True, I suppose...I just really like the idea of simultaneous picks in order to be true to game theory (which I love). But the non-2-player-games really make that a serious kink in the plan.
it works if you give the players with more or less points the choice of which row or column to select from, but have them PM that choice from the row or column so no-one has any info about what other players are doing. Maybe let players know who is picking from where.
For 8 player games you would either need a 4th grid - and I don't see where to get that from - or have 2 players left out of the selection process.
Maybe you could work a 4th grid from round limits against various scoring systems or round limits v singles,dubs,quads.
If round limits v singles,dubs,quads you would have to drop the assassin option from the 3rd grid or allow a the selection of a team game to override it. Assassin as an option would probably make scoring difficult anyway.
These 4 would allow 8 picks - each player selecting with knowledge only of who is picking from where
With 2 or 4 player games you could allow knowledge of the result of the previous 1 or 2 grids.