solutionspset6 - Ec1052: Introduction to Game Theory...

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Unformatted text preview: Ec1052: Introduction to Game Theory Handout 15 Harvard University 9 May 2004 Solutions to Problem Set 6 Problem 1. 1(a) Your optimal bid is 0. If you bid any positive value and you win the object then the value was between 0 and your bid b . Hence the expected value is V = b/ 2 and the profit you can make from it is = 3 2 b/ 2 = 3 4 b which is still less than what you paid for. 1(b) Winning is bad news in this game because it means that the true value is lower than your bid. Put differently, the seller has information about the value of the object - if you win the auction then his assessment of the value was value. Problem 2. 2(a) Assume there is a pure-strategy NE. If the highest bid is less than 1 then a player could deviate and bid more and win the dollar. If the highest bid is 1 dollar then all other players should bid 0 instead of wasting their bid. But then the highest bidder could do better by bidding . 2(b) Assume that both players mix over [0 , 1] (this can be shown to be true). Assume that their bid function has density f . Then bidding b wins the good with probability F ( b ) = R b f ( t ) dt . A bidder has to be indifferent between all bids in her support - if she bids 0 she gets exactly 0. Therefore, we have: F ( b )- b = 0 (1) This implies that...
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solutionspset6 - Ec1052: Introduction to Game Theory...

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