The Sum-the-Odds Theorem with Application to a Stopping Game of Sakaguchi

Thomas S. Ferguson. "The Sum-the-Odds Theorem with Application to a Stopping Game of Sakaguchi." Mathematica Applicanda 44.1 (2016): null. <http://eudml.org/doc/292688>.

@article{ThomasS2016,
abstract = {The optimal stopping problem of maximizing the probability of stopping on the last success of a finite sequence of independent Bernoulli trials has been studied by Hill and Krengel (1992), Hsiau and Yang (2000) and Bruss (2000). The optimal stopping rule of Bruss stops when the sum of the odds of future successes is less than one. This Sum-the-Odds Theorem is extended in several ways. First, an infinite number of Bernoulli trials is allowed. Second, the payoff for not stopping is allowed to be different from the payoff of stopping on a success that is not the last success. Third, the Bernoulli variables are allowed to be dependent. Fourth, the model is generalized to allow at each stage other dependent random variables to be observed that may influence the assessment of the probability of success at future stages. Finally, application is made to a game of Sakaguchi (1984) in which two players vie for predicting the last success, but in which one of the players is given priority of acting first.},
author = {Thomas S. Ferguson},
journal = {Mathematica Applicanda},
keywords = {},
language = {eng},
number = {1},
pages = {null},
title = {The Sum-the-Odds Theorem with Application to a Stopping Game of Sakaguchi},
url = {http://eudml.org/doc/292688},
volume = {44},
year = {2016},
}

TY - JOUR
AU - Thomas S. Ferguson
TI - The Sum-the-Odds Theorem with Application to a Stopping Game of Sakaguchi
JO - Mathematica Applicanda
PY - 2016
VL - 44
IS - 1
SP - null
AB - The optimal stopping problem of maximizing the probability of stopping on the last success of a finite sequence of independent Bernoulli trials has been studied by Hill and Krengel (1992), Hsiau and Yang (2000) and Bruss (2000). The optimal stopping rule of Bruss stops when the sum of the odds of future successes is less than one. This Sum-the-Odds Theorem is extended in several ways. First, an infinite number of Bernoulli trials is allowed. Second, the payoff for not stopping is allowed to be different from the payoff of stopping on a success that is not the last success. Third, the Bernoulli variables are allowed to be dependent. Fourth, the model is generalized to allow at each stage other dependent random variables to be observed that may influence the assessment of the probability of success at future stages. Finally, application is made to a game of Sakaguchi (1984) in which two players vie for predicting the last success, but in which one of the players is given priority of acting first.
LA - eng
KW -
UR - http://eudml.org/doc/292688
ER -