How do chess engines use game trees decide what move to make in multiplayer chess?

I understand that chess engines use game trees to decide what move to make, by first making a game tree, and then evaluating the positions at the leaf nodes of the game tree, and then evaluating each node before the leaf node as having the same advantage or disadvantage as the node on the next ply that is best for whoever's turn it is on that node. In two player chess there is no difference from player B making a move that leads to the best possible position for player B and player B making a move that leads to the worst possible position for player A. In multiplayer chess however the there can be a difference between player C making a move that leads to the best possible position for player C and player C making a move that leads to the worst possible position for player A. In three player chess for instance the move that black could play to give red the worst possible position might also worsen blacks own position. So if two players in three player chess have formed an alliance sometimes the best move for the white black federation may be different from the best move for each individual in the federation. When creating a game tree for three player chess for the nodes in the game tree, in which it is one of the other two players turns, does it evaluate the position based on the node, on the next ply, with the best position for the player to move, or does it evaluate the position based on the node, on the next ply, with the position that is worst for the computer? I mean if the computer has red pieces for instance and it's blacks turn does the computer evaluate the position based on the move that black can play to give him/her self the best possible position or does the computer evaluate the position based on the move that black can play to put red in the worst possible position regardless of how it affects blacks own individual position?