Auctions Auction types: –First price, sealed bid auction –Second price, sealed bid auction –English auction (ascending bid auction) –Dutch auction (descending bid auction) Equivalence of: Second price, sealed bid and English auctions First price, sealed bid and Dutch auctions

Second Price Auction Outcome in second price auction: –Bidder with highest value wins object. –Bidding valuation is a dominant strategy –Bidder’s payment is expected level of second highest value given winner has highest value: –Seller’s expected income is expected payment of winning bidder

First Price Auction Outcome in first price auction: –Bidder with highest value wins object. –Bid less than valuation, otherwise 0 surplus –Shade bid as a function of number of other bidders –Bidder’s payment is expected level of second highest value given winner has highest value: same as expected payment in second price auction. –Seller’s expected income is expected payment of winning bidder (same as expected payment in second price auction).

Revenue Equivalence The first and second price auctions generate same expected income for seller. Since English auction is just a second price auction and Dutch auction a first price auction, all 4 types yield same expected income for seller. Roughly speaking, with independent buyer values, any auction that: i) awards object to buyer with highest value and ii) yields zero surplus to buyer with lowest possible value, generates the same expected revenue for seller. This result is the Revenue Equivalence Theorem Implication of this result is that there is no gain to be had from trying to design a sophisticated auction form (relative to ones above) as long as conditions of theorem satisfied. Caveats: –Number of bidders participating in auction must be independent of auction form. –Bidders have sufficient resources to always be able to pay for object. –Bidders risk neutral

Affiliated value auctions Sometimes the valuations of object by different buyers are affiliated -example: artwork Contrast with independent private value objects: -private value: personal tastes determine valuation -independent: a bidder’s taste/valuation does not depend on others’

Common value auction Common-value object has the same actual value to each bidder At the time of bidding, this common-value is unknown Different bidders may have access to different information about what the actual value is Bidders estimate the unique true value of winning the object with different pieces of incomplete information Winning the object would turn out equally rewarding for all, although just how rewarding is uncertain to any of the bidders at the time of bidding

Winner’s Curse: -Often by winning an auction of this type, you have overbid and will pay too much. -You should bid as if you have the highest estimate of the object’s value

Bidder Collusion Bidding Rings can arise, but conditions are not obvious: -must be well organized -need to identify bidders -need to awarded item to a ring member -need to split up profits There is a strong incentive to deviate What can seller do to discourage collusion? -sealed bid auctions -withhold information on auction result

Reserve Price Seller can choose to set a minimum “price” below which object will not be sold. This price is a reserve price. In practice reserve prices are announced in some auctions and not in others. The purpose of the reserve price is to raise the seller’s expected income by raising the expected price paid by the winning bidder.