Problem 4 (30 points) Consider the strategic-form game depicted below: a b a 7,2 2,7 3,6 b 2,7 7,2 4,5 (a) Does this game have a Nash equilibrium in pure strategies? Explain. Let pi(a) denote the probability with which player 1 (the row player) plays strategy a, and let p(b) be the probability with which she plays strategy b. Let p2(a) be the probability with which player 2 (the column player) plays strategy a, P2(b) the probability with which he plays strategy b, and p2(c) the probability with which he plays strategy c. (b) Show that there is no mixed-strategy Nash equilibrium where p2(a) > 0, p2(b) > 0, and p2(c) > 0. (c) Show that there is no mixed-strategy Nash equilibrium where p2(a) = 0, P2(b) > 0, and p2(c) > 0. (d) Show that there is no mixed-strategy Nash equilibrium where p2(a) > 0, p2(b) > 0, and p2(C) = 0. (e) There is a (unique) mixed-strategy Nash equilibrium where p2(a) > 0, P2(b) = 0, and p2(c) > 0. Compute this equilibrium