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Title
Japanese: 
English:Lower Bounds for Bruss’ Odds Problem with Multiple Stoppings 
Author
Japanese: 松井 知己, 穴太克則.  
English: Tomomi Matsui, Katsunori Ano.  
Language English 
Journal/Book name
Japanese: 
English:Mathematics of Operations Research 
Volume, Number, Page Volume 41    No. 2    pp. 700-714
Published date Feb. 10, 2016 
Publisher
Japanese: 
English:INFORMS 
Conference name
Japanese: 
English: 
Conference site
Japanese: 
English: 
File
DOI https://doi.org/10.1287/moor.2015.0748
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.

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