Problem 3 (30 points) Consider the strategic-form game depicted below: b 3,0 0.2 6 0,2 3,0 c 2,0 2. 1 (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, let pi (b) be the probability with which she plays strategy b, and pi (c) be the probability with which she plays strategy c. Let pa(a) be the probability with which player 2 (the column player) plays strategy a and let pz(b) be the probability with which he plays strategy b. (b) Show that there is no mixed-strategy Nash equilibrium where pi(a) > 0, pi(b) > 0, and pi(c) > 0. (c) Show that there is no mixed-strategy Nash equilibrium where pi (a) > 0, pi(b) > 0, and pi(c) = 0. (d) Show that there is no mixed-strategy Nash equilibrium where pi(a) > 0, pi(b) = 0, and pi(c) > 0. (e) There is a (unique) mixed-strategy Nash equilibrium where pi(a) = 0, pi(b) > 0, and pi(e) >0. Compute this equilibrium