Bipartite instances of INFLUENCE - Duchêne, Eric; Oijid, Nacim; Parreau, Aline (Theoretical computer science, 2024)
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.