Determinacy for infinite games with more than two players with preferences Benedikt Löwe Abstract: We discuss infinite zero-sum perfect-information games with more than two players. They are not determined in the traditional sense, but as soon as you fix a preference function for the players and assume common knowledge of rationality and this preference function among the players, you get determinacy for open and closed payoff sets. Keywords: n-player games, Gale-Stewart, Determinacy