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Arena-Independent Finite-Memory Determinacy in Stochastic Games

Authors Patricia Bouyer , Youssouf Oualhadj, Mickael Randour, Pierre Vandenhove

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Author Details

Patricia Bouyer
  • Université Paris-Saclay, CNRS, ENS Paris-Saclay, Laboratoire Méthodes Formelles, 91190, Gif-sur-Yvette, France
Youssouf Oualhadj
  • Univ Paris Est Creteil, LACL, F-94010 Creteil, France
Mickael Randour
  • F.R.S.-FNRS & UMONS - Université de Mons, Belgium
Pierre Vandenhove
  • F.R.S.-FNRS & UMONS - Université de Mons, Belgium
  • Université Paris-Saclay, CNRS, ENS Paris-Saclay, Laboratoire Méthodes Formelles, 91190, Gif-sur-Yvette, France

Funding

Research supported by F.R.S.-FNRS under Grant n^∘ F.4520.18 (ManySynth), and ENS Paris-Saclay visiting professorship (M. Randour, 2019). This work has been partially supported by the ANR Project MAVeriQ (ANR-ANR-20-CE25-0012). Mickael Randour is an F.R.S.-FNRS Research Associate. Pierre Vandenhove is an F.R.S.-FNRS Research Fellow.

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Patricia Bouyer, Youssouf Oualhadj, Mickael Randour, and Pierre Vandenhove. Arena-Independent Finite-Memory Determinacy in Stochastic Games. In 32nd International Conference on Concurrency Theory (CONCUR 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 203, pp. 26:1-26:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021) https://doi.org/10.4230/LIPIcs.CONCUR.2021.26

Abstract

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 in [Bouyer et al., 2020] to stochastic ones.

Subject Classification

ACM Subject Classification
  • Theory of computation → Formal languages and automata theory
Keywords
  • two-player games on graphs
  • stochastic games
  • Markov decision processes
  • finite-memory determinacy
  • optimal strategies

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