Consider the following n player game. Simultaneously each of the n players choose between X and Y. The payoff of player i is 1 if she selects Y. In the event that player i selects X, his payoff is 2 if no other player chooses X, and his payoff is 0 if at least one other player chooses X as well. In this game, there is a mixed strategy Nash equilibrium in which each player selects Y with probability a. This value a is the same for all players. Find a.