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ps4_sol5-1

ps4_sol5-1 - Solutions to Practice Problem Set 4 ECON 100C...

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1 Solutions to Practice Problem Set 4 ECON 100C Perloff Chapter 14 9. A thug wants the contents of a safe and is threatening the owner, the only person who knows the code, to open the safe. “I will kill you if you don’t open the safe, and let you live if you do.” Should the information holder believe the threat and open the safe? The table shows the value that each person places on the various possible outcomes: Thug Safe’s owner Open the safe, thug does not kill 4 3 Open the safe, thug kills 2 1 Do not open, thug kills 1 2 Do not open, thug does not kill 3 4 a. Draw the game tree. Who moves first? The owner moves first, by either opening or not opening the safe. Don’t Kill (3,4) Open Thug Kill (1,2) Owner Don’t Kill (4,3) Don’t Open Thug Kill (2,1) b. What is the equilibrium? There is a unique subgame perfect Nash equilibrium (SPNE): (Owner Doesn’t Open; Thug Doesn’t Kill if Owner Opens, Thug Doesn’t Kill if Owner Doesn’t Open) c. Does the safe’s owner believe the thug’s threat? No, the safe owner doesn’t believe the threat. The safe owner knows that if s/he does not open the safe, the thug will receive a higher payoff from not killing him/her. d. Does the safe’s owner open the safe? No, the safe owner doesn’t open the safe. 10. Warner Bros. decides whether to release Matrix 2 on the July 4 weekend or on the July 18 weekend. Simultaneously, Terminator 3’s producer decides which of those two weekends to release its film. The payoff matrix (in millions of dollars) of the simultaneous-moves game is:

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2 a. What is the Nash equilibrium to this simultaneous-moves game? Both movies open on July 4. This is each producer’s dominant strategy. b. Which release dates maximize the sum of the profits? Explain. T-3 on July 18, Matrix 2 on July 4 – total profits are 120. Warner Bros. has a much higher payoff if the T-3 producer chooses a later weekend for the release, and the T-3 producer does not lose as much as Warner Bros. gains. c. What is the greatest price Warner Bros. is willing to pay to purchase the distribution rights to T-3 (so that it can coordinate the release dates)? What is the lowest price that T-3’s producer is willing to accept to sell the rights? Are there mutually beneficial prices at which the trade takes place? If Warner Bros. doesn’t purchase the rights, it gets a payoff of 50 (from Nash Equilibrium play). If it purchases the rights, it can select the optimal outcome and get profits of 120. The maximum amount Warner Bros. is willing to pay is 70. The lowest price the T-3 producer will accept is 50 – her equilibrium profits. At prices between \$70 and \$50, trade can occur. d. If Warner Bros. purchases the distribution rights of T-3, when does it release the film and when does it release Matrix 2? Explain. Warner Bros. Releases T-3 on July 18 and Matrix 2 on July 4. This is the joint profit maximizing distribution schedule.
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ps4_sol5-1 - Solutions to Practice Problem Set 4 ECON 100C...

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