# game theory homework help

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• Q1:Question 1 [20%] Consider the following normal form game G: X Y A B 4,-47, -7 8, -86, -6 a. [6% ] Is there a pure Nash equilibrium in G? Justify your answer. b. [14% ] Compute a mixed equilibrium using the indifference conditions of the players. Present both the equilibrium and the analysis clearly. No coding is required.See Answer
• Q2:Question 2 [25%] Ten commuters must decide simultaneously in the morning to use route A or route B to go from home (same place for all) to work (ditto). If a of them use route A, each of them will travel for 10a + 40 minutes; if b of them use route B, each of them will travel for 106 minutes. Everyone wishes to minimize his/her commuting time. Your tasks: 1 a. [12%] Describe the pure Nash equilibrium (or Nash equilibria) of this ten-person game. Compute the corresponding profile of commuting times. Explicitly list all equilibrium conditions that are satisfied. b. [6%] What is the traffic pattern (strategies) minimizing the total travel time of all commuters (the sum of their travel times)? Describe the corresponding profile of commuting times (individual payoffs/cost). c. [7% ] What does this mean about the Price of Anarchy of this game (assuming that the objective function is the total travel time)? No coding is required.See Answer
• Q3:Question 3 [25%] Consider the following normal form game G. Your task is to find the correlated equilibrium that max- imizes the sum of players' utilities, using Linear Programming in MATLAB. In your report, you need to present the equilibrium that you have computed, the linear program that you are solving (which should include the equilibrium conditions that are satisfied), and a screenshot of your MATLAB in- put AND output. Use the following ordering of variables when constructing your MATLAB input: PXA, PXB, PXC, PYA, PYB, PYC, PZA, PZB, PZC. A B с X 6,6 0,8 0,0 Y 8,0 2,2 0,0 Z 0,0 0,0 1,1See Answer
• Q5:1. Briefly explain the differences between the equilibrium concepts we discussed in game theory. What do we need to assume about people's decision making to find equilibria? See Answer
• Q6:2. Suppose that in a small town, the market for cement had five companies with market shares 0.3, 0.2, 0.2, 0.2, and 0.1. The following year, a new firm entered but the leading firm increased its share. Now the shares are 0.5, 0.1, 0.1, 0.1, 0.1, and 0.1. Did the market become more competitive or less competitive?See Answer
• Q7:3. If you were playing a game of Stag Hunt, would you rather play the simultaneous version of the game or the sequential version? Why? See Answer
• Q8:4. Explain the Bertrand paradox. How does it inform our explanations of market power in industries with a small number of firms? See Answer
• Q9:5. Why would firms want to differentiate their products?See Answer
• Q10:6. Suppose a market has a Herfindahl index of 0.1. Should we expect this market to be fiercely competitive? Does this imply efficiency? See Answer
• Q11:In an industry with two firms, their best responses are Q1=10-1/6 Q2 and Q2=8-1/6Q1. What is the total quantity exchanged on the market?See Answer
• Q12:8. Suppose an industry has three identical firms competing on quantities with demand P = 100 - 20 and constant marginal costs of MC = 1. What are the firms' best response functions? See Answer
• Q13:9. What could lead the firms in question 8 to have asymmetric best response functions? What assumption(s) would have to change? See Answer
• Q14:10. Why should a worker's wages equal their marginal revenue product? In what cases would this claim be less likely to hold? See Answer
• Q15:11. The labor supply curve is the relationship between the wage level and the quantity of labor that workers are willing to provide. Why is applying the usual ceteris paribus assumption more complicated in this case than when we use apply it to the product market? See Answer
• Q16:12. What factors do economists suppose influence the amount of education people choose to obtain? If the decision were based entirely on material considerations, how would people decide how much education they should get? Can you think of events that could influence this decision? See Answer
• Q17:Problem3 You can solve the four problems below without making a single calculation. Indicate your answer by circling TRUE or FALSE (a) Row's mixed strategy Nash equilibrium is the same in Games 1 and 3. TRUE FALSE (b) Column's mixed strategy Nash equilibrium is the same in Games 1 and 3. TRUE FALSE (c) Row's mixed strategy Nash equilibrium is the same in Games 1 and 2. TRUE FALSE (d) Column's mixed strategy Nash equilibrium is the same in Games 1 and 2. RUE FALSESee Answer
• Q18:Problem 2 (a) Solve the game for a mixed strategy equilibrium, i.e., find the values of po and go and write down the equations from which you have derived them. (b) Calculate the payoff to the Row player in the mixed-strategy Nash equilibrium. (c) List all Nash equilibria in this game. (d) Draw the best response curve for the Column player only using the coordinate system below.See Answer
• Q19:1 a) Calculate u (0.6X € 0.4Y, 0.7A Ⓒ 0.3B) [NOTE: Understanding notation, i.e., what you are asked to calculate, is a part of the problem] (b) List all best response strategies of the Row player to Column playing X.See Answer
• Q20: b) Show that this game has a unique subgame-perfect equilibrium (SPE) and find it. c) Does a player's payoff increase or decrease with his own patience? With the opponent's patience? Discuss the intuition behind your findings. d) As ₁0, player 1's SPE payoff converges to 1 - 8₂. Give a simple reason why this limit is 1 - 8₂ without actually taking a limit. (In other words, provide an intuitive explanation for this result.) a) Show that SPE payoffs are unique, and that player 1's SPE payoff is \frac{1-\delta_{2}}{1-\delta_{1} \delta_{2}} Find player 2's SPE payoff. Consider the infinite-horizon alternating-bargaining game from Section 11.3 of Tadelis, but suppose that player 1's discount factor could be different from player 2's discount \text { factor } \delta_{2} \in(0,1) \text { factor } \delta_{2} \in(0,1)See Answer

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