Lesson test: Private information and auctions

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Private information and auctions

1.[2p]
What does Harsanyi's construction do to a game of incomplete information?

It replaces the unknown payoffs with a private type drawn by nature from a commonly known distribution

Correct

It assumes every player eventually learns the others' payoffs

The answer is: It replaces the unknown payoffs with a private type drawn by nature from a commonly known distribution

It restricts attention to zero-sum games

The answer is: It replaces the unknown payoffs with a private type drawn by nature from a commonly known distribution

It removes the need for players to hold beliefs

The answer is: It replaces the unknown payoffs with a private type drawn by nature from a commonly known distribution

2.[3p]
Why does bidding your true value weakly dominate in a second-price auction?

Deviating changes the outcome only when the highest rival bid falls between your bid and your value, and that change is always for the worse

Correct

Because the seller collects less than the winning bid

The answer is: Deviating changes the outcome only when the highest rival bid falls between your bid and your value, and that change is always for the worse

Because all bidders are risk neutral

The answer is: Deviating changes the outcome only when the highest rival bid falls between your bid and your value, and that change is always for the worse

Because the number of bidders is unknown

The answer is: Deviating changes the outcome only when the highest rival bid falls between your bid and your value, and that change is always for the worse

3.[3p]
Values are uniform on the interval from 0 to 1 and there are five bidders in a first-price sealed-bid auction. What should a bidder with value 0.9 bid?

CorrectNot quite: 0.72

4.[3p]
With four bidders in that same setting, what is the expected revenue from a second-price sealed-bid auction?

CorrectNot quite: 0.6

5.[2p]
Under independent private values and risk neutrality, first-price and second-price sealed-bid auctions raise the same expected revenue.

True

Correct

False

The answer is: True

6.[3p]
Which of these break revenue equivalence between formats?

Select all that apply

Risk-averse bidders

Correct

Values that are correlated across bidders

Correct

A bidding ring that can suppress competition

Correct

Differences in how many bidders each format attracts

Correct

Changing the units the bids are denominated in

The answer is: Risk-averse bidders, Values that are correlated across bidders, A bidding ring that can suppress competition, Differences in how many bidders each format attracts

7.[3p]
Ten bidders each receive a signal drawn uniformly within 10 of a tract's common value. By how much does the highest of those signals exceed the true value on average?

CorrectNot quite: 8.18

8.[3p]
What is the correct way to avoid the winner's curse?

Estimate the value conditional on your signal and on your signal being the highest

Correct

Bid your unbiased estimate of the value

The answer is: Estimate the value conditional on your signal and on your signal being the highest

Bid more aggressively as the number of rivals rises

The answer is: Estimate the value conditional on your signal and on your signal being the highest

Refuse to bid in common value auctions

The answer is: Estimate the value conditional on your signal and on your signal being the highest

9.[2p]
Match each auction format to its defining rule.

English
Dutch
First-price sealed bid
Second-price sealed bid

price rises until one bidder is left
highest bid wins and pays its bid
price falls until someone claims the object
highest bid wins and pays the runner-up

Show the answer

English: price rises until one bidder is left Dutch: price falls until someone claims the object First-price sealed bid: highest bid wins and pays its bid Second-price sealed bid: highest bid wins and pays the runner-up

1.[2p] What does Harsanyi's construction do to a game of incomplete information?

2.[3p] Why does bidding your true value weakly dominate in a second-price auction?

3.[3p] Values are uniform on the interval from 0 to 1 and there are five bidders in a first-price sealed-bid auction. What should a bidder with value 0.9 bid?

4.[3p] With four bidders in that same setting, what is the expected revenue from a second-price sealed-bid auction?

5.[2p] Under independent private values and risk neutrality, first-price and second-price sealed-bid auctions raise the same expected revenue.

6.[3p] Which of these break revenue equivalence between formats?

7.[3p] Ten bidders each receive a signal drawn uniformly within 10 of a tract's common value. By how much does the highest of those signals exceed the true value on average?

8.[3p] What is the correct way to avoid the winner's curse?

9.[2p] Match each auction format to its defining rule.

1.[2p]
What does Harsanyi's construction do to a game of incomplete information?

2.[3p]
Why does bidding your true value weakly dominate in a second-price auction?

3.[3p]
Values are uniform on the interval from 0 to 1 and there are five bidders in a first-price sealed-bid auction. What should a bidder with value 0.9 bid?

4.[3p]
With four bidders in that same setting, what is the expected revenue from a second-price sealed-bid auction?

5.[2p]
Under independent private values and risk neutrality, first-price and second-price sealed-bid auctions raise the same expected revenue.

6.[3p]
Which of these break revenue equivalence between formats?

7.[3p]
Ten bidders each receive a signal drawn uniformly within 10 of a tract's common value. By how much does the highest of those signals exceed the true value on average?

8.[3p]
What is the correct way to avoid the winner's curse?

9.[2p]
Match each auction format to its defining rule.