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 language | English |
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Pages (from-to) | 700-714 |
Number of pages | 15 |
Journal | Mathematics of Operations Research |
Volume | 41 |
Issue number | 2 |
DOIs | |
Publication status | Published - 2016 May |
Keywords
- Lower bounds
- Multiple stopping
- Odds problem
- Optimal stopping
ASJC Scopus subject areas
- Mathematics(all)
- Computer Science Applications
- Management Science and Operations Research