Ucla Econ 101 Final Spring 2011
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Final Exam (VERSION 1): Econ 101
• Please write your name at the top of every page of this mideterm • Please write your name, TA’s name, and the time of your discussion section here
Your Name:
TA’s Name:
Discussion Time:
• The exam has one parts: Written Questions. • There should be 16 total pages (front and back). Quickly read through the exam before beginning. • There are 100 total points available. Point values are listed next to each problem part. Please allocate your time accordingly
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Written Questions
1. Consider the following payoff matrix Player L M T 2, 0 3, 1 Player 1 C 3, 4 1, 2 B 1, 3 0, 2 2 R 4,2 2,3 3,0
a. (5pnts) Find the pure strategy Nash equilibria of the simultaneous game b. (5pnts) Now suppose the game is played sequentially. Find the subgame perfect equilibrium if player 1 goes first and if player 2 goes first. c. (5pnts) Discuss whether each of the players would want to go first or second. d. (5pnts) Write down a system of equations such that the solution to the system would give a completely mixed strategy equilibrium of this game (please clearly define all of your notation). Can this system of equations be solved? (Hint: think about the condition requiring player 1 to play B with positive probability). Explain what the answer means.
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WORK SPACE
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WORK SPACE
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2. Suppose Player 1 and Player 2 are playing a simultaneous move game with the following payoff matrix: Player 2 L R T 0, 4 α, 3 Player 1 B 3, 3 4, 6 where α ≥ 0 a. (5pnts) Define a dominant strategy equilibrium. Is there any value of α for which there is a dominant strategy equilibrium. If so, find the values of α. If not, show why. b. (5pnts) Describe all the pure and mixed strategy equilibria of the game as a function of α c. (5pnts) Suppose α = 5. What would the outcome be if the players could cooperate?
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WORK SPACE
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WORK SPACE
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3. Billy has just inherited a horse ranch from his uncle. The ranch is located in
Final Exam (VERSION 1): Econ 101
• Please write your name at the top of every page of this mideterm • Please write your name, TA’s name, and the time of your discussion section here
Your Name:
TA’s Name:
Discussion Time:
• The exam has one parts: Written Questions. • There should be 16 total pages (front and back). Quickly read through the exam before beginning. • There are 100 total points available. Point values are listed next to each problem part. Please allocate your time accordingly
1
2
Written Questions
1. Consider the following payoff matrix Player L M T 2, 0 3, 1 Player 1 C 3, 4 1, 2 B 1, 3 0, 2 2 R 4,2 2,3 3,0
a. (5pnts) Find the pure strategy Nash equilibria of the simultaneous game b. (5pnts) Now suppose the game is played sequentially. Find the subgame perfect equilibrium if player 1 goes first and if player 2 goes first. c. (5pnts) Discuss whether each of the players would want to go first or second. d. (5pnts) Write down a system of equations such that the solution to the system would give a completely mixed strategy equilibrium of this game (please clearly define all of your notation). Can this system of equations be solved? (Hint: think about the condition requiring player 1 to play B with positive probability). Explain what the answer means.
2
WORK SPACE
3
WORK SPACE
4
2. Suppose Player 1 and Player 2 are playing a simultaneous move game with the following payoff matrix: Player 2 L R T 0, 4 α, 3 Player 1 B 3, 3 4, 6 where α ≥ 0 a. (5pnts) Define a dominant strategy equilibrium. Is there any value of α for which there is a dominant strategy equilibrium. If so, find the values of α. If not, show why. b. (5pnts) Describe all the pure and mixed strategy equilibria of the game as a function of α c. (5pnts) Suppose α = 5. What would the outcome be if the players could cooperate?
5
WORK SPACE
6
WORK SPACE
7
3. Billy has just inherited a horse ranch from his uncle. The ranch is located in