Lower Bounds for Bruss' Odds Problem with Multiple Stoppings

TL;DR

This paper establishes asymptotic lower bounds for Bruss' multiple stopping odds problem, revealing threshold values and implications for secretary problems with multiple stoppings, extending to broader multiple stopping scenarios.

Contribution

It provides the first asymptotic lower bounds for Bruss' multiple stopping problem, linking thresholds to optimal strategies and generalizing to other multiple stopping problems.

Findings

Asymptotic lower bounds for Bruss' odds problem derived

Threshold values in optimal strategies identified

Lower bounds applicable to broader multiple stopping problems

Abstract

We give asymptotic lower bounds of the value for Bruss' optimal stopping problem with multiple stopping chances. It interestingly consists of the asymptotic threshold values in the optimal multiple stopping strategy. Another interesting implication of the result is that the asymptotic value for each secretary problem with multiple stoppings is in fact a typical lower bound in a much more general class of multiple stopping problems as modifications of odds problem.