Problem 3 (30 points) Consider the strategicform game depicted below: a b a 3, U U, 2 E) U, 2 3, U c 2, U 2, 1 1 (a) Does this game have a Nash Equilibrium in pure strategies? Explain. Let p1(a) denote the probability with which player 1 (the row player) plays strategy a, let p1(b) be the probability with which she plays strategy b, and p1(c) be the probability with which she plays strategy (5. Let p2(a) be the probability with which player 2 (the column player) plays strategy a and let 102(3)) be the probability with which he plays strategy 3). (b) Show that there is no mixed-strategy Nash equilibrium where p1(a) > U, p1(b) > U, and p1(c) > U. (c) Show that there is no mixedstrategy Nash equilibrium where p1(a) > U, p1(b) > U, and p1(c) = U. ((1) Show that there is no mixed-strategy Nash equilibrium where p1(a) > U, p1(b) = U, and p1(c) > U. (e) There is a (unique) mixed-strategy Nash equilibrium where 101(0) 2 U, p1(b) > U, and p1(c) > U. Compute this equilibrium