Auctions%20and%20Auction%20Markets

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Auctions and Auction Markets
2
Introduction

• Auctions have an old history and are increasingly
  common
• 193 AD, Praetorian Guard auctioned off the the
  Roman Empire to Marcus Didius Salvius Julianus
• Modern Examples
• eBay (Consumers)
• Covisint/Free Markets (B2B)
• Wireless Spectrum Auction (Government2B)

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Auction Types

• Ascending Bid or English Auction
• Probably most familiarPrice starts low
• Price is raised gradually until only one bidder
  remain
• Descending Bid or Dutch
• Price starts high
• Price is lowered until someone finally wants to
  buy
• Sealed Bid Auctions
• Bids effectively submitted in sealed envelopes
• First-Price Sealed Bid Winning bidder pays
  amount bid
• Second-Price Sealed Bid Winning bidder pays
  amount equal to second-highest bid
• Private Value AuctionItem value different for
  each bidder
• Common Value AuctionItem value common to all
  bidders but each has different information about
  true common value

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The Revenue Equivalence Theorem

• Revenue to Seller is Same Regardless of Auction
  Type in a Private Value Auction
• Consider auction of textbook among 170 students
• Values start at 0.50 and increase by 0.50 with
  each student. So, top value is 85
• Consider English Auction where Auctioneer raises
  price by 1 each round
• When bid reaches 84.50, only two bidders remain
• Final winning bid will be 84.51 when only one
  bidder is left
• Second Price Sealed Bid
• If bidders bid their true values, top two bidders
  will bid 85 and 84.50, respectively
• Bidder with 85 valuation will win but pays only
  84.50 ? 84.51

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Revenue Equivalence (Cont.)

• Why bid ones true value in Second-price, sealed
  bid auction?
• What one bids determines only if one winsnot
  what one pays
• Bidding less than true value risks losing the
  object to someone who values it less than one is
  willing to pay without changing the price
• Bidding more than true value raises chance of
  winning but only by beating out a bidder with a
  higher value than your own
• You will then pay that higher value and, since it
  exceeds your own, lose out

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Revenue Equivalence (Cont.)

• Winning Bid in a First-Price, sealed bid auction
• bidders observe no other information about other
  bidders value prior to making a bid
• Winner pays the winning bid
• Suggested Strategy Bid an amount equal to ones
  best guess of next highest bid
• Treat your value as the highest (if its not,
  winning is too costly)
• If valuations are uniform, next highest is (N
  1)/N of your value
• E.g., bidder with value 85, bids (N 1)/N 85
  84.50, N 170
• Here again, winning bid is 84.50
• This is a general result and important. We dont
  want an objects value to depend on how it was
  bought

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Revenue Equivalence (Cont.)

• Dutch or descending price auction is
  strategically identical to first-price, sealed
  bid auction. Again, in both
• bidders observe no other information about other
  bidders value prior to making a bid
• Winner pays the winning bid
• Optimal strategy should be the same in both
• So, winning bid will again be 84.50
• Revenue Equivalence Regardless of auction type,
  the winning bid or payment is always 84.50
• This is a quite general result. In private
  value auctions, the revenue to the seller is the
  same regardless of what type of auction is held
• It is good that Revenue Equivalence holds. We
  do not want an objects price to depend on how it
  is bought

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Common Value Auctions

• In common value auctions, item has an unknown but
  common market value, e.g., real estate
• Bidders have different information about the true
  value
• That true value depends on what others are
  willing to pay
• Revenue Equivalence may not hold
• The Winners Curse in Common Value Auctions
• Winner of a common value auction is one with
  highest estimate of true common value, e.g.,
  highest estimate of the value of a property
• Winning can be bad news. It reveals that the
  winners information was most upward biased and
  bid was higher than the average or expectation of
  the true value

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Common Value Auctions (cont.)

• Minimizing the Winners Curse
• To avoid the winners curse, bidders need to
  shade their bids below that indicated by their
  information
• This requires recognizing that one is interested
  in the objects true value if one wins the bid,
  i.e., if one wins, that says something about the
  objects true value
• Need somehow to use this information to estimate
  the average or expected mean value of the
  property
• Again, assume that your estimate E is the highest
  (youre not interested in the objects value if
  it is not)
• If there are N bidders and the distribution is
  uniform, then highest value of E is on average,
  U(N-1)/N where U is the upper limit of the
  distribution.
• Solving for U yields U N/(N-1)E ? Average
  Estimate is N/2(N-1)E . This is the amount to
  bid. It is well below E which is why it helps
  one minimize the winners curse.

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Common Value Auctions (cont.)

• For example, if there are 100 bidders each
  drawing estimates of a propertys value such that
  those estimates are uniformly distributed and if
  my estimate is 10,000
• My best guess is that the uniform distribution
  ranges from 0 to 100/(100-1)10,000 or from 0
  to 10,101
• My guess for the average value of the estimates
  is therefore 5,050.50
• I bid much less than the estimated property value
  in an effort to avoid the winners curse of
  paying too much
• With Common Value auctions, all auction types may
  not generate the same revenue
• Ascending price auctions, for example, reveal
  more information than other types about the
  estimates of other biddersRevenue Equivalence
  can break down

11
Almost Common Value Auctions

• Some auctions are a mix of private and common
  valuations
• Almost common value auctions are those in which
  the object has a common value to nearly all
  bidders but one who values the object by some
  amount, v, above everyone else
• Surprisingly, even when v is small, the effect on
  revenue can be large. Why? Because the winners
  curse cuts doubly in this setting
• Example 5 local coffee shops and Starbucks all
  bid for a coffee store
• Whatever the store is worth to the locals, its
  worth more to Starbucks
• As a result, each local bidder faces an
  intensified winners curse
• To win the bid, it must beat Starbucks bid which
  is biased upwards
• This means that its estimate must really be
  unusually high
• Accordingly, local bidders shade their bids even
  more
• But this allows Starbucks to be more aggressive,
  causing locals to shade their bids even more
• Starbucks will win the bidding but at a much
  reduced price

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Auction Markets and Industrial Organization

• Auction markets are affected by the problems of
  monopoly and collusion that affect other markets
• Auction design can be helpful in this regard
• Ascending auction can limit winners curse
  effects but
• Facilitates collusion
• Facilitates communication of asymmetric values
• On both counts, the English auction may result in
  lower revenue
• Sealed bid designs works well
• It encourages entry because there is a chance of
  winning even if a firms estimated value is not
  the highest
• It reduces collusion opportunities
• However, there can be too many bidders. Winners
  Curse rises with the number of bidders. The
  price-raising effect of more bidders may be
  offset by the price-shading effect.