5. Stackelberg Game Now assume the same setting as in Problem 4, but the game is played as a Stackelberg game, where Firm A chooses its quantityQA first, then Firm B observes A's quantity and chooses its own quantity Qs, and Firm A knows that Firm B knows Firm A's quantity. Use backward induction to find the best response function of Firm B to Firm A's choice, and also the subgame-perfect Nash equilibrium of the game. 6. Dynamic Game in Extensive-Form and Normal-Form I In a related market, Standard Locomotive Corporation (SLC) dominates the supply of railway engines. A new generation of engines is about to come online, which is similar to international standard engines. A foreign company, Krups (K), is considering entering the market. Both SLC and K have to invest in capital equipment that is difficult to divest if they are to serve the market. Hence both firms have to choose between several investment options, and their payoffs depend on both their actions. SCL will make an investment decision first; the foreign company Krups will observe SCLs decision, and makes its own decision on entering and investment. SCL knows that Krups will observe its decision. If SLC chooses a large investment (L), profits will be 100 if K does not enter the market (O), and 50 if K does enter the market, regardless of Ks investment decision. If SLC selects a smaller investment (S), its profit will be 40 if K does not enter the market (O),-40 if K enters with a huge investment (H), or 20 if K enters with a minor investment (M). If SLC chose L, payoff for K would be 080, 10, for O, H and M, respectively. If SLC chose S, payoff for K would be 0, 50, 20, for O, H and M, respectively. (a) Draw the game tree for this extensive form game. Specify clearly the initial node, decision nodes, branches (available actions), terminal nodes, and the payoffs. (b) What are the information sets for each player in this game? (c) Is this a game of perfect or imperfect information, and why? (d) Write down the normal-form game representation of this game in the matrix table form (specify strategies as action plans at information sets as we did in class). (e) For Firm K, which strategies are strictly dominated strategies? Which are weakly dom- inated strategies? (f) Specify all pure-strategy Nash equilibria of the above strategic-form game. (g) What are the subgames in this game? Specify game tree for each subgame. (h) Find all the pure-strategy subgame-perfect Nash equilibria using backward induction. Any of the pure-strategy NE you found in (f) not a subgame-perfect NE? Why? 7. Dynamic Game in Extensive-Form and Normal-Form II Changing the assumptions from problem 6 above, SLC realizes that its technology is a bit weaker than Krups, and it realizes it has the additional option to refrain (R) from investing and keep using the current plant. This would lead to a payoff of 20 for SLC if K does not enter (O), -40 for SCL if K enters with a huge investment (H), or 10 if K enters with a minor investment (M), and K's payoff is 0, 100, and 50 for O, H and M, respectively. However, SLC also realizes that they have the ability to mask the amount they invest, but not whether or not they invest in the plant. To be specific, SLC first chooses whether or not to investIf