I understand that for 2 player chess if an engine is playing white, then the engine uses a min max algorithm, which assumes that black will always make the move that is best for black, or worst for white, and that white will always make moves that are best for white.
While in 2 player, with black to play, the move that is best for black is always the one that is worst for white, but in 3 player chess this is not always the case. As an example, let's say that there is a white rook that is undefended by any white pieces or pawns, but which is attacked by both the black queen and the red queen. Capturing the rook would not be the best move for black, and if black does take the rook the best move for red would be to take the black queen. However what would be worst for white would be if black took the white rook and red did not take the black queen as then white would just be down a rook, compared to both opponents, without compensation.
So my question is would a 3 player chess engine use a min max that assumes that the other two opponents make moves that are best for their individual positions, or would it use an algorithm that assumes that both players would make moves that are worst for the engines position regardless of how that affects their individual positions?