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

  • K. Avrachenkov
  • V. Ejov
  • J. A. FilarEmail author
  • A. Moghaddam
Article
  • 12 Downloads

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 

Mathematics Subject Classification

90D15 

Notes

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Inria Sophia AntipolisBiotFrance
  2. 2.College of Science and EngineeringFlinders University of South AustraliaBedford ParkAustralia
  3. 3.Faculty of Mechanics and MathematicsMSUMoscowRussia
  4. 4.Centre for Applications in Natural Resource Mathematics, School of Mathematics and PhysicsThe University of QueenslandSt LuciaAustralia

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