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Strategy-Stealing Is Non-Constructive

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Abstract

In many combinatorial games, one can prove that the first player wins under best play using a simple but non-constructive argument called strategy-stealing. This work is about the complexity behind these proofs: how hard is it to actually find a winning move in a game, when you know by strategy-stealing that one exists? We prove that this problem is PSPACE-Complete already for Minimum Poset Games and Symmetric Maker-Maker Games, which are simple classes of games that capture two of the main types of strategy-stealing arguments in the current literature.

BibTeX - Entry

@InProceedings{bodwin_et_al:LIPIcs:2020:11706,
  author =	{Greg Bodwin and Ofer Grossman},
  title =	{{Strategy-Stealing Is Non-Constructive}},
  booktitle =	{11th Innovations in Theoretical Computer Science Conference (ITCS 2020)},
  pages =	{21:1--21:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-134-4},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{151},
  editor =	{Thomas Vidick},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2020/11706},
  URN =		{urn:nbn:de:0030-drops-117069},
  doi =		{10.4230/LIPIcs.ITCS.2020.21},
  annote =	{Keywords: PSPACE-hard, Hex, Combinatorial Game Theory}
}

Keywords: PSPACE-hard, Hex, Combinatorial Game Theory
Seminar: 11th Innovations in Theoretical Computer Science Conference (ITCS 2020)
Issue date: 2020
Date of publication: 2020


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