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| Natura: | Preprint |
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2025
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| Accesso online: | https://arxiv.org/abs/2503.15346 |
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| _version_ | 1866912283270053888 |
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| author | Grand-Clément, Julien Vieille, Nicolas |
| author_facet | Grand-Clément, Julien Vieille, Nicolas |
| contents | This paper investigates properties of Blackwell $ε$-optimal strategies in zero-sum stochastic games when the adversary is restricted to stationary strategies, motivated by applications to robust Markov decision processes. For a class of absorbing games, we show that Markovian Blackwell $ε$-optimal strategies may fail to exist, yet we prove the existence of Blackwell $ε$-optimal strategies that can be implemented by a two-state automaton whose internal transitions are independent of actions. For more general absorbing games, however, there need not exist Blackwell $ε$-optimal strategies that are independent of the adversary's decisions. Our findings point to a contrast between absorbing games and generalized Big Match games, and provide new insights into the properties of optimal policies for robust Markov decision processes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_15346 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Playing against a stationary opponent Grand-Clément, Julien Vieille, Nicolas Computer Science and Game Theory This paper investigates properties of Blackwell $ε$-optimal strategies in zero-sum stochastic games when the adversary is restricted to stationary strategies, motivated by applications to robust Markov decision processes. For a class of absorbing games, we show that Markovian Blackwell $ε$-optimal strategies may fail to exist, yet we prove the existence of Blackwell $ε$-optimal strategies that can be implemented by a two-state automaton whose internal transitions are independent of actions. For more general absorbing games, however, there need not exist Blackwell $ε$-optimal strategies that are independent of the adversary's decisions. Our findings point to a contrast between absorbing games and generalized Big Match games, and provide new insights into the properties of optimal policies for robust Markov decision processes. |
| title | Playing against a stationary opponent |
| topic | Computer Science and Game Theory |
| url | https://arxiv.org/abs/2503.15346 |