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 language | English |
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Pages (from-to) | 499-516 |
Number of pages | 18 |
Journal | Applied Mathematics and Optimization |
Volume | 82 |
Issue number | 2 |
Early online date | 1 Nov 2018 |
DOIs | |
Publication status | Published - 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