Consider now the perturbed version of the Battle of the Sexes game: where 0 < < 1 is a fixed real number while t 1 and t 2 are independent random variables uniformly distributed on the interval [ 0 , 1 ] . Each player i observes only t i before choosing between S and D . (b) - Find a Bayesian Nash equilibrium in which each player i has some types that choose S and some other types that choose D . What strategy does the equilibrium strategy converge to as goes to zero? .