Ascending Auction: price starts at zero, and rises slowly. Buyers indicate their willing to continue bidding (keeping hand up) or can exit. Auction ends when just one bidder remains. Final bidder wins, and pays the price at which the second remaining bidder dropped out. Optimal strategy (regardless of what opponents do) is to keep bidding until the price just equals your value. Bidder with highest value will win, winner will pay second highest value. Average revenue from auction with n bidders = E* 100 b/c that's the expectation of the bid of the second highest bidder. With higher demand, the expected created value is higher (=7:r1*100), winner's surplus is lower (= nl:* 100), and seller captures a higher share of generate value (a surplus of 5*100) . . . . n . . . n-1 Expected valuation of auction winner is = m*loo and expected price of winner is = m*loo = . . . 1 revenue from auction. Winner's surplus is E* 100. Seller's surplus = average revenue from auction = 2=1*100. n+1 For example: if we repeatedly draw two values from U[0,100], on average, the highest draw will be $66.66 and the second highest will be $33.33. Average revenue from auction from 2 bidders will be $33.33. Winner pays $33.33 and winner's surplus is $33.33. Seller's surplus = $33.33 Second Price Auction: Bidder submit sealed bids. Seller opens the bids. Bidder who submitted the highest bid wins. Winner pays the second highest bid. Optimal strategy in the second price auction (regardless of what opponents do) is to bid your value. In equilibrium, everyone bids their value. Bidder with highest value wins and pays amount equal to the second highest value. This is exactly the same as the ascending auction: same winner, same price/revenue. Problem: You have decided to hold a second-price auction with no reserve to sell a painting. There are currently 3 bidders who would participate in the auction. You can also hire a marketing firm, who can bring up to 20 additional bidders to the auction at a cost of $2 per bidder. The bidder's valuations (including the 3 initial bidders) are drawn independently and uniformly at random over the interval [0,5100]. 1. How many additional bidders will you ask the marketing firm for if you want to maximize profit. 2. How many additional bidders will you ask the marketing firm for if you want to maximize winner's surplus (i.e., her valuation for the good minus her payment)