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Sample Midterm

Sample Midterm - i times(12 x T where x T = x 1 x 2 is the...

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Econ 166A Sample Midterm Questions Sinervo & Musacchio 1. Player #1 (the Serf) first chooses either to plant crops (P) or to hide the seed (H). If he chooses P, then at harvest time Player #2 (the Duke) either takes the entire crop (T) resulting in payoffs (0, 3) for the two players, or else shares (S) resulting in payoffs (2, 2). If the Serf chooses H, then the game ends with payoffs (1, 0). a. Draw the tree (i.e., the extensive form) for this game. b. Find the backwards induction (BI) solution to this game, and the corresponding payoffs. c. Write the game in normal form, and find all Nash equilibria. d. Find strategies that lead to an efficient outcome, i.e., one that maximizes the payoff sum. e. If the Duke could sign a binding contract before the game starts, could he increase his payoff? If so, what would the contract say? 2. Consider the following 2-player normal form game. Each player’s strategy set consists of all real numbers between 0 and 12. Each player i’s payoff equals her own choice x
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Unformatted text preview: i times (12- x T ), where x T = x 1 + x 2 is the sum of the two choices. a. What is player 1’s best response when player #2 chooses x 2 = 0? When x 2 = 12? b. Which strategies of player #1 are dominated? Which strategies are rationalizable? c. Find player #1’s best response to an arbitrary x 2 . Graph it in the (x 1 , x 2 ) plane. d. Find a Nash equilibrium of the game. e. How would the game change if player #1 moved first? Explain briefly. f. For extra credit, solve the extensive form game in part e., and find an interpretation in social sciences or biology or engineering for that game. 3. Chapter 2 Harrington Question 11 4. Chapter 3 Harrington Question 4 5. Chapter 3 Harrington Question 9 6. Chapter 4 Harrington Question 1 7. Chapter 4 Harrington Question 8 8. Chapter 5 Harrington Question 1 9. Chapter 5 Harrington Question 2 10. Chapter 6 Harrington Question 3 11. Chapter 6 Harrington Question 7...
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