A game version of the Cowan–Zabczyk–Bruss’ problem

Abstract

To cite this version:Krzysztof Szajowski. A game version of the Cowan-Zabczyk-Bruss' problem. Statistics and Probability Letters, Elsevier, 2009, 77 (17) This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. A c c e p t e d m a n u s c r i p t AbstractThe paper deal with the continuous-time two person non-zero sum game extension of the no information secretary problem. The objects appear according to the compound Poisson process and each player can choose only one applicant. If both players would like to select the same one, then the priority is assigned randomly. The aim of the players is to choose the best candidate. A construction of Nash equilibria for such game is presented. The extension of the game with randomized stopping times is taken into account. The Nash values for such extension is obtained. Analysis of the solutions for different priority defining lotteries are given.

Combined Games with Randomly Delayed Beginnings

“…Another reason for the interest in last-success problems is that the resulting optimization is often much more "robust" than one would intuitively expect, as exemplified by the 1/e-law of Bruss [22]. The latter concerns the case of an unknown number of candidates, but this holds also for other important modifications as shown in Szajowski [23] and Ferguson (2016) as well as in the study of bounds for multiple stopping problems (Matsui and Ano [24,25]). Hence last success settings are versatile.…”

Odds -theorem and monotonicity

“…in Matsui and Ano (2014), (2016), or modified payoffs (see e.g. Tamaki (2010), ( 2011)), or again modified in such a way that they may be helpful for related game problems in continuous-time, such as in Szajowski (2007). (For a best-choice problem with dependent criteria see e.g.…”

The Best-or-Worst and the Postdoc problems with random number of candidates

“…This was first studied in a continuous time setting by Cowan and Zabczyk [6] for a Poisson process of candidates with known arrival rate and then generalized by Bruss [3] for an unknown arrival rate. See also Szajowski's work [24] for a corresponding game version.…”