Characterization and simplification of optimal strategies in positive stochastic games

Janos Flesch*, Arkadi Predtetchinski, William Sudderth

*Corresponding author for this work

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We consider positive zero-sum stochastic games with countable state and action spaces. For each player, we provide a characterization of those strategies that are optimal in every subgame. These characterizations are used to prove two simplification results. We show that if player 2 has an optimal strategy then he/she also has a stationary optimal strategy, and prove the same for player 1 under the assumption that the state space and player 2's action space are finite.
Original languageEnglish
Pages (from-to)728-741
Number of pages14
JournalJournal of Applied Probability
Issue number3
Publication statusPublished - Sept 2018


  • Positive
  • two-person
  • zero-sum stochastic game
  • optimal stationary strategy
  • subgame-optimal strategy
  • Markov chain
  • martingale

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