ps6 - Ec1052 Introduction to Game Theory Harvard University...

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Ec1052: Introduction to Game Theory Handout 14 Harvard University 18 April 2004 Problem Set 6 Due: Saturday, May 8 (Irit’s folder) Challenging problems are marked with one star. Double-starred questions do NOT count towards the grade. They are very hard and simply for the intellec- tually curious. Remember that you can work in groups but you have to write up your own solutions. Good luck! Problem 1. You have an opportunity to buy a painting during an auction. You believe that whatever the value of the picture, V, you can sell it with a 50% profit (i.e. you’ll get 1.5V). You do not know the value of the picture but you think it is anywhere between $0 and $1000. You assign a uniform distribution to V in this range. You have to bid. The trader will reject your offer if it is below V. 1(a) What is your optimal bid ? 1(b) How is this problem related to the Winner’s Curse ? Problem 2. Consider the game ’auctioning off a dollar’ which we played in the last class. The auctioneer offers a Dollar and n players can bid in an all-pay auction (you pay your bid).
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