1. Briefly explain the logic behind backward induction, our approach to solving sequential (dynamic) games. 2. Briefly explain the difference in market structure between perfect competition, monopolistic competition, oligopoly, duopoly, and monopoly, and explain why or why not we need to use game theory to understand firms' decision-making. 3. Find all of the pure strategy Nash Equilibria of the following simultaneous move game. After solving it as a simultaneous move game, write it as a sequential move game with column moving first. Draw the game tree and solve for the Subgame Perfect Nash Equilibrium. Column + A B C D E a 9,4 1,10 15,7 2,8 15,5 b| 148 310 | 12,18 47 | 20,12 Row | 7,8 6,8 0,10 | 3,3 15,9 C d| 150 5,4 14,2 5,3 9,1 e| 20,18 2,9 10,14 3,7 19,20 4. Consider the following game matrix of payoffs: L M R t[ 11 ] 54 | 46 m| 47 | 02 | 31 b| 20 | 212 | 30 a) Find the pure strategy Nash Equilibria for the above game, assuming that it is a simultaneous move game. Suppose Column moves first, and Row moves sequentially after that. Draw a game tree and solve for the equilibrium path. Would Column want to move first? Would Row want to let them? Answer the same questions in (b) above, only assuming that Row would move first! Would Row want to do so? Would Column want to allow them to move first? Explain. 5. Answer the following questions regarding the matrix below, which represents the strategic interaction between Jackson and Dakota this past Sunday, where the two are trying to decide which games they want to play - if they both choose the same game then they get to play together! Dakota Risk Minecraft Barbies Risk 6,3 0, 2 1, 1 Jackson Minecraft 2, 0 5,5 2, 0 Barbies 1, 1 0, 2 3, 6 a) Suppose Jackson and Dakota make their decisions simultaneously. Are there pure strategy Nash equilibria? If so, what are they? Show your work. b) Suppose they move sequentially, and that Jackson moves first. First set up the game tree. What will be the equilibrium path of the subgame perfect Nash equilibrium outcome? Would Dakota want this to happen? Explain intuitively why or why not.6. You own \"Shake and Bake,\" a dessert food truck making cupcakes and milkshakes. The marginal cost of your milkshakes are constant, with MC=4. You are currently charging your customers S6 per shake. You just took an advanced series in econometrics and have estimated the demand function for milkshakes in your community, finding that the own price elasticity of demand is approximately - 2.0. Based upon what you have learned in managerial economics class, should you increase or decrease your price for shakes to increase your profits? You own a local fast-food restaurant and are introducing a new item to your menu Shakes! You must decide on a pricing strategy for burgers, fries, and shakes. The market you serve contains equal numbers of 3 types of consumers: parents, Burger Buffs, and Fries Fiends. Each consumer will purchase at most 1 of each food type. Their valuations of the two goods are listed in the following table. Assume for this problem that the costs of production are zero. Consumer Valuations Consumer Types Burgers Fries | Shakes Parents S8 S5 56 Burger Buffs S6 S3 52 Fries Fiends S3 S9 54 a. What are the optimal (separate) prices for burgers, fries, and shakes? b. What is the optimal bundle price for a meal that includes a burger, an order of fries, and a milkshake? Did bundling increase your profits? Explain. 8. Consider a perfectly competitive firm with a cost function of cc(qq) = 299 + (i)qqz, a) Solve for the firm's supply function, i.e. an expression for the firm's profit-maximizing level of output at any given market price. b) Suppose that the market demand curve is given by QQpp(PP) = 20 2PP and the market supply curve is given by QQss(PP) = 3PP 5. Solve for the equilibrium price. c) Calculate the firm's profits. Is the market in long-run equilibrium? Why or why not? If not, explain any long-run adjustments that you would expect and discuss how they would affect the firm. 9. Discuss five ways that a firm's voluntary sustainability initiatives may also affect a firm's profits