Auctions Hal R. Varian

Auctions Auctions are very useful mean of price discovery eBay: everyone’s favorite example DoveBid: high value asset sales at B2B level Google, Yahoo, MSN: sell ads via an auction

Auction Theory One item to auction off, 1 seller, many buyers Value models Private value: independent of others Common value: everyone has the same value, different information and/or estimates of that value Common forms: English, Dutch, Sealed bid, Vickrey

Types of auctions English ascending bid Highest value bidder gets item Pays 2 nd highest value Dutch auction, descending bid Sealed bid, 1 st price Your bid depends on what you think others will do Vickrey auction Sealed bid, 2 nd price

Analysis (for private values)‏ Dutch and sealed bid are “strategically equivalent” since strategy is just determining at what price you will bid English and Vickrey auctions are strategically equivalent (up to bid increment)‏

Truthtelling in auctions Will generally want to bid less than your value in a sealed bid (or Dutch) auction Will go up to your true value in English auction What about Vickrey auction?

Vickrey auction Payoff to 1 = Prob(b 1 > b 2 )[v 1 – b 2 ] If v 1 > b 2, want to max Prob(b 1 >b 2 )‏ so set b 1 =v 1 If v 1 b 2 ) so set b 1 =v 1 So always want to tell the truth Like eBay’s proxy bidding agents or Google’s Adwords Discounter

Revenue maximization A Vickrey (or English auction) maximizes surplus (= value - price) but not revenue In general, want to use a reserve price (a minimum price that the seller will accept)‏ Example 2 values in population: (10,100)‏ prob ½ of drawing either value in sample Possible outcomes (100,100)‏ (100,10)‏ (10,100)‏ (10,10)‏

Expected revenue

Revenue maximizing auction Note that revenue max auction is inefficient General form of rev max auction Use Vickrey/English auction + reserve price Similar to monopoly pricing Turns out that reserve price doesn't depend on number of bidders

Reserve price and number of bidders Reserve price only matters when High bid is above reserve Second highest bid is below reserve This becomes less likely the more bidders you have Always better to have 1 more bidder and 0 reserve, than having power to set reserve

Common value auctions Example: lease offshore drilling rights, jar of coins Winner's curse: if you bid your true estimated value, will probably overbid Should bias bid downwards: the more people there are the larger the discount due to winner's curse