveld

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

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Abstract

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.
Original languageEnglish
Pages (from-to)61-70
Number of pages10
JournalSigecom exchanges
Volume17
Issue number1
DOIs
Publication statusPublished - Apr 2019

Keywords

  • Optimal stopping
  • Prophet inequalities
  • Posted price mechanisms
  • Mechanism design
  • STOP RULE
  • SUPREMUM EXPECTATIONS

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