License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ICALP.2020.38
URN: urn:nbn:de:0030-drops-124458
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2020/12445/
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Deligkas, Argyrios ; Fearnley, John ; Savani, Rahul

Tree Polymatrix Games Are PPAD-Hard

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LIPIcs-ICALP-2020-38.pdf (0.6 MB)

Abstract

We prove that it is PPAD-hard to compute a Nash equilibrium in a tree polymatrix game with twenty actions per player. This is the first PPAD hardness result for a game with a constant number of actions per player where the interaction graph is acyclic. Along the way we show PPAD-hardness for finding an ε-fixed point of a 2D-LinearFIXP instance, when ε is any constant less than (√2 - 1)/2 ≈ 0.2071. This lifts the hardness regime from polynomially small approximations in k-dimensions to constant approximations in two-dimensions, and our constant is substantial when compared to the trivial upper bound of 0.5.

BibTeX - Entry

@InProceedings{deligkas_et_al:LIPIcs:2020:12445,
  author =	{Argyrios Deligkas and John Fearnley and Rahul Savani},
  title =	{{Tree Polymatrix Games Are PPAD-Hard}},
  booktitle =	{47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)},
  pages =	{38:1--38:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-138-2},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{168},
  editor =	{Artur Czumaj and Anuj Dawar and Emanuela Merelli},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2020/12445},
  URN =		{urn:nbn:de:0030-drops-124458},
  doi =		{10.4230/LIPIcs.ICALP.2020.38},
  annote =	{Keywords: Nash Equilibria, Polymatrix Games, PPAD, Brouwer Fixed Points}
}

Keywords: Nash Equilibria, Polymatrix Games, PPAD, Brouwer Fixed Points
Collection: 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)
Issue Date: 2020
Date of publication: 29.06.2020

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