[I'm sorry that I wasn't more specific. Please bare with me I'm a curious novice and a new comer here to stack exchange.]
original question: "Is it possible to represent any arbitrary game as a 2 player game regardless of the number of players there actually are by treating cooperating players as a single player?"
I think the main thing I'm trying to say here is.. when players work together is it possible just to consider them to be a player with an extended strategy space or to consider all players that are not working with a target player to be a single enemy.
I have an intuition but lack the skill to formalize it.
I'll try an example. 3 player Paper, Scissor, Rock.
The typical strategy space is; P, S, R for any player but say that two players were working together Then could we say they have a strategy space that looks like PP, PS, PR, .., RR?
Is this even possible? .and if so, then is it possible that any game at all is actually just a two player game?
Thank you for being patient with me.