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

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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 \epsilon -)optimal strategies in the classes of stationary and markov strategies.
Original languageEnglish
Number of pages19
JournalApplied Mathematics and Optimization
Publication statusE-pub ahead of print - 1 Nov 2018


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

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