Economics 100B

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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First homework assignment due Sunday night.

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Have you ever bid for anything on eBay?

A) Yes, frequently

B) Yes, but not frequently

C) No

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.

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)

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

auction?

A) Common Value

B) Private Values

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.

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.

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?A) $3,000,000

B) $6,000,000

C) $4,500,000

D) $1,500,000

E) $0

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

$0x1/2+$3,000,000x1/2=$1,500,000

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?A) $3,000,000

B) $6,000,000

C) $4,500,000

D) $1,500,000

E) $9,000,000

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+ ($0x1/2+$3,000,000x1/2)=$4,500,000

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 $4.5And you don’t get field. If other guy

sees 0, he bids $1.5 and you flip coin for who gets the field.

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.

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 1/2x1/2=1/4.

Prob lose $1.5 mil is ½, prob win $1.5 mil is ¼. Not a good deal.

Conclusion

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

The winner’s 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 winner’s curse.

Buying Montana I will sell a contract in which I promise to

pay $.01 for every 1000 people who live in Montana. That’s $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.

Auction Design

Possible Goals:

– Pareto efficiency

– maximization of the seller’s profit.

Auction Design

Pareto efficiency:

– the item must sell to the buyer with the highest valuation of the item.

Which auctions are Pareto efficient?

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.

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.

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.

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.

Auctions and Efficiency

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

Why Use a Reserve Price?

Suppose there are 2 buyers. The seller believes each buyer’s

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).

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.

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.

Seller’s expected revenue is($20 + $21 + $21 + $50)/4 = $28with no reserve price.

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.

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. Seller’s expected revenue is

34

5014

0 37 50 28 $ $ $ $ .

Reserve Price and Efficiency

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

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.

Second-Price, Sealed-Bid Auction

No bidder knows any other bidder’s 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.

Second-Price, Sealed-Bid Auction

Suppose object is worth $100 to me.

Can I do better than to bid $100. Two cases:

A) Highest bid by anyone else >$100

B) Highest bid by anyone else <$100

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 wouldn’t get the object.

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 bidder’s 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 don’t get the object and miss the profit I would get from bidding $100

See you next week

Don’t forget to do your homework.