HW3solution - Homework 3 - Solutions Q1 Suppose valuations...

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Homework 3 - Solutions Q1 Suppose valuations are distributed along some interval, v i 2 [0 ; v ] with v > r: 1 If i 0 s valuation is above r; and he bids below r then he gets zero for sure. Let b ± i be the highest bid among all bidders other than r: Suppose instead i bids b i where b i > r and b i v i : Then, if b ± i < b i ; v i > r bidding below r is weakly dominated by bidding anything between r and v i : On the other hand, if v i r; the agent would have to bid above his valuation if he were to bid more than r: We showed in class that this is dominated by bidding below your valuation, hence in this case, bidding below r is not dominated Q2 We need to show that bidding anything else is dominated. If the agent bids b i = v i ; and b ± i < b i = v i , he makes v i ± b 3 where b 3 denotes the third highest bid, otherwise he gets zero. If he bids b i < v i ; in the case b ± i < b i ; b ± i is greater than b i but smaller than v i he loses, and gets zero whereas if he had bid b i = v i v i ± b 3 : If he instead bids some b 0 i > v i ; and b ± i > v i but b 0 i > b ± i ; so that i wins the auction even though he is not the one with the highest valuation, it i has the second highest valuation, and wins
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HW3solution - Homework 3 - Solutions Q1 Suppose valuations...

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