Auctions - Module 4

Question 1

What does auction theory help create?

Answer 1

Institutions, e.g. auctions, markets, matching processes

Question 2

What 3 main purposes does mechanism design serve to optimise?

Answer 2

Efficiency
Allocation
Information discovery

Question 3

Through what actions do auctions elicit information?

Answer 3

Bids

Question 4

What are the two key properties of auctions?

Answer 4

They are universal, any type of good or service

They are anonymous, identity doesn’t play a role

Question 5

What is a forward auction?

Answer 5

One seller, many buyers

Question 6

What is a reverse auction?

Answer 6

Many sellers, one buyer

Question 7

What is a double auction?

Answer 7

Many sellers, many buyers

Question 8

What is the key difference between sealed-bid and open format auctions?

Answer 8

Information is revealed either only to the auctioneer, or publically

Question 9

What price is paid in a first price reverse auction?

Answer 9

The lowest price bid

Question 10

What’s another name for a second-price auction?

Answer 10

Vickrey auction

Question 11

What’s another name for an auction with time constraints?

Answer 11

Auction by the candle

Question 12

What does it mean that private values for a good are i.i.d?

Answer 12

Independent, other’s valuation doesn’t affect my own
Identically distributed, probability my value is less than x is the same probability that someone else’s value is also less than x. Anonymous

Question 13

What special case do we consider when considering the distribution and expectations of private values?

Answer 13

Private values follow uniform distribution [0,1]

Question 14

Given that private values are i.i.d and follow the uniform distribution [0,1], what is the expected maximum value with N agents?

Answer 14

N/(N+1)

Question 15

If private values are i.i.d and follow the uniform distribution [0,1] what is the second highest expected value, where x is the highest value?

Answer 15

((N-1)/N)*x

Question 16

If private values are i.i.d and follow uniform distribution [a,b] what is the expected maximum value?

Answer 16

a + (N/(N+1))*(b-a)

Question 17

If private values are i.i.d and follow uniform distribution [a,b], and the highest expected value is z, what is the second highest expected maximum value?

Answer 17

x = (z-a)/(b-a)

a + ((N-1)/N)x(b-a)

Question 18

In a second-price sealed bid auction with private values and risk neutrality, what is the dominant strategy for agent i to bid?

Answer 18

Their full private value

Question 19

Given private values are i.i.d and follow uniform distribution [0,1] in a second price sealed-bid auction, what price should agent i expect to pay?

Answer 19

((N-1)/N)*vi (vi=their private valuation)

Question 20

In an English auction with private values, which agent wins?

Answer 20

The one with the highest value

Question 21

In an English auction with private values, what does the agent that wins pay?

Answer 21

Roughly the second price

Question 22

In a first-price sealed-bid auction with i.i.d private values following a uniform distribution and risk neutrality, what is the symmetric Nash equilibrium strategy?

Answer 22

bi = ((N-1)/N)*vi

Question 23

Assuming CRRA, what is the expected utility of agent i?

Answer 23

bi = ((N-1)/(N-1+p))*vi

Question 24

If risk aversion =1, what does the expected utility of agent i equal?

Answer 24

bi = vi

Question 25

In a Dutch auction with i.i.d private values following a uniform distribution and risk neutrality, what is the symmetric Nash equilibrium strategy?

Answer 25

bi = ((N-1)/N)*vi

Question 26

With i.i.d private values following a uniform distribution and risk neutrality, a first-price sealed-bid auction is theoretically equivalent to which other auction?

Answer 26

Dutch auction

Question 27

What does risk aversion lead to in a first-price sealed bid auction and a Dutch auction?

Answer 27

Pushes bids closer to the agent's private value rather than the expected second highest value

Question 28

Which auction allows us to observe private values?

Answer 28

Second-price sealed-bid auction

Question 29

Why do Dutch, English and first-price sealed-bid auctions not offer the opportunity to observe private values?

Answer 29

Because optimal bidding strategy is to bid some fraction of private values

Question 30

What do strategies in second-price sealed bid and English auctions have in common when values are private?

Answer 30

Beliefs about others' values do not influence my strategy

Question 31

Which auction is theoretically equivalent to a Dutch auction?

Answer 31

First-price sealed-bid

Question 32

Which auction is theoretically equivalent to First-price sealed-bid?

Answer 32

Dutch auction

Question 33

What is the revenue equivalence principle?

Answer 33

When private values are i.i.d and agents are risk neutral, the expected revenue of the seller is the same in all 4 auctions. the expected utility of the buyer is also the same for all 4 auctions.

Question 34

What is the expected revenue for the seller in all 4 auctions with private values that are i.i.d and agents are risk neutral?

Answer 34

(N-1)/(N+1)

Question 35

What are the two possible goals when choosing an auction?

Answer 35

Information revelation and maximising revenue

Question 36

What auctions tend to maximise revenues when private values are not i.i.d?

Answer 36

English, followed by second-price sealed-bid, followed by first-price sealed-bid

Question 37

In what auctions does risk neutrality affect strategies?

Answer 37

Risk averse bidders bid more in first-price sealed-bid and Dutch auctions with private values

Question 38

When might it be best not to play the symmetric Nash equilibrium strategy?

Answer 38

If you think others aren't playing the symmetric Nash equilibrium strategy?

Question 39

What is the key benefit of being a big player?

Answer 39

Having the ability to impose the rules of the game

Question 40

What do we call a negotiation where there is one seller and one buyer?

Answer 40

Bilateral negotiation

Question 41

What is the revenue equivalence principle?

Answer 41

If all bidders are risk neutral with i.i.d private values, the 4 auction formats should generate the same expected price paid/revenue

Question 42

In a reverse Dutch or first-price sealed-bid auction, how does risk aversion impact the buyer?

Answer 42

Increases revenue