Preprint No.
A-02-09
Ehrhard Behrends
Parrondo's paradox: a priori and adaptive strategies
Abstract:
Several hundred pages in the WWW and a number of articles in (mostly)
popular journals deal with Parrondo's paradox: it states that
there are losing gambling games which, when being combined
stochastically or in a suitable deterministic way,
give rise to winning games.
Here we investigate the probabilistic background, methods from graph
theory, (elementary) functional analysis and stochastic control theory
come into play.
We show how the properties of the
equilibrium distributions of the Markov chains under consideration
give rise to the paradoxical behaviour, and we provide methods how to
find the best a priori and adaptive strategies.
Keywords:
Parrondo, paradox, Markov chain, stochastic
control theory
Mathematics Subject Classification (MSC2000):
60J10, 60J20
Language: ENG
Available: Pr-A-02-09.ps
Contact: Ehrhard Behrends, Freie Universität Berlin, Fachbereich Mathematik und Informatik, Arnimallee 2-6, D-14195 Berlin, Germany (behrends@math.fu-berlin.de)
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