Before revision:  We show that competing players explore less than a single player: there is p^* \in (m, g (\mu, \beta) ) so that for all p > p^*, the players stay at the predictable arm.
After revision:  We show that competing players explore less than a single player: there is p^* \in (m, g ) so that for all p > p^*, the players stay at the predictable arm.