Using subPCP
Currently, when using Wilson algorithm, at a level below the maximum one, we fixed variable associated to players above this one. To potentially improve a little the performances and possible facilitate the implementation of futur modification (for hypergraphical game in particular), we should, when in a level below the maximum one, create a sub pcp from a subgame.
Using the initial arbitrary joint strategy, we create a subgame with k players where the player from k+1 to N play their actions in this joint strategy. We then create the PCP of this subgame. Considering that we use a set Z and W as "coordinate" of a node there will be no issue going from one level to another and compute the correct node and arc. The level with 1 player will be once again a particular case, it is possible to use a PCP as we've previously done, however we can also use the best response of the game to get the correct couple to choose.