Before revision:  For general m-player games, we show that the swap regret of each player decays at rate O(m^{1/2} (n/T)^{3/4}) when they combine optimistic Hedge with the classical external-to-internal reduction of Blum and Mansour \mbox{%DIFAUXCMD blum2007external .
After revision:  For general m-player games, we show that the swap regret of each player decays at rate O(m^{1/2} (n/T)^{3/4}) when they combine optimistic Hedge with the classical external-to-internal reduction of Blum and Mansour (JMLR'07) .