WHEN TO STOP: A ZERO-SUM GAME MODEL
Minoru Sakaguchi · 1971
This paper examines a class of optimal stopping problems in which two competitive players are involved. Let XI, X 2 , ••• be independent and identically distributed random variables that can be observed se quentially at cost c per observation. Two players I and 11 have the right to stop the sampling process: player I on the interval Ca, 00), player 11 on (- ex> , b). The real numbers a and b are prescribed. If player I or 11 stops the process after observing X n, then 11 pays Xn-nc to 1. The common distribution function of each Xi is assumed to be known to both players. We are required to derive optimal strategies for both players in this zero-sum game. Explicit results are obtained for the case where c=O and N(=the maximum possible number of observations permitted to the players) is finite and the case where c>O and N= 00.