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Optimal doubling strategy against a suboptimal opponent

Part of: Stochastic processes Game theory

Published online by Cambridge University Press:  14 July 2016

Konstantinos V. Katsikopoulos  and
Özgür Şimşek
Konstantinos V. Katsikopoulos*
Affiliation:
University of Massachusetts, Amherst and Max Planck Institute for Human Development
Özgür Şimşek*
Affiliation:
University of Massachusetts, Amherst
*
∗Postal address: Center for Adaptive Behavior and Cognition, Max Planck Institute for Human Development, Lentzeallee 94, Berlin, 14195, Germany. Email address: katsikop@mpib-berlin.mpg.de
∗∗Postal address: Department of Computer Science, University of Massachusetts, 140 Governors Drive, Amherst, MA 01003, USA.
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Abstract

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For two-person zero-sum games, where the probability of each player winning is a continuous function of time and is known to both players, the mutually optimal strategy for proposing and accepting a doubling of the game value is known. We present an algorithm for deriving the optimal doubling strategy of a player who is aware of the suboptimal strategy followed by the opponent. We also present numerical results about the magnitude of the benefits; the results support the claim that repeated application of the algorithm by both players leads to the mutually optimal strategy.

Keywords

Gamblingdoublingoptimal strategy

MSC classification

Primary: 60G40: Stopping times; optimal stopping problems; gambling theory
Secondary: 91A05: 2-person games
Type
Short Communications
Information
Journal of Applied Probability , Volume 42 , Issue 3 , September 2005 , pp. 867 - 872
Copyright
© Applied Probability Trust 2005 

References

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