text: If more than one player controls an Opposition Agent, and another player searches their library, the controller of the Opposition Agent that most recently entered the battlefield controls that player during the search. Because the last ability of each Opposition Agent is trying to exile the card and give permission to play it, the owner of the exiled card chooses which effect wins. However, that owner will be under another player's control, so that player controlling that owner actually makes the decision. In other words, the player who controls the Opposition Agent whose effect applies (and thus controls the opponent) can choose to give themselves all the play permissions unless they're feeling very generous.