Second-Price Auction: Truthful Bidding Payoff

Problem

You participate in a sealed-bid second-price (Vickrey) auction. The highest bidder wins the item but pays a price equal to the second-highest bid.

Your private value for the item is v = 60. There are n = 2 rival bidders, and each rival's private value is drawn independently from a Uniform[0, M] distribution with M = 100. Every bidder (including you) bids according to the weakly dominant strategy of the auction.

Compute your expected surplus (expected value minus payment), where surplus is 0 in any outcome where you do not win.

Enter your answer as a decimal rounded to 4 decimal places.