Expected price: 33.3 If seller has zero value, equal split of price, consumer surplus. With three bidders Expected value of winner: 75 and Expected price: 50 With more demand, expected value creation is higher and seller is able to capture a higher price (and p/value?). With 10 bidders, exp. value of winner is 10/11, exp. price is 9/11 of 100. Second Price Auction Bidders submit sealed bids. Seller the bids. Bidder who submitted the highest bid wins. Winner pays the second highest bid. How should you bid? Claim. An optimal strategy in the second price auction (regardless of what opponents do) is to bid your value. Proof Compare bidding v to bidding some b > v. Only way the higher bid matters is if opponent bid is above but less than b. Then you lose if you bid v and win if you bid b, but you pay above your value. So better to have bid v. Compare bidding v to bidding some b < v. Only way the lower bid matters is if opponent bid is above b but less than v. Then you lose if you bid b and win if you bid v. So bidding v is better you win and pay less than your value. – In equilibrium, everyone bids value. Bidder with highest value wins. Pays an amount equal to second highest value. Exactly the same as the ascending auction! Same winner, same price/revenue. Example: three bidders with values 25, 33, 75. Winner has value 75, pays 33, as in ascending auction. Vickrey Auction
Expected price: 33.3 If seller has zero value, equal split of price, consumer surplus. With three bidders Expected value of winner: 75 and Expected price: 50 With more demand, expected value creation is higher and seller is able to capture a higher price (and p/value?). With 10 bidders, exp. value of winner is 10/11, exp. price is 9/11 of 100. Second Price Auction Bidders submit sealed bids. Seller the bids. Bidder who submitted the highest bid wins. Winner pays the second highest bid. How should you bid? Claim. An optimal strategy in the second price auction (regardless of what opponents do) is to bid your value. Proof Compare bidding v to bidding some b > v. Only way the higher bid matters is if opponent bid is above but less than b. Then you lose if you bid v and win if you bid b, but you pay above your value. So better to have bid v. Compare bidding v to bidding some b < v. Only way the lower bid matters is if opponent bid is above b but less than v. Then you lose if you bid b and win if you bid v. So bidding v is better – you win and pay less than your value. In equilibrium, everyone bids value. Bidder with highest value wins. Pays an amount equal to second highest value. Exactly the same as the ascending auction! Same winner, same price/revenue. Example: three bidders with values 25, 33, 75. Winner has value 75, pays 33, as in ascending auction. Vickrey Auction
ECON1010-Entire-Semester.docx