MidF07 - Name:_____________ SID:______________...

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Unformatted text preview: Name:_____________ SID:______________ GSI:______________ Game Theory in the Social Sciences Political Science 135/Economics 110 Midterm Fall 2007 Question 1 I NSTRUCTIONS FOR THE M IDTERM : This midterm is open book and open note. Answer all of the following three questions, and be sure to justify all of your answers. There are 160 points possible (2 points per minute), and the numbers in parentheses indicate the number of points for that question. Budget your time carefully. Some questions are easier and some are harder. If you get stuck on a hard question, go on to the easier ones. Good luck! Explain all of your answers. A correct but unexplained answer will not receive full credit. Fall 2007 Question 1 (40 points/20 minutes): The early presidential primaries have eliminated all but four candidates. Two Democrats remain, Ms C and Mr. O ; and two Republicans remain, Mr. G and Mr. T. Polling data reveals that C would lose to G but beat T. O would beat G but lose to T . The dilemma facing the parties is captured in the game below where the Von Neumann-Morgenstern payoffs are vote shares. G Rep T ( t ) C (c) 45, 55 60, 40 Dem O 65, 35 45. 55 Let c denote the probability that Dem nominates candidate C and t be the probability that Rep nominates T . (a, 10 pts): Suppose Dem nominates C with probability c = .8. What strategy maximizes Rep s payoff? 1 Fall 2007 2 (b, 15 pts): Draw Rep s best-reply. (c, 15 pts): Find the mixed equilibrium of the game. How likely is Dem to nominate Ms C and Rep to select Mr. T ? Name:_____________ SID:______________ GSI:______________ 1 G AME T HEORY IN THE S OCIAL S CIENCES Political Science 135/Economics 110 Midterm Fall 2007 Question 2 I NSTRUCTIONS FOR THE...
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MidF07 - Name:_____________ SID:______________...

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