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**Unformatted text preview: **Motivation Categorization FPA SPA Open auctions Other auction formats Game Theory: Auctions
Tomá² Miklánek Tomá² Miklánek Game Theory: Auctions 1 Motivation Categorization FPA SPA Open auctions Other auction formats Jar with money Tomá² Miklánek Game Theory: Auctions 2 Motivation Categorization FPA SPA Open auctions Other auction formats Jar with money You are going to place your bids for the jar full of coins.
You will write your bid on the piece of paper together with
your name.
A bidder with the highest bid wins the jar a pays me his/her
bid.
Amount of money in the jar will not be announced publicly.
By submitting the bid, you agree with these rules. Tomá² Miklánek Game Theory: Auctions 2 Motivation Categorization FPA SPA Open auctions Other auction formats The winner's curse The estimates are correct, on average Tomá² Miklánek Game Theory: Auctions 3 Motivation Categorization FPA SPA Open auctions Other auction formats What is an Auction? 1. A public sale in which property or merchandise are sold to the
highest bidder.
2. A market institution with explicit rules determining resource
allocation and prices on the basis of bids from participants.
3. Games: The bidding in bridge
[Latin: aucti o, aucti on from auctus, past participle of aug ere, to
increase] Tomá² Miklánek Game Theory: Auctions 4 Motivation Categorization FPA SPA Open auctions Other auction formats Examples of auctions
Internet EBay.com, Amazon.com, airline companies
Government Treasury Bills, mineral rights (e.g. oil elds), assets (e.g.
privatization)
Electromagnetic spectrum
Stocks IPO: Google, Repurchases
Procurement auctions/Subcontracting Automobiles: Valeo (GM, Daimler-Chrysler, etc..), Visteon
(Ford) Tomá² Miklánek Game Theory: Auctions 5 Motivation Categorization FPA SPA Open auctions Other auction formats Examples of auctions
Internet EBay.com, Amazon.com, airline companies
Government Treasury Bills, mineral rights (e.g. oil elds), assets (e.g.
privatization)
Electromagnetic spectrum
Stocks IPO: Google, Repurchases
Procurement auctions/Subcontracting Automobiles: Valeo (GM, Daimler-Chrysler, etc..), Visteon
(Ford)
Are auctions a competitive market?
Are auction outcomes pareto-optimal?
Tomá² Miklánek Game Theory: Auctions 5 Motivation Categorization FPA SPA Open auctions Other auction formats Spectrum auctions UK 2000: EUR 38.3 billions
Germany 2008: EUR 50.8 billions
CR 2016: EUR 100 millions Tomá² Miklánek Game Theory: Auctions 6 Motivation Categorization FPA SPA Open auctions Other auction formats Ways to Categorize Auctions Number of objects We focus on single object auctions, but ideas apply to
multi-unit auctions
Role of information / Type of valuation Private value vs. Common value
Rules of auction Ascending (Ebay or Sotheby's), rst-price
(oil tracts), etc.. Tomá² Miklánek Game Theory: Auctions 7 Motivation Categorization FPA SPA Open auctions Other auction formats Auction Formats
Open outcry auction
Ascending Auctions (English) Auctioneer announces ever increasing prices to solicit bids.
Continues until only one person left in.
Descending Auctions (Dutch) Auctioneer announces decreasing prices until someone puts up
their hand.
Sealed bid (closed) auction
Everyone puts bids in envelopes and gives to seller at the same
time. First price, Second price Tomá² Miklánek Game Theory: Auctions 8 Motivation Categorization FPA SPA Open auctions Other auction formats Example: Art Auction 3 individuals with private values of $60,000, $70,000 and
$80,000 compete for a work of art
What will happen in the ascending auction?
What if we used a descending auction? Tomá² Miklánek Game Theory: Auctions 9 Motivation Categorization FPA SPA Open auctions Other auction formats Ascending vs. Descending Auctions Do bidders bid their true valuation in ascending or descending
auctions?
Ascending: Yes - bidding up to your true valuation is the
dominant strategy
Descending: No - each bidder shades down his bid. Risk averse bidders shade less Tomá² Miklánek Game Theory: Auctions 10 Motivation Categorization FPA SPA Open auctions Other auction formats More Bidders Matters What if there were more bidders, say with private values of
$60,000, $61,000, ... , $79,000, $80,000?
More revenue in both ascending and descending
Ascending: Second-highest value is now $79,000
Descending: Less incentive to shade bid since it's more likely
someone else will jump in with more bidders Tomá² Miklánek Game Theory: Auctions 11 Motivation Categorization FPA SPA Open auctions Other auction formats Bidding for an Oil Block Five People will bid, in one-time rst-price auction. The top
bid gets the block
The true value of the eld = X True , but no bidder knows
what X True is. It will be revealed (drilled) after the bidding.
Each bidder hires his/her own consultant to give an expert
estimate of the value. Tomá² Miklánek Game Theory: Auctions 12 Motivation Categorization FPA SPA Open auctions Other auction formats How Good Are the Experts?
Oil experts can estimate reserves only with some error.
The distribution of these types of oil estimates tends to be the
following: True + 40 with prob. 1/5 X True + 20 with prob. 1/5 X
Consultant's estimate= X True
with prob . 1/5 True
X
− 20 with prob. 1/5 True
X
− 40 with prob. 1/5
Given your consultant's estimate, how much will you bid? Tomá² Miklánek Game Theory: Auctions 13 Motivation Categorization FPA SPA Open auctions Other auction formats Winner's Curse Winner's Curse = Tendency to overbid due to the fact that
bidder with highest estimate (or signal) will win An issue in all common value auctions, worse with more
bidders participating
To avoid the curse, simply assume your signal is the most
overly optimistic when bidding Tomá² Miklánek Game Theory: Auctions 14 Motivation Categorization FPA SPA Open auctions Other auction formats First Price Auction Tomá² Miklánek Game Theory: Auctions 15 Motivation Categorization FPA SPA Open auctions Other auction formats First Price Auction Everybody submits her/his bid.
A bidder with the highest bid wins the price.
What is the best strategy? Tomá² Miklánek Game Theory: Auctions 15 Motivation Categorization FPA SPA Open auctions Other auction formats Bidding your valuation? Tomá² Miklánek Game Theory: Auctions 16 Motivation Categorization FPA SPA Open auctions Other auction formats Outcomes Tomá² Miklánek Game Theory: Auctions 17 Motivation Categorization FPA SPA Open auctions Other auction formats Bid shading Tomá² Miklánek Game Theory: Auctions 18 Motivation Categorization FPA SPA Open auctions Other auction formats FPA First price auction presents tradeos bidding your valuation: no surplus
Lower your bid below your valuation Smaller chance of winning, lower price
Bid shading Depends on the number of bidders
Depends on your information
Optimal bidding strategy is complicated! Tomá² Miklánek Game Theory: Auctions 19 Motivation Categorization FPA SPA Open auctions Other auction formats Bidding in FPA
Imagine that one good is sold in an FPA auction there are 2
bidders: bidder X and bidder Y.
You are bidder X. You do not know the value or the bid of
bidder Y for the good, but you know the value of Y will be between 0 and 1, with all values having
an equal probability (a uniform distribution). Tomá² Miklánek Game Theory: Auctions 20 Motivation Categorization FPA SPA Open auctions Other auction formats Bidding in FPA
Imagine that one good is sold in an FPA auction there are 2
bidders: bidder X and bidder Y.
You are bidder X. You do not know the value or the bid of
bidder Y for the good, but you know the value of Y will be between 0 and 1, with all values having
an equal probability (a uniform distribution).
Y doesn't know the value or the bid of bidder X, but Y knows the value of X will be between 0 and 1, with all values having
an equal probability (a uniform distribution). Tomá² Miklánek Game Theory: Auctions 20 Motivation Categorization FPA SPA Open auctions Other auction formats Bidding in FPA
You also know that Y has a strategy to bid ½ his value, thus:
1
by (vy ) = vy .
2 Tomá² Miklánek Game Theory: Auctions 21 Motivation Categorization FPA SPA Open auctions Other auction formats Bidding in FPA
You also know that Y has a strategy to bid ½ his value, thus:
1
by (vy ) = vy .
2
So for example, if Y happens to have a value of 1 for the
good, what will Y bid? 0.5
If Y happens to have a value of 0.8 for the good, what will Y
bid? 0.4 Tomá² Miklánek Game Theory: Auctions 21 Motivation Categorization FPA SPA Open auctions Other auction formats Bidding in FPA
You also know that Y has a strategy to bid ½ his value, thus:
1
by (vy ) = vy .
2
So for example, if Y happens to have a value of 1 for the
good, what will Y bid? 0.5
If Y happens to have a value of 0.8 for the good, what will Y
bid? 0.4
What is your optimal bidding strategy bx (vx ) (the bid you
would make as a function of the value for the good for you)? Tomá² Miklánek Game Theory: Auctions 21 Motivation Categorization FPA SPA Open auctions Other auction formats Optimal bidding strategy My prot function is given by:
PROFIT= (GAIN OF WINNING) * (PROBABILITY OF
WINNING) Tomá² Miklánek Game Theory: Auctions 22 Motivation Categorization FPA SPA Open auctions Other auction formats Optimal bidding strategy My prot function is given by:
PROFIT= (GAIN OF WINNING) * (PROBABILITY OF
WINNING)
GAIN OF WINNING= (vx − bx ) Tomá² Miklánek Game Theory: Auctions 22 Motivation Categorization FPA SPA Open auctions Other auction formats Probability? Tomá² Miklánek Game Theory: Auctions 23 Motivation Categorization FPA SPA Open auctions Other auction formats What if... Tomá² Miklánek Game Theory: Auctions 24 Motivation Categorization FPA SPA Open auctions Other auction formats Y bids half of his value... Tomá² Miklánek Game Theory: Auctions 25 Motivation Categorization FPA SPA Open auctions Other auction formats Y bids half of his value... Tomá² Miklánek Game Theory: Auctions 26 Motivation Categorization FPA SPA Open auctions Other auction formats Y bids half of his value... Tomá² Miklánek Game Theory: Auctions 27 Motivation Categorization FPA SPA Open auctions Other auction formats Optimal bidding Tomá² Miklánek Game Theory: Auctions 28 Motivation Categorization FPA SPA Open auctions Other auction formats Nash
Is this a Nash equilibrium?
by = 12 vy
bx = 21 vx Given that me (X) and Y have a value uniformly distributed on
[0,1] Tomá² Miklánek Game Theory: Auctions 29 Motivation Categorization FPA SPA Open auctions Other auction formats Nash
Is this a Nash equilibrium?
by = 12 vy
bx = 21 vx Given that me (X) and Y have a value uniformly distributed on
[0,1]
I maximize my prot given that Y has the strategy of bidding
half its value Y maximizes its prot given that I have the
strategy of bidding half its value
YES! Is a Nash equilibrium. Tomá² Miklánek Game Theory: Auctions 29 Motivation Categorization FPA SPA Open auctions Other auction formats If Y bids dierently...
You also know that Y has a strategy to bid ¼ his value, thus:
1
by (vy ) = vy .
4
So for example, if Y happens to have a value of 1 for the
good, what will Y bid? 0.25,
If Y happens to have a value of 0.8 for the good, what will Y
bid? 0.2
What is your optimal bidding strategy bx (vx ) (the bid you
would make as a function of the value for the good for you)? Tomá² Miklánek Game Theory: Auctions 30 Motivation Categorization FPA SPA Open auctions Other auction formats Optimal bidding My prot function is given by: PROFIT= (GAIN OF
WINNING) * (PROBABILITY OF WINNING)
GAIN OF WINNING= (vx − bx ) Tomá² Miklánek Game Theory: Auctions 31 Motivation Categorization FPA SPA Open auctions Other auction formats Probability of winning Tomá² Miklánek Game Theory: Auctions 32 Motivation Categorization FPA SPA Open auctions Other auction formats Probability of winning Tomá² Miklánek Game Theory: Auctions 33 Motivation Categorization FPA SPA Open auctions Other auction formats Probability of winning Tomá² Miklánek Game Theory: Auctions 34 Motivation Categorization FPA SPA Open auctions Other auction formats Probability of winning Tomá² Miklánek Game Theory: Auctions 35 Motivation Categorization FPA SPA Open auctions Other auction formats Probability of winning Tomá² Miklánek Game Theory: Auctions 36 Motivation Categorization FPA SPA Open auctions Other auction formats Optimal bidding Thus my prot function is: PROF= (GAIN OF WINNING) *
(PROBABILITY OF WINNING)
PROFIT= (vx − bx ) ∗ 4bx
Dierentiate wrt bx , gives the First Order Condition (FOC): Tomá² Miklánek Game Theory: Auctions 37 Motivation Categorization FPA SPA Open auctions Other auction formats Optimal bidding Thus my prot function is: PROF= (GAIN OF WINNING) *
(PROBABILITY OF WINNING)
PROFIT= (vx − bx ) ∗ 4bx
Dierentiate wrt bx , gives the First Order Condition (FOC):
FOC: 4(vx − bx ) − 4bx = 0
4vx − 8bx = 0 =⇒ Tomá² Miklánek x= b 1
2 vx Game Theory: Auctions 37 Motivation Categorization FPA SPA Open auctions Other auction formats Is this Nash Equilibrium? y= b 1
4 vy and x= b 1
2 vx Given that me (X) and Y have a value uniformly distributed on
[0,1] Tomá² Miklánek Game Theory: Auctions 38 Motivation Categorization FPA SPA Open auctions Other auction formats Is this Nash Equilibrium? y= b 1
4 vy and x= b 1
2 vx Given that me (X) and Y have a value uniformly distributed on
[0,1]
I maximize my prot given that Y has the strategy of bidding
half its value (for values lower than 1/2).
Y maximizes its prot given that I have the strategy of bidding
half its value? No! This is not a Nash equilibrium. Tomá² Miklánek Game Theory: Auctions 38 Motivation Categorization FPA SPA Open auctions Other auction formats Second Price Auction An auction in which the bidder who submitted the highest bid
is awarded the object being sold and pays a price equal to the
second highest amount bid.
Alternately, in a procurement auction, the winner is the bidder
who submits the lowest bid, and is paid an amount equal to
the next lowest submitted bid.
The theoretical nicety of second price auctions, rst pointed
out by William Vickrey, is that bidding one's true value is a
dominant strategy. Tomá² Miklánek Game Theory: Auctions 39 Motivation Categorization FPA SPA Open auctions Other auction formats Bidding higher than my valuation Tomá² Miklánek Game Theory: Auctions 40 Motivation Categorization FPA SPA Open auctions Other auction formats Bidding lower than my valuation Tomá² Miklánek Game Theory: Auctions 41 Motivation Categorization FPA SPA Open auctions Other auction formats Best strategy In a second price auction, always bid your true valuation
Winning bidder's surplus Dierence between the winner's valuation and the second
highest valuation
Surplus decreases with more bidders Tomá² Miklánek Game Theory: Auctions 42 Motivation Categorization FPA SPA Open auctions Other auction formats Which auction to use? In a second price auction bidders bid their true value auctioneer receives the second highest bid
In a rst price auction bidders bid below their true value auctioneer receives the highest bid Tomá² Miklánek Game Theory: Auctions 43 Motivation Categorization FPA SPA Open auctions Other auction formats In practice- inexperienced subjects Tomá² Miklánek Game Theory: Auctions 44 Motivation Categorization FPA SPA Open auctions Other auction formats In practice- experienced subjects Tomá² Miklánek Game Theory: Auctions 45 Motivation Categorization FPA SPA Open auctions Other auction formats English Auction Auction procedure:
I start with a price of zero
Everybody who keeps his hand in the air is bidding.
I increase the price slowly If the price becomes too high, you
can withdraw from the auction by drawing back your hand
The auction is over when only one bidder is still in the auction
The bidder left in the auction wins
And pays the price level the auction stopped at. Tomá² Miklánek Game Theory: Auctions 46 Motivation Categorization FPA SPA Open auctions Other auction formats Optimal bidding strategy in English Auction Tomá² Miklánek Game Theory: Auctions 47 Motivation Categorization FPA SPA Open auctions Other auction formats Dutch Auction Auction procedure:
I start with a price of . . .
I slowly decrease the price
The auction is over when one bidder raises his/her hand
The rst bidder to raise the hand wins the auction
And pays the price level the auction stopped at Tomá² Miklánek Game Theory: Auctions 48 Motivation Categorization FPA SPA Open auctions Other auction formats Dutch Auction Auction procedure:
I start with a price of . . .
I slowly decrease the price
The auction is over when one bidder raises his/her hand
The rst bidder to raise the hand wins the auction
And pays the price level the auction stopped at
What will be your strategy in such auction? Tomá² Miklánek Game Theory: Auctions 48 Motivation Categorization FPA SPA Open auctions Other auction formats Overview Closed auctions FPA
SPA (Vickrey auction)
Open auctions English (ascending price auction)
Dutch (descending price auction)
Outcome equivalence between FPA & Dutch
SPA & English Tomá² Miklánek Game Theory: Auctions 49 Motivation Categorization FPA SPA Open auctions Other auction formats All pay auction Auction procedure:
Write down a bid on a paper
The person with the highest bid wins And pays the price (s)he bid
All the others also pay the price they bid Tomá² Miklánek Game Theory: Auctions 50 Motivation Categorization FPA SPA Open auctions Other auction formats All pay auction Auction procedure:
Write down a bid on a paper
The person with the highest bid wins And pays the price (s)he bid
All the others also pay the price they bid
Examples? Tomá² Miklánek Game Theory: Auctions 50 Motivation Categorization FPA SPA Open auctions Other auction formats All pay auction: examples
Tender competitions Time and eort to prepare a prospectus
Elections Advertising & promotion costs
Lobbying eort
Legal action Lawyers
Expert reports from forensic specialists, statisticians,
economists, psychologists Tomá² Miklánek Game Theory: Auctions 51 Motivation Categorization FPA SPA Open auctions Other auction formats Revenue equivalence theorem In any auction where: The bidder with the highest bid wins the auction
Values are distributed independently and identically
All bidders are risk neutral
The expected payment of a bidder with value zero is zero Tomá² Miklánek Game Theory: Auctions 52 Motivation Categorization FPA SPA Open auctions Other auction formats Revenue equivalence theorem In any auction where: The bidder with the highest bid wins the auction
Values are distributed independently and identically
All bidders are risk neutral
The expected payment of a bidder with value zero is zero
The seller yields the same expected revenue Tomá² Miklánek Game Theory: Auctions 52 Motivation Categorization FPA SPA Open auctions Other auction formats Multiple units More than 1 unit of the good is sold at the same time.
You can also post (dierent or the same) bids for more than 1
unit.
Types: Discriminating auction (Pay-Your-Bid)
Modied Dutch auction (uniform price auction) Tomá² Miklánek Game Theory: Auctions 53 Motivation Categorization FPA SPA Open auctions Other auction formats Discriminating auction (Pay-Your-Bid) Tomá² Miklánek Game Theory: Auctions 54 Motivation Categorization FPA SPA Open auctions Other auction formats Modied Dutch auction (uniform price auction) Tomá² Miklánek Game Theory: Auctions 55 Motivation Categorization FPA SPA Open auctions Other auction formats Uniform price (example) Tomá² Miklánek Game Theory: Auctions 56 ...

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- Fall '17
- Mammad Rzayev
- Auction, FPA