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Auctions Auctions Hal R Varian

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									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 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
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(b1 > b2)[v1 – b2]
       If v1 > b2 , want to max Prob(b1>b2)‫‏‬so set
        b1=v1
       If v1 < b2 , want to min Prob(b1>b2) so set
        b1=v1
   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

Values             Revenue reserve=0 Revenue
                                     reserve=100
(100,100)          100               100
(100,10)           10                100
(10,100)           10                100
(10,10)            10                0
Expected revenue   32.50             75.00
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

								
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