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 |
|---|---|
| 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 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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Cite this
Matsui, T., & Ano, K. (2016). Lower bounds for bruss' odds problem with multiple stoppings. Mathematics of Operations Research, 41(2), 700-714. https://doi.org/10.1287/moor.2015.0748