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Strategy-Stealing Is Non-Constructive

Authors Greg Bodwin, Ofer Grossman

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Author Details

Greg Bodwin
  • Georgia Tech, Atlanta, GA, USA
Ofer Grossman
  • MIT, Cambridge, MA, USA

Funding

  • Bodwin, Greg: Supported in part by NSF awards CCF-1717349, DMS-183932 and CCF-1909756.
  • Grossman, Ofer: Supported by the Fannie and John Hertz Foundation fellowship, an NSF GRFP award, NSF CNS-1413920, DARPA/NJIT 491512803, Sloan Foundation 996698, and MIT/IBM W1771646. This work was done in part at the Simons Institute for the Theory of Computing.

Cite AsGet BibTex

Greg Bodwin and Ofer Grossman. Strategy-Stealing Is Non-Constructive. In 11th Innovations in Theoretical Computer Science Conference (ITCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 151, pp. 21:1-21:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)
https://doi.org/10.4230/LIPIcs.ITCS.2020.21

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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Problems, reductions and completeness
Keywords
  • PSPACE-hard
  • Hex
  • Combinatorial Game Theory

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