Name. Midterm, Econ 171, February 27, 2014
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- Bartholomew Daniel Hawkins
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1 Name Midterm, Econ 171, February 27, 2014 There are 6 questions. Answer as many as you can. Good luck! Problem 1. Two players, A and B, have a chance to contribute effort to supplying a resource that is valuable to both of them. Where X A is the effort level of Player A and X B the effort level of Player B, the amount of the resource that will be supplied is equal to max{x A, X B }, which is the maximum of X A and X B. Each player can choose one of two effort levels, 0 or 5. If a player exerts effort level X and the amount of the resource supplied is Y, the payoff to that player is 2Y X. The players must move simultaneously, without observing each others actions. A) Show an extensive form representation of this game, labeling relevant information sets.
2 B) Show a strategic form representation of this game. Does this game have any strictly dominated strategies. If so, what are they? Write down the strategy profile(s) of all Nash equilibria for this game. Problem 2. A) The game is as in Problem 1, except that Player A moves first and Player B observes Player A s effort level before deciding how much effort to provide. Draw an extensive form representation of this game, labeling relevant information sets.
3 B) Construct the strategic form representation of this game. C) How many strategies are possible for Player A and how many strategies are possible for Player B? D) List any strategies for this game that are strictly dominated. List any strategies for this game that are weakly dominated. Does this game that have any Nash equilibria? If so write down their strategy profiles.
4 Problem 3. Consider the game described in extensive form below. A) List the strategies that are available to the mugger and list the strategies that are available to Simon. B) What strategies, if any, can be eliminated by iterated deletion of strictly dominated strategies?
5 C) Describe the game in Problem 3 in strategic form. D) Find the Nash equilibrium or equillibria if there are any.
6 Problem 4. The game has three players, the Pope, the Grand Inquisitor, and Galileo. The extensive form of the game is as follows, and the strategic form of this game is seen below. Find and list all of the Nash equilibrium strategy profiles for this game The Nash equilibria are: are (C/C, torture, refer), (C/DNC, torture, refer), (DNC/C, DNT, do not refer), (DNC/DNC, torture, do not refer) and (DNC/DNC, DNT, do not refer).
7 Problem 5. Firm A currently has a monopoly. Firm B is considering entering the industry. If Firm B does not enter the industry, Firm A will have profits of $10 million and Firm B will have profits of 0. If Firm B does enter the industry, Firm A can choose either to start a price war or to share the market. If Firm B enters and Firm A starts a price war, Firm A will lose $1 million and firm B will lose $1 million. If Firm B enters and Firm A shares the market, Firm A will have profits of $4 million and Firm B will have profits of $2 million. A) Describe this game in strategic form. B)What are the Nash equilibrium strategy profiles for this game? C) What strategy profiles remain after Iterated Deletion of Weakly Dominated Strategies?
8 Problem 6. As in the previous problem, Firm A currently has a monopoly and Firm B is considering entering the industry. But this game has an extra stage. Before Firm B decides whether to enter the industry, Firm A offers a bribe of $1 million to Firm B to stay out of the industry. If Firm A does not offer a bribe, then the game is as in the previous problem. Firm B can either enter or not and if firm B does enter, firm A can either fight or share. As in Problem 5 if Firm B enters and Firm A fights, both firms will lose $1 million. If Firm B enters and Firm A shares, Firm A has profits of $4 million and Firm B has profits of $2 million. If Firm A offers the bribe, Firm B can do one of two things. He can either accept the bribe and stay out of the industry or can reject the bribe and enter the industry. If the bribe is accepted, Firm A s profits are $9 million and Firm B s profits are $1 million. If the bribe is rejected and Firm B enters, Firm A can either fight or share. If Firm A fights, both lose $1 million. If Firm A shares, Firm A will have profits of $4 million and Firm B will have profits of $2 million. A) Draw an extended form representation of this game.
9 B) Show the strategic form payoff matrix for this game. C) What are the Nash equilibrium strategy profiles for this game?
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