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 |
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Keywords
- Lower bounds
- Multiple stopping
- Odds problem
- Optimal stopping
ASJC Scopus subject areas
- Mathematics(all)
- Computer Science Applications
- Management Science and Operations Research
Cite this
Lower bounds for bruss' odds problem with multiple stoppings. / Matsui, Tomomi; Ano, Katsunori.
In: Mathematics of Operations Research, Vol. 41, No. 2, 01.05.2016, p. 700-714.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Lower bounds for bruss' odds problem with multiple stoppings
AU - Matsui, Tomomi
AU - Ano, Katsunori
PY - 2016/5/1
Y1 - 2016/5/1
N2 - 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.
AB - 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.
KW - Lower bounds
KW - Multiple stopping
KW - Odds problem
KW - Optimal stopping
UR - http://www.scopus.com/inward/record.url?scp=84963750713&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84963750713&partnerID=8YFLogxK
U2 - 10.1287/moor.2015.0748
DO - 10.1287/moor.2015.0748
M3 - Article
AN - SCOPUS:84963750713
VL - 41
SP - 700
EP - 714
JO - Mathematics of Operations Research
JF - Mathematics of Operations Research
SN - 0364-765X
IS - 2
ER -