Positive zero-sum stochastic games with countable state and action spaces

Janos Flesch, Arkadi Predtetchinski*, William Sudderth

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

Abstract

A positive zero-sum stochastic game with countable state and action spaces is shown to have a value if, at every state, at least one player has a finite action space. The proof uses transfinite algorithms to calculate the upper and lower values of the game. We also investigate the existence of (epsilon-)optimal strategies in the classes of stationary and Markov strategies.

Original languageEnglish
Pages (from-to)499-516
Number of pages18
JournalApplied Mathematics and Optimization
Volume82
Issue number2
Early online date1 Nov 2018
DOIs
Publication statusPublished - 2020

Keywords

  • Fixed point
  • Markov strategy
  • Tarski fixed point theorem
  • Transfinite algorithm
  • optimal strategy
  • value of the game
  • zero-sum stochastic game
  • Optimal strategy
  • Zero-sum stochastic game
  • Value of the game
  • STRATEGIES

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