Arena-Independent Finite-Memory Determinacy in Stochastic Games
We study stochastic zero-sum games on graphs, which are prevalent tools to model decision-making in presence of an antagonistic opponent in a random environment. In this setting, an important question is the one of strategy complexity: what kinds of strategies are sufficient or required to play opti...
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| Published in: | Logical methods in computer science Vol. 19, Issue 4; pp. 6420 - 6425 |
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| Main Authors: | , , , |
| Format: | Journal Article |
| Language: | English |
| Published: |
Logical Methods in Computer Science Association
01.12.2023
Logical Methods in Computer Science e.V |
| Subjects: | |
| ISSN: | 1860-5974, 1860-5974 |
| Online Access: | Get full text |
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| Summary: | We study stochastic zero-sum games on graphs, which are prevalent tools to
model decision-making in presence of an antagonistic opponent in a random
environment. In this setting, an important question is the one of strategy
complexity: what kinds of strategies are sufficient or required to play
optimally (e.g., randomization or memory requirements)? Our contributions
further the understanding of arena-independent finite-memory (AIFM)
determinacy, i.e., the study of objectives for which memory is needed, but in a
way that only depends on limited parameters of the game graphs. First, we show
that objectives for which pure AIFM strategies suffice to play optimally also
admit pure AIFM subgame perfect strategies. Second, we show that we can reduce
the study of objectives for which pure AIFM strategies suffice in two-player
stochastic games to the easier study of one-player stochastic games (i.e.,
Markov decision processes). Third, we characterize the sufficiency of AIFM
strategies through two intuitive properties of objectives. This work extends a
line of research started on deterministic games to stochastic ones. |
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| ISSN: | 1860-5974 1860-5974 |
| DOI: | 10.46298/lmcs-19(4:18)2023 |