Auction Theory and Practice

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Auction Theory and Practice Powered By Docstoc
					             Eyal Winter
 Center for the Study of Rationality
The Hebrew University of Jerusalem
Herodotus of Ancient Greece 500 BC
 Women are sold for marriage by their families through
  auctions (they used Dutch Auctions).
 Auctions are held as mandatory for selling women into
Rome 193 AD
 Pertinax the Emperor is executed for the failing
  economy in Rome.
 The entire empire is sold by an auction to the highest
 Julianus wins the auction and becomes the new
Auction vs. Bargaining
 Auction: When the number of potential buyers is
  large and the seller’s information about the buyers’
  willingness to pay is limited.
 Bargaining: Mainly in bilateral transactions or when
  the good has better-defined market value.
 In many cases one can combine an auction with
  bargaining (there are downsides and upsides).
Auction Types
 Common Value: All bidders have the same monetary
  value for the object but this value is unknown.
 Private Value: Different bidders have different values
  for the object but each bidder is fully informed about
  his own value (and is not informed about other
  bidders’ values).
The Winner’s Curse
Popular Auction Mechanisms
 First Price Sealed Bid: Bidders submit bids in sealed
  envelopes. The highest bidder wins the object and pays
  his bid.
 Second Price Sealed Bid: Like the first price sealed
  bid, except that the winner pays the second highest
  price instead of his own price.
 English Auction: The auction involves ascending
  prices. Bids are announced publicly and have to exceed
  those currently in the system. The winner is the last to
 Dutch Auction: A pointer points and there is a very
  high price that gradually declines. The pointer stops
  with the first “stop” call of a bidder. This bidder pays
  the price at which the pointer stops.
 Japanese Auction: The auction starts at a very low
  price that gradually rises. People leave the room when
  the price exceeds their willingness to pay. The last to
  remain wins and pays the price at which the next to
  last left the room.
 Israeli Auction: Like first price sealed bid, except that
  the winner is the cousin of the mayor and he pays 50%
  of the lowest bid.
Vickery Theorem
 In the Second Price Sealed Bid auction, there is a
  dominant strategy for each bidder, which is to bid the
  true value of the object.
 Proof: Denote by x the highest bid (apart from mine).
  Assume that my value for the object is 1000 EUR.
 If x < 1000, then any bid above x will make me the
  winner and will make me pay x. Any bid below x will
  make me lose. So saying 1000 is best.
 If x > 1000, then bidding above x will make me win the
  object but lose money, and bidding below x (regardless
  of the bid and including 1000) will give me zero profit.
 Proxy servers in Internet auctions create a second price
The Equivalence of Auction
 First Price Sealed Bids and Dutch Auctions are
 Second Price Sealed Bids and English Auctions are
 The Revenue Equivalence Theorem (Vickery 1961;
  Myerson 1980): All efficient auctions are revenue
The Analysis of First Price Auctions
 v1 ,…vn (bidders’ valuations) are iid with the cumulative
  distribution F.
 b(v) is the bidding function of each player.
 In equilibrium each player’s bidding function has to
  maximize his expected profit, given the bidding
  functions of the rest.
 Expected profit of player i is given by
 Ei(b)= P (player i has the highest bid) [v – b(v)].
 P(i’s the highest bid) = P(bi(vi)) > bj(vj)) for all j ≠i) =
  p(vi > vj for all j ≠i) = [F(vi)]n-1
 E(b)= [F(vi)]n-1[v-b(v)]
 Equilibrium Conditions: argmaxw[F(w)] n-1[v-b(w)]=v
 (n-1)[F(w)] n-2F’(w)[v-b(w)]-b’(w)[F(w)] n-1|w=vi= 0
 (n-1)F’(v)[v-b(v)]=b’(v)[F(v)]

  If vi ~ U[0,1] then b(v) =
Laboratory Results
 First price auctions generate more revenue than Dutch
 Average bids increase with the number of bidders in
  the auction.
The Cellular Auctions
 From 1993 to 2001 governments in the world made a
  revenue of 100 billion USD.
 In 1994 the New York Times announced the British
  Cellular Auction as the largest auction ever, totaling a
  revenue of 34 billion USD.
 Ken Binmore designed the auction and became Sir
  Ken Binmore.
The New Zealand Failure
 The auction used was second price sealed bids.
 On one batch of frequencies the highest bid was 7
  million NZD, and the second highest bid only 5000
 On another batch the highest bid was 100,000 and the
  second highest only 6 NZD!!!
The FCC Auction in the US
 The auction runs in stages.
 At each stage each bidder can introduce new bids and
  withdraw his existing bids.
 New bids have to exceed those in the system.
 Bids that are withdrawn incur a potential fine on the
  bidder. The bidder has to pay the difference between
  his withdrawn bid and the price at which the batch is
  eventually sold.
Auctions in Google
 Any query in Google earns around 10 cents for the
 The participating companies compete on the location
  in the ad and bid on any query.
 Google estimates the number of clicks per query for
  each company and ranks pages to maximize revenue.
Large Auctions in Israel
 In 2006 the government share in the national
  telephone company was sold in an auction. The
  highest bid was around 200m EUR.
 After the auction ended the government requested an
  additional 6m EUR and received it.
 Is it a good strategy?
 The country’s storage facilities for gas were sold in
  2007. There were 3 sites.
 The mechanism used was a combinatorial auction
  (with ascending prices).
 The government earned 350m EUR where expert
  estimates were about 60m EUR.
 The largest Israeli newspaper announced this auction
  as the most successful one in the history of the
Legal Issues in Auctions
 Collusion: Why is it banned by most governments?
 Around 50% of the Anti-Trust cases in the US are on
 collusion in auctions.
Other “Tricks”
 Sellers “hide” reservation prices and make bidders
  believe that they will sell to the highest bidder at any
 Sellers make fictitious bids to boost prices in auctions.
 They inform one bidder of the price of another bidder
  to get a higher price.
Why is it wrong to allow it?
 Manipulation destroys the efficiency of the market
“Tacit” Collusion in Auctions
 On batch no. 128 in the US FCC auction someone bids
 The California Electricity Market: Tacit collusion
  requires long term interactions between bidders.
  Contracts in the electricity market in CA were too
  short and facilitated long-term interactions (Repeated
Behavioral Aspects of Auctions
 Snipping
 The Afternoon Effect

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