Auctions - Module 4 Flashcards
What does auction theory help create?
Institutions, e.g. auctions, markets, matching processes
What 3 main purposes does mechanism design serve to optimise?
Efficiency
Allocation
Information discovery
Through what actions do auctions elicit information?
Bids
What are the two key properties of auctions?
They are universal, any type of good or service
They are anonymous, identity doesn’t play a role
What is a forward auction?
One seller, many buyers
What is a reverse auction?
Many sellers, one buyer
What is a double auction?
Many sellers, many buyers
What is the key difference between sealed-bid and open format auctions?
Information is revealed either only to the auctioneer, or publically
What price is paid in a first price reverse auction?
The lowest price bid
What’s another name for a second-price auction?
Vickrey auction
What’s another name for an auction with time constraints?
Auction by the candle
What does it mean that private values for a good are i.i.d?
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
What special case do we consider when considering the distribution and expectations of private values?
Private values follow uniform distribution [0,1]
Given that private values are i.i.d and follow the uniform distribution [0,1], what is the expected maximum value with N agents?
N/(N+1)
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?
((N-1)/N)*x
If private values are i.i.d and follow uniform distribution [a,b] what is the expected maximum value?
a + (N/(N+1))*(b-a)
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?
x = (z-a)/(b-a)
a + ((N-1)/N)x(b-a)
In a second-price sealed bid auction with private values and risk neutrality, what is the dominant strategy for agent i to bid?
Their full private value
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?
((N-1)/N)*vi (vi=their private valuation)
In an English auction with private values, which agent wins?
The one with the highest value
In an English auction with private values, what does the agent that wins pay?
Roughly the second price
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?
bi = ((N-1)/N)*vi
Assuming CRRA, what is the expected utility of agent i?
bi = ((N-1)/(N-1+p))*vi
If risk aversion =1, what does the expected utility of agent i equal?
bi = vi
In a Dutch auction with i.i.d private values following a uniform distribution and risk neutrality, what is the symmetric Nash equilibrium strategy?
bi = ((N-1)/N)*vi
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?
Dutch auction
What does risk aversion lead to in a first-price sealed bid auction and a Dutch auction?
Pushes bids closer to the agent’s private value rather than the expected second highest value
Which auction allows us to observe private values?
Second-price sealed-bid auction
Why do Dutch, English and first-price sealed-bid auctions not offer the opportunity to observe private values?
Because optimal bidding strategy is to bid some fraction of private values
What do strategies in second-price sealed bid and English auctions have in common when values are private?
Beliefs about others’ values do not influence my strategy
Which auction is theoretically equivalent to a Dutch auction?
First-price sealed-bid
Which auction is theoretically equivalent to First-price sealed-bid?
Dutch auction
What is the revenue equivalence principle?
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.
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?
(N-1)/(N+1)
What are the two possible goals when choosing an auction?
Information revelation and maximising revenue
What auctions tend to maximise revenues when private values are not i.i.d?
English, followed by second-price sealed-bid, followed by first-price sealed-bid
In what auctions does risk neutrality affect strategies?
Risk averse bidders bid more in first-price sealed-bid and Dutch auctions with private values
When might it be best not to play the symmetric Nash equilibrium strategy?
If you think others aren’t playing the symmetric Nash equilibrium strategy?
What is the key benefit of being a big player?
Having the ability to impose the rules of the game
What do we call a negotiation where there is one seller and one buyer?
Bilateral negotiation
What is the revenue equivalence principle?
If all bidders are risk neutral with i.i.d private values, the 4 auction formats should generate the same expected price paid/revenue
In a reverse Dutch or first-price sealed-bid auction, how does risk aversion impact the buyer?
Increases revenue
