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Exercise 5.14. (a) A gives Player 1 an expected payoff of 1.5, B an expected payoff of 0. C and expected payoff of 1.5 and D an expected payoff of 2. Thus D is a best reply to those beliefs. The functions are as follows: A(p. q) =3pq. B(p.q) =3(1-p)q+3p(1-q). C(p.q) = 3(1-p)(1-q), D(p.q)=2pq+2(1-p)(1-q). (b) A(p.q) = D(p.q) at those points (p.q) such that q =- _ 2-2P. The set of such 2-P points is the red curve in the diagram below. The region where A(p. q) > D(p.q) is the region above the red curve. (c) C(p.q) = D(p.q) at those points (p.q) such that q=- . The set of such 1+p points is the blue curve in the diagram below. The region where C(p.q) > D(p.q) is the region below the red curve. (c) B(p.q) = D(p. q) at those points (p.q) such that 9 5-10p 2-3P (for p # { ). The set of such points is given by the two green curves in the diagram below. The region where B(p. q) > D(p. q) is the region between the two green curves. 0.8 4A( P)O.6 4c(p) 4p(P) 0.2 0.2 0.4 0.6 0.8 P Since at every point in the (p.q) square there is a pure strategy which is strictly better than D, it follows that there is no mixed-strategy o, against which D is a best reply