Economics 100C

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Economics 100C

• April 6, 2010

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Have you ever bid for anything on eBay?

1. Yes, frequently
2. Yes, but not frequently
3. No

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Equilibrium bids in first and second price sealed
bid auctions with private values.

• Second price bid true value.
• First price bid less than true value.
• With uniform distributions if values and n
  bidders, equilibrium in first price auction has
  bidders bid fraction (n-1)/n of values.

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Expected revenues with 2 bidders.

• Second-price auctionExpected value of second
  highest bid.
• First price auction---Expected value of half of
  highest bid.
• If values are uniformly distributed on an
  interval 0,A, these both turn out to equal A/3.
  See posted notes.

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Expected revenues with n bidders.

• Second-price auctionExpected value of second
  highest bid.
• First price auction---Expected value of half of
  highest bid.
• If values are uniformly distributed on an
  interval 0,A, these both turn out to equal
  A(n-1)/(n1). See notes.

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An Oil Auction

• This illustrates a common value auction in
  which different bidders have partial information
  about the value of object being auctioned.
• Two bidders. Each has explored half of the oil
  field.
• Whole oil field is up for bids.

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Instructions Classroom Experiment

• Form groups of 3. Choose one person to be
  Auctioneer, one to be Player A and one to be
  Player B.
• Players A and B not allowed to talk to each
  other.
• Value of the oil field the sum of last two
  digits of As perm number and last two digits of
  Bs
• Players A and B write their perm numbers and bids
  on slip of paper and pass them to auctioneer.
• High bidder gets oilfield. Profits are value of
  oil field minus bid. Low bidders profits are
  zero.
• Auctioneer records total value, bids and profits.

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Is this oilfield auction a common value auction
or a private values auction?

• Common Value
• Private Values

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Answer

• This is a common values auction. The oilfield is
  worth the same amount to whoever gets it.
• The only difference between the bidders is that
  they have different bits of information.
• This would be a private values auction if e.g.
  one firm could use the oilfield more effectively
  than the other.

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In this auction, if you are Player A and your
side of the oil field is worth 60, what is the
expected value of the whole oil field?

1. 60
2. 90
3. 110
4. 120
5. 150

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Expected Value or whole field if my side is worth
60

• Value of other side is a random variable
  uniformly distributed on 0,100
• Expected value of other side is 50.
• Expected total value is 6050110.

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What happens if bidders bid expected values?

• Each bidder would bid xi50 where xi is the value
  of his own side.
• Winner would be person with higher xi
• Suppose that A wins and has value xA Given that
  he won, it must be that xBltxA
• What is the expected value of xB conditional on
  xBltxA?
• xA/2
• So expected value of oil field is xA/2 xA
  3xA/2lt xA50.
• On average, winning bidder would lose money.

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The winners curse

• In this auction, you would on average lose money
  if you bid as high as your expected value.
• The expected value conditional on winning the
  auction is lower than the expected value.
• This effect is called the winners curse.

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Buying Montana

• I will sell a contract in which I promise to pay
  1 for every 100,000 people who live in Montana.
• The sale will be by an English auction.
• Top bidder pays me his bid. I pay top bidder 1
  for every 100,000 people who live in West
  Montana.

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Was there aWinners Curse?

• If so, why?

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See you Thursday
Dont forget your clicker.