Final_2010

# Final_2010 - MS&E 246 Feryal Erhun Final Examination...

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MS&E 246 Final Examination Feryal Erhun March 15, 2010 Instructions 1. Take alternate seating. 2. Answer all questions in the blue books provided. If needed, additional blue books will be available at the front of the room. Answers given on any other paper will not be counted. 3. Notes, books, calculators, and other aids (except the cheat sheet) are not allowed. 4. The examination begins at 3:30 pm, and ends at 6:30 pm. 5. Show your work! Partial credit will be given for correct reasoning. Honor Code In taking this examination, I acknowledge and accept the Stanford University Honor Code. NAME (signed) NAME (printed) 1

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Problem 1 (15 points). Answer each of the following questions TRUE or FALSE. If TRUE, provide a brief (1-2 sentence) justification for your answer; if FALSE, provide a brief counterexample. (1 point per correct answer; 4 points per correct justification/counterexample) (a) (5 points) Consider the following payoff table and assume g > h > 0 , w > 0 , v > 0 . Company Monitor No monitor Worker Work 0 , - h w , - w Shirk w - g , v - w - h w - g , v - w This game is dominance solvable when w < g . (b) (5 points) Consider the following game: Player 2 C D Player C 1 , 1 - 1 , 2 1 D 2 , - 1 0 , 0 Suppose that this game is played infinitely many times with discount fac- tor δ . Consider the following strategies: Play C if all previous outcomes have been (C,C), otherwise, play D forever. These strategies form a Nash equilibrium when δ 1 / 2 . (c) (5 points) Alice is a moderate drinker who plans to buy a bottle of wine. Her utility is U = θq - t where q is the quality of the wine, t is the price of the wine, θ is a positive parameter that indexes her taste for quality. If Alice decides not to buy any wine, her utility is 0. Alice may either be a “coarse” (in which case her θ is θ 1 = 5 ) or a “sophisticated” (in which case her θ is θ 2 = 10 ) drinker with equal probability.
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