Auctions Hal R Varian Auctions are very useful

Auctions Hal R. Varian

Auctions are very useful mean of price discovery e. Bay: everyone’s favorite example Dove. Bid: high value items, not so well known Google, Yahoo, MSN: sell ads via an 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 Common forms: English, Dutch, Sealed bid, Vickrey

Types of auctions English ascending bid Dutch auction, descending bid Sealed bid, 1 st price Highest value bidder gets item Pays 2 nd highest value 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) If v 1 < b 2 , want to min Prob(b 1>b 2) So always want to tell the truth Like e. Bay’s proxy bidding agents or Google’s Adwords Discounter

Revenue maximization A Vickrey (or English auction) maximizes surplus 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, 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 However, inefficiency goes away as there are more bidders with dispersed values