Bipartite instances of INFLUENCE

The game Influence is a scoring combinatorial game that has been introduced in 2021 by Duchêne et al. [5]. It is a good representative of Milnor's universe of scoring games, i.e. games where it is never interesting for a player to miss their turn. New general results are first given for this un...

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Published inTheoretical computer science Vol. 982; p. 114274
Main Authors Duchêne, Eric, Oijid, Nacim, Parreau, Aline
Format Journal Article
LanguageEnglish
Published Elsevier B.V 08.01.2024
Elsevier
Subjects
Combinatorics
complexity
Game on graphs
Mathematics
Milnor's universe
scoring game
temperature
Game on graphs
temperature
complexity
Milnor's universe
scoring game
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Summary:The game Influence is a scoring combinatorial game that has been introduced in 2021 by Duchêne et al. [5]. It is a good representative of Milnor's universe of scoring games, i.e. games where it is never interesting for a player to miss their turn. New general results are first given for this universe, by transposing the notions of mean and temperature derived from non-scoring combinatorial games. Such results are then applied to Influence to refine the case of unions of segments started by Duchêne et al. [5]. The computational complexity of the score of the game is also solved and proved to be PSPACE-complete. We finally focus on some specific cases of Influence when the graph is bipartite, by giving explicit strategies and bounds on the optimal score on structures like grids, hypercubes or tori.
ISSN:0304-3975
1879-2294
DOI:10.1016/j.tcs.2023.114274