Problem 3 (30 points) Consider the strategicform game depicted below: a, b a, 3,0 0,2 I) 0,2 3,0 0 2,0 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((:) be the probability with which she plays strateg' 6. Let 3);; (a) be the probability with which player 2 (the column player) plays strategy a. and let p2(b) be the probability with which he plays strategy 6. (b) Show that there is no mixedstrategy Nash equilibrium where p1(a) > 0, P1(b) > 0, and p1(c) > 0. (c) Show that there is no mixedstrategy Nash equilibrium where 391051) > 0, p1 (b) > 0, and p1(c) = 0. (d) Show that there is no mixedstrategy Nash equilibrium where 331051) > 0, 131(5) = 0, and 131(0) > 0- (6) There is a (unique) mixed-strategy Nash equilibrium where 131(0) = 0, p1(b) > 0, and p1(c) > 0. Compute this equilibrium