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.FSTTCS.2021.41
URN: urn:nbn:de:0030-drops-155522
URL: https://drops.dagstuhl.de/opus/volltexte/2021/15552/
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Bordais, Benjamin ; Bouyer, Patricia ; Le Roux, St├ęphane

From Local to Global Determinacy in Concurrent Graph Games

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LIPIcs-FSTTCS-2021-41.pdf (1 MB)


Abstract

In general, finite concurrent two-player reachability games are only determined in a weak sense: the supremum probability to win can be approached via stochastic strategies, but cannot be realized.
We introduce a class of concurrent games that are determined in a much stronger sense, and in a way, it is the largest class with this property. To this end, we introduce the notion of local interaction at a state of a graph game: it is a game form whose outcomes (i.e. a table whose entries) are the next states, which depend on the concurrent actions of the players. By definition, a game form is determined iff it always yields games that are determined via deterministic strategies when used as a local interaction in a Nature-free, one-shot reachability game. We show that if all the local interactions of a graph game with Borel objective are determined game forms, the game itself is determined: if Nature does not play, one player has a winning strategy; if Nature plays, both players have deterministic strategies that maximize the probability to win. This constitutes a clear-cut separation: either a game form behaves poorly already when used alone with basic objectives, or it behaves well even when used together with other well-behaved game forms and complex objectives.
Existing results for positional and finite-memory determinacy in turn-based games are extended this way to concurrent games with determined local interactions (CG-DLI).

BibTeX - Entry

@InProceedings{bordais_et_al:LIPIcs.FSTTCS.2021.41,
  author =	{Bordais, Benjamin and Bouyer, Patricia and Le Roux, St\'{e}phane},
  title =	{{From Local to Global Determinacy in Concurrent Graph Games}},
  booktitle =	{41st IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2021)},
  pages =	{41:1--41:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-215-0},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{213},
  editor =	{Boja\'{n}czy, Miko{\l}aj and Chekuri, Chandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2021/15552},
  URN =		{urn:nbn:de:0030-drops-155522},
  doi =		{10.4230/LIPIcs.FSTTCS.2021.41},
  annote =	{Keywords: Concurrent games, Game forms, Local interaction}
}

Keywords: Concurrent games, Game forms, Local interaction
Collection: 41st IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2021)
Issue Date: 2021
Date of publication: 29.11.2021


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