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DOI: 10.4230/LIPIcs.FUN.2024.2

Poset Positional Games

Authors: Guillaume Bagan, Eric Duchêne, Florian Galliot, Valentin Gledel, Mirjana Mikalački, Nacim Oijid, Aline Parreau, and Miloš Stojaković

Published in: LIPIcs, Volume 291, 12th International Conference on Fun with Algorithms (FUN 2024)

Abstract

We propose a generalization of positional games, supplementing them with a restriction on the order in which the elements of the board are allowed to be claimed. We introduce poset positional games, which are positional games with an additional structure - a poset on the elements of the board. Throughout the game play, based on this poset and the set of the board elements that are claimed up to that point, we reduce the set of available moves for the player whose turn it is - an element of the board can only be claimed if all the smaller elements in the poset are already claimed. We proceed to analyze these games in more detail, with a prime focus on the most studied convention, the Maker-Breaker games. First we build a general framework around poset positional games. Then, we perform a comprehensive study of the complexity of determining the game outcome, conditioned on the structure of the family of winning sets on the one side and the structure of the poset on the other.

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Guillaume Bagan, Eric Duchêne, Florian Galliot, Valentin Gledel, Mirjana Mikalački, Nacim Oijid, Aline Parreau, and Miloš Stojaković. Poset Positional Games. In 12th International Conference on Fun with Algorithms (FUN 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 291, pp. 2:1-2:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{bagan_et_al:LIPIcs.FUN.2024.2,
  author =	{Bagan, Guillaume and Duch\^{e}ne, Eric and Galliot, Florian and Gledel, Valentin and Mikala\v{c}ki, Mirjana and Oijid, Nacim and Parreau, Aline and Stojakovi\'{c}, Milo\v{s}},
  title =	{{Poset Positional Games}},
  booktitle =	{12th International Conference on Fun with Algorithms (FUN 2024)},
  pages =	{2:1--2:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-314-0},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{291},
  editor =	{Broder, Andrei Z. and Tamir, Tami},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FUN.2024.2},
  URN =		{urn:nbn:de:0030-drops-199100},
  doi =		{10.4230/LIPIcs.FUN.2024.2},
  annote =	{Keywords: Positional games, Maker-Breaker games, Game complexity, Poset, Connect 4}
}

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Poset Positional Games

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