midterm 2 practice problems fall06

midterm 2 practice problems fall06 - Midterm 2 Practice...

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Midterm 2 Practice Problems The new generation of i-pod has just been introduced and every student at the U of M is deciding whether to buy it or not. The net benefit of buying the new i-pod depends on what percentage of U of M students also buy it as follows: 350 + x, if 0≤x≤30 470 – 3x, if 30≤x≤100 where x is the percentage of students that buy the new i-pod. If a student doesn’t buy the new i-pod, than the net benefit for him or her is 365, 1. Which of the following is true: a. there is no equilibrium b. x = 15 is the only equilibrium c. x = 15 and x = 35 are the only equilibria d. x = 15, x = 35 and x=100 are the only equilibria e. x = 0 , x = 15 and x = 35 are the only equilibria For the next two questions suppose that the net benefit from buying the new i-pod is 400 – 2x for all x and that the net benefit of not buying the new i-pod is 200. 2. Which of the following is true: a. there is no equilibrium b. x = 0 is a unique stable equilibrium c. x = 0 is a unique unstable equilibrium d. x = 100 is an unique stable equilibrium e. x = 100 is an unique unstable equilibrium 3. Suppose that the number of students at the U of M is 100. Then, if x is equal to the socially optimal percentage of people buying the new i-pod, the total benefit is equal to: a. 15000 b. 20000 c. 25000 d. 40000 e. 50000
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4. Consider the table below: Nikolay A B C Tanya 1 1, 0 3, 2 5,1 2 2, 2 0, 1 1,0 3 3, 3 1, 4 2,3 The equilibrium payoff of Tanya is: a. 1 b. 5 c. 3 d. 2 e. 0 1 Tanya 2 In this game Tanya first chooses to go 1 or 2, and then she and Nikolay play simultaneously a game in which Tanya is the Row player and Nikolay is the Column player 5. How many Subgame Perfect Nash Equilibria in pure strategies does this game have? a. 0 b. 1 c. 2 d. 3 e. 4 Left Right Up 3, 3 0, 2 Down 0, 0 1, 1 Left Right Up 1, 4 2, 1 Down 2, 2 1, 0
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6. After you apply Forward Induction, which one of the following is Nikolay’s equilibrium payoff: a. 0 b. 1 c. 2 d. 3 e. 4 7. Tanya and Nikolay are playing the following infinitely repeated game of Prisoners’ Dilemma (Tanya is the row player and Nikolay is the column player): Deny Confess Deny 7,7 2,10 Confess 8,4 3,5 In this game, what is the highest interest rate that will support the cooperative outcome (Deny, Deny) in every period if both players are playing grim strategy? a. 0 b. 0.5 c. 0.66 d. 1 e. 1.5 8. What is the highest interest rate that will support the cooperative outcome (Deny, Deny) in every period if both players are playing tit-for-tat strategy? a. 0 b. 0.5 c. 1 d. 1.5 e. 2
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9. Party Problem: There are 100 people who want to have a party. If n of them help set-up the payoff from the party for someone who helps set up is: S( n ) = n And the payoff to coming to the party without helping set up is: P( n ) = 2 n + 2 In this model, the outcome may not be socially optimal. This is because: a. For high enough values of n , the payoff to just partying is higher than the payoff to setting up, so only a few people will set up. b.
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midterm 2 practice problems fall06 - Midterm 2 Practice...

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