pls assist to answer (a) and (b)

Wask 4. Mixed Strategies (25 points) L . Consider a game G = (S, w)ie(1,2) such that Up go, S1 = {up, down} $2 = {left, right} down o, O. and us : S1 X S2 - R is given by the following payoff matrix I-B left right up 2 2 0,0 down 0,0 1, 1 Bresq Denote by o1 = (@, 1 -a) the mixed strategy of player 1 by which he plays up with proba- bility a. Accordingly, denote by o2 = (8, 1 - B) the mixed strategy of player 2 by which he plays left with probability B. . Derive the individual best response correspondence of player 1, 4, : (S2) - (Sy), and of player 2, 42 : A (S1) - A (S2). . Determine all Nash equilibria in mixed strategies for this game. . Does there exist a fixed point of the game's best response correspondence by (a) Brouwer's fixed point theorem? (Argue) (b) Kakutani's fixed point theorem? (Argue)