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Poset Positional Games

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

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Author Details

Guillaume Bagan
  • Univ Lyon, CNRS, UCBL, INSA Lyon, LIRIS, UMR5205, F-69622 Villeurbanne, France
Eric Duchêne
  • Univ Lyon, CNRS, UCBL, INSA Lyon, LIRIS, UMR5205, F-69622 Villeurbanne, France
Florian Galliot
  • Univ. Bordeaux, CNRS, Bordeaux INP, LaBRI, UMR 5800, F-33400 Talence, France
Valentin Gledel
  • Université Savoie Mont Blanc, CNRS UMR5127, LAMA, Chambéry, F-73000, France
Mirjana Mikalački
  • Department of Mathematics and Informatics, Faculty of Sciences, University of Novi Sad, Serbia
Nacim Oijid
  • Univ Lyon, CNRS, UCBL, INSA Lyon, LIRIS, UMR5205, F-69622 Villeurbanne, France
Aline Parreau
  • Univ Lyon, CNRS, UCBL, INSA Lyon, LIRIS, UMR5205, F-69622 Villeurbanne, France
Miloš Stojaković
  • Department of Mathematics and Informatics, Faculty of Sciences, University of Novi Sad, Serbia

Funding

This research was partly supported by the french ANR project P-GASE (ANR-21-CE48-0001-01), by Provincial Secretariat for Higher Education and Scientific Research, Province of Vojvodina (Grant No. 142-451-2686/2021) and by Ministry of Science, Technological Development and Innovation of Republic of Serbia (Grants 451-03-66/2024-03/200125 & 451-03-65/2024-03/200125).

Cite AsGet BibTex

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)
https://doi.org/10.4230/LIPIcs.FUN.2024.2

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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Algorithmic game theory
Keywords
  • Positional games
  • Maker-Breaker games
  • Game complexity
  • Poset
  • Connect 4

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