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Reports (Research Report) Year : 2022

Bipartite instances of INFLUENCE

Eric Duchene
Nacim Oijid
Aline Parreau


The game influence is a scoring combinatorial game that has been introduced in 2021 by Duchene et al [DGP + 21]. 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 his 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 in [DGP + 21]. 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.
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hal-03694758 , version 1 (14-06-2022)



Eric Duchene, Nacim Oijid, Aline Parreau. Bipartite instances of INFLUENCE. LIRIS UMR 5205 CNRS/INSA de Lyon/Université Claude Bernard Lyon 1/Université Lumière Lyon 2/École Centrale de Lyon. 2022. ⟨hal-03694758⟩
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