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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Vydáno v:	Logical methods in computer science Ročník 19, Issue 4; s. 6420 - 6425
Hlavní autoři:	Bouyer, Patricia, Oualhadj, Youssouf, Randour, Mickael, Vandenhove, Pierre
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Logical Methods in Computer Science Association 01.12.2023 Logical Methods in Computer Science e.V
Témata:	Computer Science computer science - computer science and game theory computer science - formal languages and automata theory computer science - logic in computer science Computer Science and Game Theory
ISSN:	1860-5974, 1860-5974
On-line přístup:	Získat plný text
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Popis
Shrnutí:	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.
ISSN:	1860-5974 1860-5974
DOI:	10.46298/lmcs-19(4:18)2023