1 Chapter 6: Auctions SCIT1003 Chapter 6: Auctions Prof. Tsang

What are Auctions? p A way to sell something, e.g. paintings or antiques in Sotheby’s. Liquidation sale in a bankruptcy. Governments can use it to buy things or services, the lowest bidder will get the contract. There are different types of auctions. 2

English Auctions Auctioneer calls out ascending bids in fixed increments starting from the minimum bid. Bidders indicate they bid at the price calling out by raising their hands. Price keeps going up until no bidder will take the higher bid. The last active bidder win. 3

Japanese auctions Similar to English auctions. Bidders participate in the bidding by raising their hands. Price starts from the minimum bid and goes up in fixed increment. You drop out from the bidding by lower your hand. Once you drop out, you cannot get back in. The last active bidder wins. 4

In an English auction – Bidders can jump in or out of the bidding any time during the auction. – You don’t know who are your competitors. In a Japanese auction – Once you are out you cannot get back in. – You know who are your competitors. 5 Difference between English & Japanese auctions

The last person bidding will be the one with highest valuation. Item is sold to the bidder with the highest valuation. Seller receives the second highest valuation. Bidders may have different valuation of the item they bid on. Strategy: bid lower than your valuation. 6 Similarity between English & Japanese auctions

Vickrey (second-price) auction Proposed by Nobel economist William Vickrey in All bids are placed in individual sealed- envelopes. Open all envelopes to determine the winner, i.e. the highest bidder. The winner pays the second highest bid. Strategy: bid at your valuation. 7

Simple strategy for bidders – Just bid at their true values – No need to worry about the bid increment Result is the same as the English or Japanese auctions Variant being used in on-line auctions, e.g. eBay. 8 Advantage of Vickrey auction

Sealed-bid auctions Bidders put their bid in individual sealed- envelopes. The envelopes are opened and the highest bidder wins. Winner pays his/her bid. 9

In a sealed-bid auction Important strategy: bidding as if you have won. Look ahead to figure out the consequence of you actions. Avoid winner’s curse. 10

Example: you are going to bid for a company “ABC” Suppose you know that if you own ABC you can increase its value by 50%. You know ABC currently values with equal likelihood between $2 to $12 million. The seller will accept any bid that exceeds the current value and reject otherwise. How should you bid in order that you may profit from this deal? 11

Things to consider? The mean value of ABC is $7 million. If you can increase its value by 50%, then it will worth $10.5 million in future. Does that mean you may bid at $10 million and expect to make a bit profit at $0.5 million? What if it worths $8 million of just $4 million? 12

If you offer at $10.5 m & the seller agrees, It means ABC worths less than $10.5 m Then the expected/mean valuation of ABC is at most $(2+10.5) = $6.25 m After you increase its value by 50% it will worth at most $9.375 m Then you will lose at least $ m = $1.125 m! 13

How to come up with a bid? Assume you bid at x and is accepted You then expect ABC to worth (2+x)/2 If you don’t want this to be losing deal, you need 1.5*(2+x)/2 > x i.e. 3*(2+x) > 4x or x<6 14

Dutch auctions Price start high and fall until the first bidder indicates his/her participation. If you raise your hand in a Dutch auction, the auction stops and you have won. It is the reverse of the Japanese auction. It is similar to a sealed-bid auction. Use same strategy as in a sealed-bid auction: bid as if you have won. 15