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Auctions

Hal R. Varian. Auctions. Auctions. Auctions are very useful mean of price discovery eBay: everyone’s favorite example DoveBid: 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

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Auctions

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  1. Hal R. Varian Auctions

  2. Auctions Auctions are very useful mean of price discovery eBay: everyone’s favorite example DoveBid: high value items, not so well known Google, Yahoo, MSN: sell ads via an auction

  3. 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

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

  5. 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)‏

  6. 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?

  7. Vickrey auction Payoff to 1 = Prob(b1 > b2)[v1 – b2] If v1 > b2 , want to max Prob(b1>b2)‏ If v1 < b2 , want to min Prob(b1>b2) So always want to tell the truth Like eBay’s proxy bidding agents or Google’s Adwords Discounter

  8. 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)‏ (10,100)‏ (10,10)‏

  9. Expected revenue

  10. 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

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