Private Value Auctions

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Private Value Auctions

• Econ 333
• Fall 2009

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Auctions

• Auctions are most useful in selling a commodity
  of undetermined value.
• If a seller is unsure of the price he can get
  then auctions are particularly useful.
• More flexible than setting a fixed price
• Less time-consuming and less expensive than
  negotiating a price
• An auction tries to deliver the object to the
  person who values it the most.

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History of auctions

• Auctions extend back to 500BC in Babylon when
  Herodotus reported the use of an auction
• Women sold under condition they be married after
  purchase
• Less attractive women had to pay a dowry
  (negative price)
• Roman empire used auctions to liquidate property
  and sell goods acquired sub hasia (under the
  spear)

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Roman empire for sale

• 193 AD entire Roman empire was auctioned off by
  Praetorian Guard
• They killed Pertinax (emperor) and announced that
  highest bidder could have the empire!
• Didius Julianus outbid others to become emperor
• 6250 drachmas per Guard
• Beheaded 2 months later when Septimus Severus
  conquered Rome
• Winners curse???

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History of auctions

• Earliest modern recording of an auction in Oxford
  English Dictionary 1595
• Auctions probably preceded this date
• Popular in late 17th century
• 18th century London auction houses
• Sothebys 1744
• Christies 1766
• USA liquidate estates, slave auctions
• eBay

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Value of the good

• Two types of values
• 1. Private value
• Each bidder has his/her own unique value for the
  item, e.g. art auction
• Nothing about the other bidders affects your
  value
• (But may affect your bid, depending upon
  institution)
• What they know
• What they are WTP
• Source of uncertainty others bids and values
• Others bids may determine own bid

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Value of the good

• Types of value (cont.)
• 2. Common value
• Value is the same for all bidders, but that value
  is unknown at time of bidding
• Each bidder only has an estimate of the value
• e.g. leases for unproven oil fields
• Source of uncertainty value of object ( others
  bids)

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Types of auctions

• One-sided auctions
• Only one side of the market is active, usually
  buyers bidding (and no seller asks)
• e.g. English auction, Dutch auction
• Two-sided auctions
• Both sides of the market are active

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Number of units sold

• Single unit auctions
• Multi-unit auctions
• Typically have more complex bidding strategies

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Private Value Auctions (single unit)
Open outcry
Sealed Bid
The 2nd price sealed bid auction is often
referred to as a Vickrey Auction.
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Properties of auctions

• Is it incentive compatible??
• Is it demand revealing??

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English auction

• Also known as an open outcry or ascending price
  auction
• Commonly used for sale of art, wine,
  collectibles, livestock, eBay
• Auctioneer begins with lowest acceptable price
  (reserve price)
• Proceeds to solicit successively higher bids
  until no one will increase the bid
• Sold to highest bidder at (slightly more than)
  the second highest bid.
• Winner does not pay his/her actual value for the
  good

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Dutch auction

• Also known as descending price auction
• FYIin financial markets, Dutch can refer to a
  Vickrey auction.
• In this class, the Dutch and Vickrey are
  different institutions!! Dont confuse the two!
• Bidding starts at an extremely high price.
• Clock ticks down progressively lowering price
  until a buyer claims it.
• Examples
• Flower in the Netherlands
• Fish in England and Israel
• Less obvious example Filenes

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Dutch Clock Auction
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Bidding Strategies

• Dutch auction
• Wait for price to drop below value (bid lt value)
• But how much below value should you bid??
• Waiting longer lower price, but could lose
  auction
• Trade-off higher price vs. better chance of
  winning
• Bid is NOT independent of action taken by others
• English auction
• Keep increasing bid until bid value
• Essentially pay second highest bid
• Price paid 2nd highest bid a little bit
• Incentive compatible no incentive to
  misrepresent willingness-to-pay (bid value)
• No trade-off of price vs. probability
• Bid is independent of action taken by others

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Sealed-bid auctions

• Buyers submit sealed bids
• Not an open outcry, so bidder only knows his/her
  bid before auction ends
• Two stages
• Bidding period
• Resolution phase
• Bids opened, winner is person with highest bid
• Types of sealed bid auctions
• First-price Winner pays his/her own bid price
• Second-price Winner pays 2nd highest bid price

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2nd price sealed bid

• If you win, does the price you pay depend upon
  your bid?
• Why is this important?
• What if you bid below your value?
• What if you bid above your value?
• So what is your dominant bidding strategy?
• Does it depend upon the values of others?
• Does it depend upon risk preferences?

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Bidding Strategies

• First-price sealed bid
• High bid better chance of winning, but high
  price
• Low bid lower chance of winning, but better
  price
• Trade-off price vs. probability of winning
• Bid below value but by how much??
• Second-price sealed bid (Vickrey auction)
• Price you pay is independent of what you bid
• No price vs. probability trade-off
• Bid value ? incentive compatible

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Isomorphic auctions

• Iso- same
• morph shape
• being of identical or similar form, shape, or
  structure
• Important parallels between auctions.
• Which auctions are strategically equivalent?

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Isomorphic auctions

• English 2nd price sealed bid auctions
• Dutch 1st price sealed bid auctions
• Why are these pairs strategically equivalent?

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How do the English and 2nd price auctions differ?

• English auction is easier to figure out
  strategy
• Bidder with highest value discovers that it is
  not necessary to pay more than 2nd highest price
• No calculation necessary
• Compare current price to private value
• 2nd price sealed bid
• Optimal bid needs to be deduced

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Dutch 1st price auctions

• Price winners bid
• Do not want to bid above value
• Bid value ? Profit 0
• ? Bid lt value. By how much???
• Optimal bid depends upon beliefs about
  competitors bids.
• Lower bid ? more profits, decrease chances of
  winning.
• Higher bid ? less profits, increase chance of
  winning
• Profit/Probability trade-off

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1st price Dutch auctions equilibrium bidding
strategies

• N bidders
• Each bidder, i, has a private value vi
• Bidder knows own private value
• Bidder does not know others values
• Does know probability distribution of others
  values
• Independent draw from uniform distribution
• Bidder, i, must determine optimal bid, bi
• Assume bidders are all risk neutral

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1st price auctions equilibrium bidding strategies

• Dominant bidding strategy

• Example
• (N9 people per group)

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Bidding (2008) n12

• 1st price sealed bid auction (Bid/value)
• 3 rounds, 12 people ? 36 observations
• Mean b/v 0.89, Median b/v 0.94
• b/v lt 0.92 0.02 12
• b/v 0.92 0.02 5
• b/v gt 0.92 0.02 19
• b/v above 1.00 0

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Bidding (2006) n9

• 1st price sealed bid auction (Bid/value)
• Number of obs. 36
• Mean b/v 0.87, Median b/v 0.94
• b/v lt 0.89 0.02 9
• b/v 0.89 0.02 1
• b/v gt 0.89 0.02 26
• b/v above 0.95 17
• b/v above 1.00 1

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2008 bidding 2nd price auctions

• Strategy reveal your value
• Howd you do? ( obs 36)
• b/v above 1.00 9
• b/v 0.99 or 1.00 16
• b/v between 0.95-0.98 5
• b/v between 0.90-0.95 4
• b/v between 0.80-0.89 1
• b/v under 0.80 1

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2006 bidding 2nd price auctions

• Strategy reveal your value
• Howd you do? ( obs 36)
• b/v above 1.00 4
• b/v 0.99 or 1.00 15
• b/v between 0.90-0.98 13
• b/v between 0.80-0.89 1
• b/v between 0.70-0.79 1
• b/v under 0.70 2

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Mean bid/value ratios (2006)
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Bid/Value Frequency Distribution2006
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Efficiency

• How do we know if our auction resulted in an
  efficient allocation?

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Did Highest Value Win? (2006)

• 1st Price 0 / 4
• 2nd Price 3 / 4
• English 3 / 5
• Dutch 4 / 5

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Did Highest Value Win? (2008)

• 1st Price 2 / 3
• 2nd Price 3 / 3
• English 1 / 5 (winners lost , confused??)
• Dutch 4 / 5

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Seller revenue in different auctions

• In a 1st price auction, bids are below values.
  Does this mean that the seller will receive a
  lower selling price on average, than in a 2nd
  price auction?

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Revenue equivalence

• Assuming risk neutrality, in theory, all 4
  auctions will yield the same expected seller
  revenue
• Example
• 1st price auction with 2 bidders (N2)
• Values in the interval 0,100
• Assume v1 2/3 100 67
• Assume v2 1/3 100 33
• For each person, optimal bid ½ Value
• Note b1 ½ v1 33 v2

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Revenue equivalence (cont.)
v1 and v2 are the expected values of the highest
and lowest draws from a uniform distribution

• 1st price auction
• b1 ½ (v1) 33
• b1 v2
• Price 33
• English auction
• 1 wins, pricev2
• Price 33

f(x)
Uniform density
1/100
b1
x
See spreadsheet with example.
100
0
v2
v1
33
67
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Revenue equivalence (cont.)

• With N bidders, uniform distribution 0,Vmax

• In our experiments (N9, Vmax250)

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2006 Expected sales revenue 4.00

• Average prices in experiments

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Experimental evidence

• Theory Same outcomes in Dutch and 1st price
• Lab Average revenue is 5 lower in the Dutch
  auction
• Waiting game, suspense of waiting?
• Theory Same outcomes in English and 2nd price
• Lab Prices are 11 higher than predicted in 2nd
  price
• With experience, price does converge to
  prediction
• Subjects slow to realize that bidding above value
  not profitable
• Could lose money if you overbid

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Experimental evidence

• Theory Assuming risk neutral buyers, all four
  auctions produce same average revenue
• Lab Prices higher in sealed bid auctions where
  buyers explicitly state prices. Why?
• Kagel (1995) suggests reason is psychological
• Sealed-bid focus on price
• Open-outcry focus on profitability
• Observed efficiency (eenglish, ddutch)
• Ee E2 gt E1 gt Ed

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Examples of auctions

• US Treasury bill auctions
• In the 70s were auctioned using a discriminative
  price sealed-bid auction
• Proposals to change to uniform pricing because of
  potential collusion
• Theory and experiments showed that seller
  revenues likely to be higher with uniform price

Vernon Smith. 1967. Experimental Studies of
Discrimination versus Competition in Sealed Bid
Auction Markets, Journal of Business.
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Initial allocation of NZ IFQs

• NZ considered auctioning allowances for new
  species
• Objectives
• Allocative efficiency
• Market share of large players
• Maximize auction revenue
• Three multi-unit mechanisms considered
• Kth price (uniform)
• K1 price (uniform)
• Discriminative price

Anderson Holland. 2006. Land Economics
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Regional Green House Gas Initiative (RGGI)

• Coalition of Northeast states
• Auction off initial rights to emit carbon
• Charlie Holt and others were instrumental in
  designing auction mechanism
• Found that sealed bid auctions led to higher
  revenues than an English clock
• Potential collusion with the clock auction

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Virginia NOx auctions

• One of the first known cases of auctioning off
  initial rights to emissions with goal of
  maximizing govt revenues
• June 30, 2004, VA auctioned off 3710 allowances
  with sequential English clock raising over 10
  million.

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Right-to-choose auctions

• Auctioning off multiple heterogeneous goods
• Condos in a new development
• Nevada wildhorses
• Rather than auctioning off each item
  sequentially, the winner gets to choose the item.
• Auction then restarts until all goods sold
• Evidence suggests that RTC auctions generate
  higher seller revenues

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FCC spectrum licenses

• Combinatorial auctions
• Package bidding, all-or-nothing bids
• First developed by Steve Rassenti for auctioning
  off airport landing slots
• Right to depart from NY has no value unless you
  also have right to land in Chicago about 3 hours
  later
• PCS spectrum auctions
• 99 licenses auctioned for 7.7 Billion

Salant, D. 2000. Auctions and Regulation
Reengineering of Regulatory Mechanisms. Journal
of Regulatory Economics. 17195-204.
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Reverse auctions

• Auctioneer has a fixed budget and wants to
  acquire as much of the good as possible
• Single, budget constrained buyer
• Georgia Irrigation Reduction Auction
• State run auction in 2001
• Goal was to reduce irrigation and leave more
  water instream
• Legislature set aside 10 million to compensate
  farmers to voluntarily forego irrigating for a
  year