Economics 100B

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Economics 100B

• Instructor Ted Bergstrom
• T.A. Oddgeir Ottesen
• Syllabus online at www.econ.ucsb.edu (Class
  pages)
• Or at www.econ.ucsb.edu\tedb
• (Econ 100B)

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Dont forget to register with Aplia

• First homework assignment due Sunday night.
• Instructions for signing up on class website.

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Lets get registered
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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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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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Auction Details

• Coin flips determine value of each side 3 m if
  head, 0 if tails.
• Bidder A sees result only for side A
• Bidder B sees result only for side B
• Bidders submit sealed bid for the whole oil field
  (both sides)

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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 you see
that your side of the field is worth 0, could
you make a profit by bidding 3 million or more?

• Yes, this would be a good strategy.
• Yes, but chances are low, so this is not a good
  strategy.
• No, I could never make money and I may lose money
  with such a bid.

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

1. 3,000,000
2. 6,000,000
3. 4,500,000
4. 1,500,000
5. 0

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Expected Value is sum of possible values times
probabilities of each value.

• Two possible outcomes
• Other side has value 0.
• Other side has value 3,000,000.
• Each outcome has probability 1/2
• My side of the field is worth 0.
• So expected value of whole field is
• 0x1/23,000,000x1/21,500,000

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In this auction, if you are Player A and your
side of the oilfield is worth 3,000,000 what is
your expected value for the whole field?

1. 3,000,000
2. 6,000,000
3. 4,500,000
4. 1,500,000
5. 9,000,000

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Expected Value or whole field if my side is worth
3,000,000

• Two possible outcomes
• Other side has value 0.
• Other side has value 3,000,000.
• Each outcome has probability 1/2
• So expected value of whole field is
• 3,000,000 (0x1/23,000,000x1/2)4,500,000

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What happens if bidders bid expected values?

• They would bid 1.5 mil if their own side worth
  0 and 4.5 mil if their own side is worth 3
  mil.
• Suppose you see 0 and bid 1.5 mil.
• If other guy sees 3 mil, he will bid 4.5
• And you dont get field. If other guy sees 0, he
  bids 1.5 and you flip coin for who gets the
  field.

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How did you do?

• If you saw 0 and bid 1.5 million, you will not
  get the field if it is valuable, but you have a
  50-50 chance of paying 1.5 million for a
  worthless field.
• Not a good outcome for you.

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Similar problem if you see 3 mil and bid 4.5
mil.

• If other guy saw 0, he bids 1.5 mil and you get
  3 mil worth of oil field for 4.5 mil. This
  happens with probability ½.
• If other guy sees 3 mil, he bids 4.5 mil. Coin
  is flipped. You might win coin toss and get 6
  mil worth of oil for 4.5 mil. But this happens
  only with probability 1/2x1/21/4.
• Prob lose 1.5 mil is ½, prob win 1.5 mil is ¼.
  Not a good deal.

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Conclusion

• In this auction, you would on average lose money
  if you bid as high as your expected value.

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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
  .01 for every 1000 people who live in Montana.
  Thats 1 for every 100,000 people in Montana.
• The sale will be by an English auction.
• Top bidder pays me his bid. I pay top bidder .01
  for every thousand people who live in Montana.

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Auction Design

• Possible Goals
• Pareto efficiency
• maximization of the sellers profit.

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Auction Design

• Pareto efficiency
• the item must sell to the buyer with the highest
  valuation of the item.
• Which auctions are Pareto efficient?

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Auctions and Efficiency

• English auction with no reserve price must be
  efficient since, if a buyer with a low valuation
  was about to buy, the highest valuation buyer
  would bid higher.

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Auctions and Efficiency

• English auction with a reserve price need not be
  efficient since if the reserve price is set above
  the (unknown to the seller) highest buyer
  valuation, then there will be no sale and so no
  gains-to-trade.

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Auctions and Efficiency

• Dutch auction need not be efficient. No buyer
  knows other buyers valuations, so the highest
  valuation buyer may delay too long and lose to
  another bidder.

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Auctions and Efficiency

• Sealed-bid first-price auction need not be
  efficient. No buyer knows other buyers
  valuations, so the highest valuation buyer may
  bid too low and lose to another bidder.

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Auctions and Efficiency

• Sealed-bid second-price auction is Pareto
  efficient even though no buyer knows the other
  buyers valuations (more on this later).

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Why Use a Reserve Price?

• Suppose there are 2 buyers.
• The seller believes each buyers valuation is 20
  with chance 1/2 and 50 with chance 1/2.
• I.e. with chance 1/4 each, the seller believes
  she faces buyer valuations (20,20), (20,50),
  (50,20) and (50,50).

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Why Use a Reserve Price?

• I.e. with chance 1/4 each, the seller believes
  she faces buyer valuations (20,20), (20,50),
  (50,20) and (50,50).
• Use an English auction.
• Bids must be raised by at least 1.
• With chance 1/4 each, winning bids will be 20,
  21, 21 and 50 if there is no reserve price.

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Why Use a Reserve Price?

• With chance 1/4 each, winning bids will be 20,
  21, 21 and 50 if there is no reserve price.
• Sellers expected revenue is(20 21 21
  50)/4 28with no reserve price.

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Why Use a Reserve Price?

• With chance 1/4 each, the seller believes she
  faces buyer valuations (20,20), (20,50),
  (50,20) and (50,50).
• Set a reserve price of 50.
• With chance 1/4 there will be no sale.
• With chance 3/4 the winning bid will be 50.

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Why Use a Reserve Price?

• Set a reserve price of 50.
• With chance 1/4 there will be no sale.
• With chance 3/4 the winning bid will be 50.
• Sellers expected revenue is

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Reserve Price and Efficiency

• The reserve price causes an efficiency loss
  since, with chance 1/4, there is no trade.

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Second-Price, Sealed-Bid Auction

• bids are private information
• bids are made simultaneously
• highest bidder wins
• winner pays second-highest bid
• also known as a Vickrey auction.

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Second-Price, Sealed-Bid Auction

• No bidder knows any other bidders true
  valuation of the item for sale.
• Yet, it is individually rational for each bidder
  to state truthfully his own valuation. Why?
• E.g. two bidders with true valuations v1 and v2.

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Second-Price, Sealed-Bid Auction

• Suppose object is worth 100 to me.
• Can I do better than to bid 100.
• Two cases
• Highest bid by anyone else gt100
• Highest bid by anyone else lt100

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Case A) Highest bid by anyone else is Greater
than 100.

• Would I gain by bidding more than 100?
• No, because second highest bid would still exceed
  100 and object is only worth 100 to me.
• Would I gain by bidding less than 100?
• No, because I still wouldnt get the object.

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Case B) Highest bid by anyone else less than
100.

• Would I gain by bidding more than 100?
• No, because I get the object either way at the
  second bidders price.
• Would I gain by bidding less than 100?
• No. If my bid is between the second highest bid
  and 100, I still get object at second bid. If
  my changed bid is less than second highest bid, I
  dont get the object and miss the profit I would
  get from bidding 100

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See you next week
Dont forget to do your homework.