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Two-person red-and-black stochastic games

Part of: Stochastic processes

Published online by Cambridge University Press:  14 July 2016

Piercesare Secchi
Piercesare Secchi*
Affiliation:
Università di Pavia
*
∗Postal address: Dipartimento di Economia Politica e Metodi Quantitativi, Università di Pavia, Via San Felice, 5, 27100 Pavia, Italy.
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Abstract

We define a leavable stochastic game which is a possible two-person generalization of the classical red-and-black gambling problem. We show that there are three basic possibilities for a two-person red-and-black game which, by analogy with gambling theory, we call the subfair, the fair and the superfair cases. A suitable generalization of what in gambling theory is called bold play is proved to be a uniformly ε-optimal stationary strategy for player I in the fair and the subfair cases whereas a generalization of timid play is shown to be ε-optimal for player I in the superfair possibility.

Keywords

STOCHASTIC GAMESLEAVABLE GAMESRED-AND-BLACKGAMBLING

MSC classification

Primary: 60G40: Stopping times; optimal stopping problems; gambling theory
Type
Research Papers
Information
Journal of Applied Probability , Volume 34 , Issue 1 , March 1997 , pp. 107 - 126
Copyright
Copyright © Applied Probability Trust 1997 

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