Lower bounds for bruss' odds problem with multiple stoppings

Tomomi Matsui, Katsunori Ano

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

This paper addresses Bruss' odds problem with multiple stopping chances. A decision maker sequentially observes a sequence of independent 0/1 (failure/success) random variables to correctly predict the last success with multiple stopping chances. First, we give a nontrivial lower bound of the probability of win (obtaining the last success) for the problem with m-stoppings. Next, we show that the asymptotic value for each classical secretary problem with multiple stoppings attains our lower bound. Finally, we prove a conjecture on the classical secretary problem, which gives a connection between the probability of win and the threshold values of the optimal stopping strategy.

Original languageEnglish
Pages (from-to)700-714
Number of pages15
JournalMathematics of Operations Research
Volume41
Issue number2
DOIs
Publication statusPublished - 2016 May 1

Keywords

  • Lower bounds
  • Multiple stopping
  • Odds problem
  • Optimal stopping

ASJC Scopus subject areas

  • Mathematics(all)
  • Computer Science Applications
  • Management Science and Operations Research

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