Problem 3 (30 points) Consider the strategicform game depicted below: a b a 3,0 0,2 3.: 052 3,0 (3 2:0 2 l u (a) Does this game have a Nash equilibrium in pure strategies? Explain. Let gun (a) denote the probability with which player 1 (the row player) plays strategy a, let 101(5) be the probability with which she plays strategy b, and p1(c) be the probability with which she plays strategy 0. Let p2(a} be the probability with which player 2 (the column player) plays strategy a and let 3326)) he the probability with which he plays strategy 6. (b) Show that there is no mixed-strategy Nash equilibrium where 331 (a) > 0, 131(5) > 0, and p1(C) > 0. (c) Show that there is no mixed-strategy Nash equilibrium where 391 {a} > 0, 101(5) > 0! and 101(5) = 0+ ((1) Show that there is no mixedstrategy Nash equilibrium where p1 (a) ;> 0, 191(5) 2 0: and 101(0) > 0- (e) There is a {unique} mixed-strategy Nash equilibrium where p1(a) = 0, 101(5) > D, and 391(6) > 0. Compute this equilibrium