License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.CONCUR.2021.26
URN: urn:nbn:de:0030-drops-144037
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2021/14403/
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Bouyer, Patricia ; Oualhadj, Youssouf ; Randour, Mickael ; Vandenhove, Pierre

Arena-Independent Finite-Memory Determinacy in Stochastic Games

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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.

BibTeX - Entry

@InProceedings{bouyer_et_al:LIPIcs.CONCUR.2021.26,
  author =	{Bouyer, Patricia and Oualhadj, Youssouf and Randour, Mickael and Vandenhove, Pierre},
  title =	{{Arena-Independent Finite-Memory Determinacy in Stochastic Games}},
  booktitle =	{32nd International Conference on Concurrency Theory (CONCUR 2021)},
  pages =	{26:1--26:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-203-7},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{203},
  editor =	{Haddad, Serge and Varacca, Daniele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2021/14403},
  URN =		{urn:nbn:de:0030-drops-144037},
  doi =		{10.4230/LIPIcs.CONCUR.2021.26},
  annote =	{Keywords: two-player games on graphs, stochastic games, Markov decision processes, finite-memory determinacy, optimal strategies}
}

Keywords: two-player games on graphs, stochastic games, Markov decision processes, finite-memory determinacy, optimal strategies
Collection: 32nd International Conference on Concurrency Theory (CONCUR 2021)
Issue Date: 2021
Date of publication: 13.08.2021

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