Zero-Sum Stochastic Games over the Field of Real Algebraic Numbers

K. Avrachenkov (), V. Ejov, J. A. Filar () and A. Moghaddam ()
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K. Avrachenkov: Inria Sophia Antipolis
V. Ejov: Flinders University of South Australia
J. A. Filar: The University of Queensland
A. Moghaddam: The University of Queensland

Dynamic Games and Applications, 2019, vol. 9, issue 4, No 7, 1026-1041

Abstract: Abstract We consider a finite state, finite action, zero-sum stochastic games with data defining the game lying in the ordered field of real algebraic numbers. In both the discounted and the limiting average versions of these games, we prove that the value vector also lies in the same field of real algebraic numbers. Our method supplies finite construction of univariate polynomials whose roots contain these value vectors. In the case where the data of the game are rational, the method also provides a way of checking whether the entries of the value vectors are also rational.

Keywords: Stochastic games; Ordered field property; Algebraic numbers; Algebraic variety; Gröbner basis polynomial equations; 90D15 (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1007/s13235-018-00293-w

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