2- Simple auctions II Flashcards

1
Q

What is a first-price sealed-bid auction?

A

Bidders simultaneously submit a secret bid, whichever is highest wins paying their own bid

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
2
Q

Why is there no incentive to bid one’s valuation (or above) in a first-price auction?

A

Since you pay your own bid, any price at your valuation or above yields no utility

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
3
Q

What are the 3 main assumptions on bidders’ functions?

A

-Bidders’ strategies are symmetric: If two bidders have the same valuation, v, they bid the same s(v)
-Bidders’ strategies are strictly increasing in valuation
-For each bidder i, s(vi) ≤ vi

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
4
Q

What is the fundamental trade off for bidders in a first-price sealed auction?

A

Higher bids increase probability of winning but reduce payoff if they do

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
5
Q

What is the strategy of a bidder [s(v)]?

A

The strategy maps a valuation to a bid e.g. bid half my valuation s(v) = v/2

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
6
Q

What is a simple way of expressing a bidding strategy?

A

b = αv
where 0≤α≤1 scales down bidder’s valuation

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
7
Q

What is the optimal bid in first-price sealed with n i.i.d bidders with private valuations?

A

(n-1)v/n
i.e. second highest valuation, if we win our valuation v is the highest

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
8
Q

Outline how a Dutch/descending price auction works

A

Price clock showing a decreasing price, auction stops as soon as someone says ‘mine’

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
9
Q

Why are Dutch auctions strategically equivalent to first-price sealed-bid?

A

Because bidding one’s true valuation is not a dominant strategy

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
10
Q

What is the main difference between Dutch and first-price sealed-bid auctions?

A

First-price is a strategic form game, Dutch is an extensive form game

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
11
Q

What is the revenue equivalence theorem?

A

Expected seller revenue is the same for first-price & second-price sealed-bid auctions

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
12
Q

What are the 4 conditions for the revenue equivalence theorem?

A

-Private and i.i.d valuations
-Strictly increasing CDF F(v) = v/r
-Winner is bidder with highest valuation
-Bidder with lowest valuation has expected payoff 0

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
13
Q

What is a reserve price?

A

Only bids above the reserve price are considered

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
14
Q

What is a main pro and con of having a reserve price?

A

-Pro: guarantees a minimum revenue for seller if sold
-Con: if no bid meets the reserve price then the seller will make nothing

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
15
Q

What is the fundamental trade off when setting a reserve price?

A

Lower probability of selling but higher revenue if you do

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
16
Q

What is the optimal auction reserve price theorem?

A

If bidders’ valuations are drawn independently from the distribution F then a seller’s optimal auction consists of choosing and running a Vickrey auction with the reserve price r that satisfies ψ(r) = 0, where
ψ(r) = r - (1-F(r))/f(r)

17
Q

What is the intuition behind the optimal auction reserve price theorem?

A

Seller revenue is maximised when Marginal Revenue is zero

18
Q

What is the virtual valuation of a bidder ψ(v)?

A

The marginal revenue brought by the bidder

19
Q

What is the probability a bidder will win a first-price sealed-bid auction?

A

P(b>αv̅) = (b/αr)ⁿ⁻¹
Probability their bid is greater than the next highest valuation scaled down as per strategy

20
Q

What is the expected payoff of a bid EU(b)?

A

(b/αr)ⁿ⁻¹ x (v-b)
Probability of winning times payoff

21
Q

What is the expected revenue for the seller in first & second price sealed-bid auctions?

A

r(n-1/n+1)
Where r is max valuation

22
Q

What is the probability density function (PDF) of valuations f(v)?

A

f(v) = 1/r

23
Q

What is the cumulative distribution function (CDF) of valuations F(v)?

A

F(v) = v/r