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

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.
Complete list of metadatas

Cited literature [26 references]  Display  Hide  Download

https://hal.inria.fr/hal-02413402
Contributor : Konstantin Avrachenkov <>
Submitted on : Monday, December 16, 2019 - 11:04:46 AM
Last modification on : Monday, January 13, 2020 - 1:18:52 AM

File

OrderedField19Dec2018(1).pdf
Files produced by the author(s)

Identifiers

Collections

Citation

Konstantin Avrachenkov, Vladimir Ejov, Jerzy Filar, Amir Moghaddam. Zero-Sum Stochastic Games over the Field of Real Algebraic Numbers. Dynamic Games and Applications, Springer Verlag, 2019, 9 (4), pp.1026-1041. ⟨10.1007/s13235-018-00293-w⟩. ⟨hal-02413402⟩

Share

Metrics

Record views

17

Files downloads

69