  The game INFLUENCE is a scoring combinatorial game that has been introduced
in 2020 by Duchene et al. 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. 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 torus.
