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# Auctions. (Lecture 10)

## 1. LECTURE 10 AUCTIONS

## 2. What is an auction?

2Economic markets:

Many buyers & many sellers

One buyer & one seller

Many buyers & one seller

traditional markets

bargaining

auctions

A public sale in which property or merchandise are sold to

the highest bidder.

IPOs

Emissions permits

Oil drilling lease

Mineral rights

Treasury bills

Wine

Art

Flowers

Fish

Electric power

## 3.

3## 4. Terminology and auction types

4Terminology and auction

types

Terminology:

Bids B,

Bidder’s valuation V,

Next-highest rival bid R

Small in/decrement in current highest bid: e

Classifying auctions:

Open or sealed

Multiple or single bids

Ascending or descending

First-price or second-price

Private or common-value

## 5. Sources of uncertainty

5Private Value Auction

Bidders differ in their values for the object

e.g., memorabilia, consumption items

Each bidder knows only his value for the object

Common Value Auction

The item has a single though unknown value

Bidders differ in their estimates of the true value of the

object

e.g. drilling for oil

## 6. Four standard types of auction (private value auctions)

6Four standard types of

auction (private value

auctions)

Open Auctions (sequential)

English Auctions

Dutch Auctions

Sealed Auctions (simultaneous)

First Price Sealed Bid

Second Price Sealed Bid

## 7. English Auction (Ascending Bid)

7English Auction (Ascending

Bid)

Bidders call out prices

Highest bidder wins the item

Auction ends when the 2nd highest bid R is made, and the

bidder with Vmax will bid extra e and wins

Winner’s profit is Vmax-(R+e)>0

e

R

B

Vmax

Strategy: keep bidding up to your valuation V.

## 8. Dutch auction

“Price Clock” ticks down the price.First bidder to “buzz in” and stop the clock is the

winner.

Pays price indicated on the clock.

8

## 9. Dutch auction

9Strategy: Buzz in after price falls sufficiently below V,

and make a positive profit.

“Shading”: waiting longer may increase the profit, but

also increases the chance of losing the auction.

profit

R

B

Vmax

## 10. Dutch auction for British CO2 emissions

Greenhouse Gas Emissions TradingScheme Auction, United Kingdom,

2002.

UK government aimed to spend £215

million to get firms reduce CO2

emissions.

Clock auction used to determine what

price to pay per unit, which firms to

reward.

The clearing price was £53.37 per

metric ton.

## 11. First Price Auctions

11All buyers submit bids simultaneously.

The bidder who submits the highest bid wins, and

the price he pays is the value of his bid.

WINNER!

Pays $700

$70

0

$50

0

$40

$30

## 12. First Price Auctions

12Profit is Vmax - B

Profit

R

B

Vmax

Shading: B must be below V to generate profit.

Amount of shading is trade-off between risk of losing and

greater profit (similar to Dutch auction).

Shading depends on risk attitude and beliefs about other

bidders’ Vs.

## 13. Second Price Auctions

13All bidders submit bids simultaneously.

The bidder who submits the highest bid wins, and

the price he pays the second highest bid.

WINNER!

Pays $500

$70

0

$50

0

$40

$30

## 14. Second Price Auctions

14It is strategically equivalent to an English

auction

$500

$400

$300

## 15. Second Price Auctions

15Possible bids: B>V or B=V or B<V: which is best?

Bidding V is a dominant strategy

Second price auctions makes bidders reveal their true

valuations

Why bid V?

The amount a bidder pays does not depend on his bid,

so no reason to bid less than V.

## 16. Second Price Auctions Bidding higher than my valuation

Second Price Auctions16

Bidding higher than my valuation

B wins, pays R, profit is V-R, same result if B=V

low

V

B

high

B

high

B wins, pays R, negative profit

low

R

V

R

B loses, profit is 0, same result if B=V

low

V

B

R

high

To bid higher than V yields either an equal or lower payoff

than to bid V Prefer B=V to B>V

## 17. Second Price Auctions Bidding lower than my valuation

Second Price Auctions17

Bidding lower than my valuation

B wins, pays R, profit is V-R, same result if B=V

low

R

high

B loses, while bidding B=V would have won a profit

low

V

B

B

R

V

high

R

high

B loses, same result if B=V

low

B

v

To bid lower than V yields either an equal or lower payoff

than to bid V Prefer B=V to B<V

## 18. Second Price Auction

18In a second price auction, always bid your true

valuation (Vickrey’s truth serum).

Winning bidder’s surplus: Difference between the

winner’s valuation and the second highest

valuation.

## 19. Which auction is better for the seller?

19Which auction is better for the

seller?

In a second price auction

Bidders bid their true value

Seller receives the second highest bid

In a first price auction

Bidders bid below their true value

Seller receives the highest bid

## 20. Revenue Equivalence

20All 4 standard auction formats yield the same

expected revenue

Any auctions in which:

The prize always goes to the person with the highest

valuation

A bidder with the lowest possible valuation expects

zero surplus

…yield the same expected revenue

The seller is indifferent between the 4 standard

auctions.

## 21. Revenue Equivalence

21Winner pays

Optimal bid

English

Second highest V

Raise bid until V

Dutch

Vmax-shading

Shading (<V)

First-price

Vmax-shading

Shading (<V)

Second-price

Second highest V

Bid V

On average, Vmax-shading = 2nd highest V.

The optimal shading strategy is such that the winner

ends up paying the 2nd highest V.

## 22. Are all auctions truly equivalent?

22Are all auctions truly

equivalent?

For sellers, all 4 standard auctions are theoretically

equivalent. However, this may not be the case if

bidders are risk-averse or inexperienced.

Risk Aversion

Does

not affect the outcomes of 2nd price auctions and

English auctions.

However, in 1st price auctions and Dutch auctions,

risk-averse bidders are more aggressive than riskneutral bidders. Bidders ‘shade’ less, so bid higher

than if risk-neutral!

Risk aversion 1st price or Dutch are better for the

seller, because bidders shade less.

## 23. Are all auctions truly equivalent?

23Are all auctions truly

equivalent?

Inexperienced bidders

In

second-price auctions, it is optimal to bid V.

Inexperienced bidders tend to overbid in 2nd price

auctions (B>V), in order to increase their odds of

winning.

With inexperienced bidders second-price auctions

increase the revenue of the seller.

## 24. Collusion in auctions

24In second-price auctions, bidders may agree not to bid

against a designated winner.

e.g. there are 10 bidders, John’s valuation is $20, others have

valuation of $18.

Bidders agree that the designated winner John bids any

amount more than $18, others bid $0 - no incentive for

anyone to do differently. The bidder wins the item for $0.

In first-price auctions, instead, if John bids $18, he pays

$18 to the seller.

## 25. Collusion in auctions

25Collusion is also possible in English auctions. Bidders

may be able to signal their true valuations the way that

they bid in early stages.

Bidders who realize that they do not have the highest

valuations may collude with the Vmax bidder by

accepting not to raise their bid.

## 26. Number of Bidders

26Having more bidders leads to higher prices.

Example: Second price auction

Two bidders

Each has a V of either 20 or 40.

There are four possible combinations:

Pr{20,20}=Pr{20,40}=Pr{40,20}=Pr{40,40}= ¼

Expected price = ¾ (20)+ ¼ (40) = 25

## 27. Number of Bidders

27Three bidders

Each has a V of either 20 or 40

There are eight possible combinations:

Pr{20,20,20}=Pr{20,20,40}=Pr{20,40,20}

= Pr{20,40,40}=Pr{40,20,20}=Pr{40,20,40}

= Pr{40,40,20}=Pr{40,40,40}= 1/8

Expected price = ½ (20)+ ½ (40) = 30

## 28. Number of Bidders

28Assume more generally that valuations are drawn

uniformly from [20,40]:

Expected Price

40

35

30

25

20

1

10

100

Number of Bidders

1000

## 29. The European 3G telecom auctions

29The European 3G telecom

auctions

The 2000-2001 European auctions of 3G mobile

telecommunication licenses were some of the largest in

history. The total revenue raised was above $100bn, with

enormous variations between countries.

UK

5 licences; 4 incumbents. At least one new entrant would win a

license.

Used English auction. New entrants knew they had a chance so they

bid aggressively, forcing incumbents to do the same.

Revenue: 39bn euros.

## 30. The European 3G telecom auctions

30The European 3G telecom

auctions

Netherlands

4 licences; 4 incumbents.

Potential entrants could not realistically compete with the

incumbents. Therefore they decided to collude with them. They let

them win against compensation.

Used English auction. Raised only 3bn euros.

Another problem is the sequencing. Because the auction took

place after the UK one, bidders had learned how to collude.

The same problem occurred in countries that organized

auctions later, e.g. Italy and Switzerland. Bidders had learned

how to collude.

## 31. Common Value Auctions

31Common Value Auction

The item has a single though unknown value, and bidders

differ in their estimates.

Example: Oil drilling lease

Value of oil is roughly the same for every participant.

No bidder knows for sure how much oil there is.

Each bidder has some information.

## 32. Hypothetical Oil Field Auction

32Hypothetical Oil Field

Auction

Each bidder knows the amount

of oil in his or her quadrant

Bidder 1 Bidder 2

Bidder 3 Bidder 4

Total value of oil field:

Sum of the values of the four quarters

Type of auction:

First price sealed bid

## 33. The winner’s curse

33$40

$70

$50

$60

$60

The estimates are correct, on average

$80

## 34. The winner’s curse

34Winner’s curse = In common value auctions, winners

are likely to overpay, and make a loss.

BB

BB BB

B BB B B B B B

B B B B B BB B B B

low

V

high

## 35. Dealing with the winner’s curse

35Dealing with the winner’s

curse

Given that I win an auction …All others bid less

than me …Thus the true value must be lower than I

thought.

Winning the auction is “bad news”. One must

incorporate this into one’s bid, i.e. lower your bid.

Assume that your estimate is the most optimistic.

## 36. Avoiding the winner’s curse

36Bidding with no regrets:

Since winning means you have the most optimistic

signal, always bid as if you had the highest signal, i.e.

lower your bid.

If your estimate is the most optimistic –what is the item

worth?

Use that as the basis of your bid.

## 37. All-pay auctions

37Common value first-price auction in which bidders

pays the amount of their bid, even if they lose.

Example 1: Olympic games

Competing cities spend vast amount of resources to win

the vote.

Example 2: Political contests (elections)

Candidates spend time and money, whether they win or

lose.

In the 2012 US presidential election, total campaign

spending was close to $2bn.

## 38. All-pay auctions

38Example 3: Research and development, patent race.

Competing pharmaceutical firms search for a new

treatment/molecule; only one winner.

Investment in R&D is risky, since even losers lose their

“bid”.

Bid is useless unless you win…hence bid

aggressively or don’t bid at all.

Typically, the sum of the bids is much higher than

the value of the prize, which is good for the seller.

## 39. All-pay auctions Optimal strategy

All-pay auctions39

Optimal strategy

If everyone else bids aggressively, your best

response is to bid 0

If everyone else bids 0, your best response is to bid

a small positive amount

Equilibrium bidding strategy must be a mixed

strategy.

## 40. All-pay auctions Equilibrium

All-pay auctions40

Equilibrium

Consider an all-pay auction with prize worth 1, n

bidders.

Bid x between 0 and 1

Let P(x) be the probability one’s bid is not higher

than x.

Indifference principle: With mixed strategies bidders

must be indifferent between the choice of x

## 41. All-pay auctions Equilibrium

All-pay auctions41

Equilibrium

The bidder win if all remaining bids are less than x.

The expected payoff for bidding x is then:

1*[P(x)]n-1-x

Indifference condition between bidding 0 and x (the

expected profit is 0):

[P(x)]n-1-x =0, i.e. P(x)=x 1/(n-1)

## 42. All-pay auctions Equilibrium

All-pay auctions42

Equilibrium

When n=2, players play each value of x with equal

probability.

As n increases, bidders bid lower.

P(x)=x choose each x with equal probability

Expected profit: 1*x-x=0

For n=3, P(x)=√x

E.g. x=1/4 P(x)=1/2, i.e. the probability to bid less than

¼ is ½.

The higher is n, the less likely bidders are to win, and

the lower they bid.

## 43. All-pay auctions Overbidding

All-pay auctions43

Overbidding

Class experiments: Auction of a $20 bill

Students start bidding $3, $4…

When the price approaches $20, the bidders realize that

they could end up having to pay a lot of money and not

win.

If you had bid $19, and another bidder bids $20. What

would you do? Is it better to bid $21 or pay $19 for

nothing?

These games routinely end with the winning bid being 50

percent higher than the value of the prize.

## 44. Summary

44Different types of auctions

Bidding strategies

Implications for sellers: Revenue equivalence

Risk aversion /collusion

Common value auctions: Winner’s curse.

All-pay auctions: mixed strategies, and overbidding.