(c) Construct the payoff table of the sequential-move game and show the Nash equilibria on the table. (No proof that candidates are Nash equilibiia is necessary here.) Remember the ORDER in the TREE MATTERS. To avoid confusion graph the TREE in the same order as the ACTIONS are DISPLAYED in the PAYOFF TABLE. How many Nash equilibria of sequentialmove game are there? List all the equilibria. (d) One of the Nash equilibria for the sequential-move game described in part (b) is given by the strategy prole (Du, (51111)\") . (i) PROVE that this strategy prole is a Nash equilibrium for the sequential-move game described in (b). (ii) Show that this Nash equilibrium is NOT subgame perfect. Q3 Competition in Quantities (Homogeneous Products) Suppose that the inverse market demand for a commodity is given by P = 240 g Q The cost curves of the two rms which could serve this market are 1 TCl(q1)=30ql and TC2(q2)=q (a) Draw the best-response functions for the two rms if they compete in quantities and identify the point associated with the Nash equilibrium of the Cournot game. (1:) Determine the collusive outcome which maximizes joint prots. Identify the point which corresponds to the collusive outcome in the diagram of part (a), Does each rm have an incentive to collude? Explain. Would one rm want to make a side payment to the other in order to reach a collusive agreement? If the rms sign a collusive agreement, does either rm have an incentive to defect? Does this depend on the side payment? Explain. (c) Suppose that the two rms choose output sequentially, rather than simultaneously. Firm 1 moves first by choosing its output level. After Firm 1 has chosen its output level, Firm 2 observes q1 and chooses its output level. Find the subgame-perfect equilibrium quantities of the CournotStackelberg game