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Characterization and simplification of optimal strategies in positive stochastic games

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Article
Author/s: 
János Flesch, Arkadi Predtetchinski and William Sudderth
Journal of Applied Probability
Issue number: 
Access Volume 55, Issue 3, September 2018
Publisher: 
Springer
Year: 
2018
Journal pages: 
728-741
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.
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