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ps8s Duopolies

ps8s Duopolies - Problem Set 8 Econ 115a Be sure to mark...

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Problem Set 8 Econ 115a March 30, 2008 Be sure to mark your paper with your name, your teaching assistant’s name and section time. 1. Define (a) Price discrimination (b) Nash equilibrium (c) Duopoly 2. Two Congressmen are trying to decide whether to vote for a proposed law. Call the two Congressmen Frank and Beans.The Congressmen’s constituents hate the law. Each belongs to the party that wants the law, and each knows that the law needs two (and only two) more votes to pass. That is, the law will pass only if both of them vote for it, but it will not pass if either votes against it. Each Congressman knows that if they vote for this law, many people will praise them but they are likely to face strong opposition for reelection. Think of their utility in two parts: they get one source of utility from doing what their constituents want, and another from doing what their party leadership wants. (a) Construct a two-by-two normal-form game that will help you to analyze the decision these Congressmen face. There are two players (the Congressmen) and two actions: vote for or against. Each Congressman su ers a utility penalty of -10 if they vote against their constituents’ wishes. On the other hand, if they both vote “no” then they will get to make joint appearances on Wolf News, which gives each Congressman a utility of 20. (b) What is the Nash equilibrium to this game? (c) Now assume that each Congressman gets a further utility of C i (that is, C F for Frank and C B for Beans) for going along with the party leadership. C F and C B will be delivered to each Congressmen in the form of money for a reelection campaign, should they vote for the law. Re-write the normal-form game with these C’s included. (d) Derive an expression for each C that describes the minimum utility that the party leadership has to o er to get Frank and Beans to vote for the law. In other words, 1
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the party leader wants to set C F and C B such that the Nash equilibrium is for each Congressman to vote for the law. (e) Explain in words why this situation is “strategic.” That is, why does Frank care what Beans does and vice-versa?
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