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Problem 1 We consider the case of a sealed bid second price auction with 1?. bidders. We assume that all the bidders act optimally, hence they bid truthfully by indicating own valua- tions. The valuations of the bidders are independently and randomly drawn from a triangular distribution with probability density function (PDF) f (v) = év, with 'U E [0, 2].
1. Calculate the optimal reserve price for a 2nd price auction.
2. Suppose now we're running a ?rst price auction (without reserve price). Calculate the optimal bid function of a bidder with valuation v.
3. Use your answer from the previous question and calculate the Optimal bid function when the number of bidders goes to in?nity.
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