Welcome
Auctions
Jonathan D. Wareham
[email protected]
What is an auction ?
 A method for allocating scarce resources
based on competition
 Bidding mechanism:
 the seller (auctioneer) defines the auction
rules:
 how the winner is determined
 how much he must pay
 each buyer chooses a bidding strategy
 The auction rules define a game among
buyers
 should use game-theoretic concepts to analyze
auctions
Examples
 Ancient cases:
 500BC: Herodotus mentions about auctions in
Babylon
 Ancient Rome: commercial trading, selling war
booty
 193 A.D.: auction for the entire empire
 More recent cases: auctions




for rare collective items
in wholesale markets of fish, flowers, etc.
for public contracts
in stock market
 Very recent cases: auctions
 over Internet (E-bay, ONSALE, etc.)
 for bandwidth (Interxion, RateX, etc.) ,
spectrum
Auctions and resource allocation
 An auction is a market mechanism that
 allocates resources (goods) to buyers
 generates value for the consumers
 generates revenue for the seller
 generates revenue for the producer
 Is used where traditional market
mechanisms (e.g. fixed price) can not be
used
 can serve as an internal mechanism
value
Seller
revenue
Vi
buyers
Performance Measures
 When choosing an auction design, a variety of
assessment criteria and measures may be used:
 social efficiency (maximize the total value to buyers:
Vickrey)
 revenue (seller profit)
 bidder profit
 time, complexity, susceptibility to collusion
 Why is it hard to design? Due to lack of
10
 Auction: incentive mechanism
information!
seller
20
 buyer: maximizes expected profit
 seller: maximizes performance
measure
Bidder and seller characteristics
 Valuation
 private
values
 common
values
 correlation
U i  Vi
Buyer i
U i  V , Vi  V  xi
i
U i  aVi  b V j
Vi
j i
U (h)
 Risk
assessment
 risk neutral
 risk averse
 Symmetry
V
 symmetric 1
 asymmetric
h V  p
h
V2
Auctions
 Uses
 Major types of Auction




English
First-price, sealed-bid
Second-price, sealed-bid (Vickrey)
Dutch
English Auction
 An ascending
sequential bid auction.
 Bidders observe the
bids of others and
decide whether or not
to increase the bid.
 The item is sold to the
highest bidder.
English Auction
V
 ascending bid, open-outcry
 item is sold at least at the reservep  V
2
price
V
 best strategy for ibidder
3
4
 bid a small amount more than the
previous high bid until bidder’s valuation
is reached, then stop
 auctioneer has great influence
 most emotional and competitive of
auctions
 much information regarding demand
is revealed
V2
V1
r
First-Price, Sealed-bid
 An auction whereby
bidders simultaneously
submit bids on pieces
of paper.
 The item goes to the
highest bidder.
 Bidders do not know
the bids of other
players.
First price, sealed-bid
 first price wins
 sealed (each bidder is ignorant of
other bids)
 usually each participant is allowed
one bid
 two parts
 bidding period
 resolution (winner determination)
phase
 bidder’s strategy: shade bids
 to generate positive profit
 to avoid winner’s curse (for
common value)
 little information on demand is
V1
b1
p
V2
b2
V3
b3
Vn
bn
Second Price, Sealed-bid
 The same bidding
process as a first
price auction.
 However, the high
bidder pays the
amount bid by the
2nd highest bidder.
Developed for Social Efficiency: Vickrey
auction
 second price wins, sealed
 the item is awarded to the highest
bidder at a price equal to the second
highest bid
 dominant strategy: submit a bid
equal to true valuation 
incentive compatibility
V1
b1
b2
b3
p
V2
V3
 less fear of winner’s curse (for
common value)
b
b
V
b
b
b
b
V
bn
Vn
Why???? Asymmetric Cases
 Different distributions for bidders’
valuations
 Revenue equivalence does not apply
 First price auctions not socially
optimal
 Public authorities should use second
price auctions for efficiency purposes
 otherwise, possibility for inefficiency
u
Intuition
1. Aggressive bidders receive sure and certain
awards but pay a price closer to market
consensus.
2. The price that winning bidder pays is
determined by competitors' bids alone and does
not depend upon any action the bidder
undertakes
3. Hence, closer to real market valuation and
socially optimal
4. Less bid shading or collusion occurs because
people don't fear winner's curse.
5. Hence, they may adjust bid upwards.
6. Bidders are less inclined to compare notes
before an auction.
Dutch Auction
 A descending
price auction.
 The auctioneer
begins with a
high asking price.
 The bid decreases
until one bidder is
willing to pay the
quoted price.
 Strategically
equivalent to a
first-price auction
Dutch Auction
 descending price (often by “Dutch clock”),
open-outcry
 first price wins
 auctioneer usually has no influence
 little information on demand is revealed
price
V1
V2
V3
V4
b1
b2
b3
b4
Information Structures
 Independent private values
 Bidders know their own valuation of the item, but not
other bidders’ valuations
 Bidders’ valuations do not depend on those of other
bidders
 Affiliated (or correlated) value estimates
 Bidders do not know their own valuation of the item or
the valuations of others
 Bidders use their own information to form a value
estimate
 Value estimates are affiliated: the higher a bidder’s
estimate, the more likely it is that other bidders also
have high value estimates.
 Common values is the special case in which the true
(but unknown) value of the item is the same for all
bidders
Optimal Bidding Strategy in an English
Auction
 With independent private valuations,
the optimal strategy is to remain
active until the price exceeds your
own valuation of the object.
Optimal Bidding Strategy in a First-Price, SealedBid Auction
 If there are n bidders who all
perceive valuations to be evenly (or
uniformly) distributed between a
lowest possible valuation of L and a
highest possible valuation of H, then
the optimal bid for a risk-neutral
player whose own valuation is v is
v L
b v
.
n
Example
 Two bidders with independent private
valuations (n = 2)
 Lowest perceived valuation is unity (L
= 1)
 Optimal bid for a player whose
valuation is two (v = 2) is given by
v a
2 1
b v
 2
 $1.50
n
2
Optimal Bidding Strategy in a Second-Price
Sealed-Bid Auction
 The optimal strategy is to bid your
own valuation of the item.
 This is a dominant strategy.
 You don’t pay your own bid, so bidding
less than your value only increases the
chance that you don’t win.
 If you bid more than your valuation, you
risk buying the item for more than it is
worth to you.
Optimal Bidding Strategies with Affiliated Value
Estimates
 Difficult to describe because
 Bidders do not know their own valuations
of the item, let alone the valuations
others.
 The auction process itself may reveal
information about how much the other
bidders value the object.
 Optimal bidding requires that players
use any information gained during
the auction to update their own value
estimates.
The Winner’s Curse
 In a common-values auction, the
winner is the bidder who is the most
optimistic about the true value of the
item.
 To avoid the winner's curse, a bidder
should revise downward his or her
private estimate of the value to
account for this fact.
 The winner’s curse is most
pronounced in sealed-bid auctions.
Common value auctions
 Value of bidder is not fixed before the
auction
 True value of item is not known ex-ante,
although defined
 Value to bidder i depends on other bidder’s
values
 examples: sealed box with coins, oil-lease
 Complex strategies, no general results
 Winner’s curse: the winner discovers that
he overestimated the value of the item
 Strategic approach: shade the bid to
account for the adverse selection bias
Expected Revenues in Auctions with Risk Neutral
Bidders
 Independent Private Values
 English = Second Price = First Price =
Dutch
 Affiliated Value Estimates
 English > Second Price > First Price =
Dutch
 Bids are more closely linked to other
players information, which mitigates
players’ concerns about the winner’s
curse.
Collusion
 Bidders make collusive agreements to get
the item at a lower price:
 they select their designated winner (the one
with the highest valuation)
 others promise to follow a specific strategy
(abstain from bidding)
 Which auctions are more collusive than
others ?
 Enforcement issue: incentives for non-winners
to keep their promise
Collusion (cont.)
 First price sealed bid and Dutch auctions:
not self-enforcing! no possibility for
pmin   ,
punishment
 In FP: winner places bid =
other
bidders may abstain or break the ring by bidding
slightly higher
 In Dutch: one of the others may shout “mine”
and win!
 English and Second price auctions: selfenforcing!
 In English: if one of the others bids higher than
promised, then the winner may overbid again
 In SP: winner’s bid = valuation of others’ bid