4. Consider the following (and by now quite familiar) Bos game : B S B 2,1 0,0 S 0,0 1,2 Recall that this game has three Nash Equilibria : (B,S), (S,B), and the mixed strategy equilibrium where 1 plays B with probability 2/3 and 2 plays B with probability 1/3. Now consider the following alternative game for some &> 0, which we will call the E-perturbation of the original game : B S B 2+En1,1+En2 En 1,0 S 0,En2 1,2 Where, for i = 1,2, nis distributed according to CDF GF(n;) and its realization is privately known by player i. (a) Suppose there exists a Bayesian equilibrium in the &-perturbed game that take the form "Player i plays B if and only if nin* "; find an expression for 17i and 172. (Hint : this expression should involve the CDFs GF) and verify that this is indeed a Bayes-Nash Equilibrium. (b) ShowthatwecanchooseGE suchthat, whengoestozero, theBayesianNashequilibriumdescribed above gives the same strategies as in the strictly mixed strategy Nash Equilibrium of the original game. (This is an application of Harsanyi's "purification theorem", which states that every mixed strategy Nash equilibrium can be obtained as the limit of pure strategy Bayes Nash equilibria of some perturbed game.)