Finding a Nash equilibrium in zero-sum games with three or more players is at least as hard (because a dummy player can be added to the two-player game to make it a three-player zero-sum game). Even approximating a Nash equilibrium is hard (except in special cases) in theory (15), and in games with more than two players, even the best complete algorithm can only address games with a handful of possible strategies per player (16).
Moreover, even if a Nash equilibrium could be computed efficiently in a game with more than twoplayers,it is not clear that playing such an equilibrium strategy would be wise. If each player in such a game independently computes and plays a Nash equilibrium, the list of strategies that they play (one strategy per player) may not be a Nash equilibrium and players might haveanincentive todeviate to a different strategy.