Abstract
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 language | English |
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Pages (from-to) | 728-741 |
Number of pages | 14 |
Journal | Journal of Applied Probability |
Volume | 55 |
Issue number | 3 |
DOIs | |
Publication status | Published - Sept 2018 |
Keywords
- Positive
- two-person
- zero-sum stochastic game
- optimal stationary strategy
- subgame-optimal strategy
- Markov chain
- martingale