3. (4 points) Show in two ways that the symmetric equilibrium bidding strategy of a first price auction with N symmetric

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3 4 Points Show In Two Ways That The Symmetric Equilibrium Bidding Strategy Of A First Price Auction With N Symmetric 1 (56.36 KiB) Viewed 34 times

3. (4 points) Show in two ways that the symmetric equilibrium bidding strategy of a first price auction with N symmetric bidders each with values distributed according to F, can be written as b(v) = v - F los F(X), N-1 dr. = ) For the first way, use the solution from the notes (textbook) and apply inte- gration by parts. For the second way, use the fact that FN-1(r)(v — b(r)) is maximized in r when r = v and then apply the envelope theorem to conclude that d(FN-1()(v – Ô(u))/dv = FN-1(u); now integrate both sides from 0 to u = V.