W6L1NewAuction_________________Theory .pdf

Auction Theory

1. MIT Center for
Transportation & Logistics
Auction Theory

2. Auction Theory
Each Procurement Event is an Auction
•The auctioneer is the company (procurement
department)
•The bidders are the suppliers or service providers
•The auctioneer tries to choose the bidder that
satisfies certain criteria:
nLowest price
nHighest service
nEasiest to do business with
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3. Auction Theory
Auctions -Examples
•As old as the hills…
•Fixed price is only ~150+ years old
•Consumer auctions (art, eBay…)
•Procurement auctions (MRO and direct material) –
aka reverse auctions
•Auction of public properties (electromagnetic
spectrum for cell phones; TV; pagers… industry in
Russia; transportation assets in the UK; oil leases;
timber rights…)
•Government contracts (military hardware,
construction, bonds…)
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4. Auction Theory
Auctions –What and Why?
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What?
•An auction is an allocation & pricing mechanism.
It determines:
nWho wins ?
nHow much they pay ?
Why?
•Auctions elicit information about how much buyers are
willing to pay (price discovery/value determination).
•In addition:
nUniversal -in principle, open to all bidders
nAnonymous –typically not in procurement auctions
nEfficient -Give it to the buyer who wants it most
nTransparent -Avoid dishonest “smoke-filled-room” dealings

5. Auction Theory
Television Broadcasting Rights for Sports
•Baseball TV rights in the US
nStarted with team deals which were low –owners reverted to the league to
conduct auctions
n1964 –Network paid $14 million/year for a two year baseball deal
n1998 –Network paid $2 billion/year for a two year baseball deal
•Premier League in the UK conducted an auction for the TV rights
n£45 million in 1992
n£537 million in 2000
n£5.1 billion in 2015
•Olympic games (IOC is the auctioneer)
nNBC paid $705 million for the Sydney games (2000)
nNBC paid $3.5 billion for 2004 and 2008
•The auctions unlockedthe value
nIt is difficult to argue that savvy network executives will pay a price that is
“too high” over and over again…
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6. MIT Center for
Transportation & Logistics
Auction Metrics

7. Auction Theory
Auction Metrics (the Auctioneer)
•Revenue–auctioneers are looking for the auction that will
yield the maximum revenue for the item sold.
•Efficiency–an auction is successful if the bidder that values
the item most ex post-actually gets it.
nIn most procurement auctions there is no secondary
markets
nSecondary markets involve extra transaction costs
•Time and Effort –many B2B auctions involves the trading of
many items while soliciting bids from multiple suppliers.
Furthermore such auctions are conducted periodically.
•Simplicity–Keeping the rules simple, especially knowing that
many suppliers have to respond to hundreds of auctions
every month, helps increase bidders’ participation.
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8. Auction Theory
The Framework
•What does it mean for a bidder to “win” ?
•We assume that each bidder has a value for the item
•If he is able to purchase the item it does not mean a “win”
•It is a win only if his value is higher than the purchase price. If
his value is lower, the bidder actually loses…
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9. Auction Theory
Information Distribution
VS.
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10. Auction Theory
Information distribution
•Both buyers and seller are uncertain what the true value
of the item sold is.
•Private values–each bidder knows the value to himself
(no bidder knows the valuation of other bidders; in any
case it will not affect the self valuation)
•Common values–the value is the same for all bidders
(example: mineral rights –the real value becomes known
later)
•Interdependent values–bidders modify their estimate
during the bidding process. Both common and private
elements
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11. MIT Center for
Transportation & Logistics
Types of Auctions

12. Auction Theory
Simple Auctions (Single Item)
•Open bids:
nEnglish auction–auctioneer calls increasing price until one
bidder left. Bidder pays the price at that point (Japanese
auction –digital version).
nDutch auction–auctioneer starts high and lower price.
First bidder to call gets the item
•Sealed bids:
nFirst price–highest bid wins
nSecond price–highest bid wins but pays the second-
highest bid
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13. Auction Theory
Equivalent auctions
English
1
st
PriceDutch
In both cases bidders have no information
about the others and in both cases the highest
bidder wins and pays his bid. In both cases the
strategy is the same –bidders have to decide
a-priorihow much to bid and this is what the
auctioneer will get in either auction. Thus they
are strategically equivalent
=
PV
CV
=
PV
When the last bidder stays in
English (Japanese) he pays
the price when the next-to-
last bidder dropped. Also in
PV auctions, the bidding will
be identical in both. In CV
there is value in watching the
bidding. In both cases bidders
bid truthfully.
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2
nd
Price

14. Auction Theory
2
nd
Price –Bidding Strategies
V
ΔV
Bid
ΔV
V
Bid
Dominant strategyin 2
nd
price (and English) auctions:
Bid your value! (“truth telling”). It is a dominant strategy
Because it does not depend on what strategy other bidders use
1
b
-maxb
-max
2
b
-max
3
2
b
-max
1
b
-max
3
b
-max
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Surplus
Surplus

15. Auction Theory
1
st
Price –Bidding Strategy
Intuition:
•since the winning bidder will have to pay his
bid, the strategy is to bid lower than his value
•Not too much lower because the lower the
bid, the lower the chances to win (this is
stronger the more bidders there are)
•So: this is a tradeoff between the amount
“won” (the surplus) and the probability of
winning
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16. Auction Theory
1
st
Price –Bidding Strategy
•E[winning]=(v-b)·P(b)
nv–valuation of the object by the bidder
nb–The bid
nP(b) –Probability of winning with bid b
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•The optimal bid solves:
•−−=
*
*()
()()0
dP b
vb Pb
db
•When there are nbidders and the valuations
are drawn from U(0,1) i.i.d. distribution*:
−
=•
* 1n
bv
n
______________________
*Proof in the accompanying PDF

17. Auction Theory
Revenue Equivalence Theorem
•In 2
nd
price participants bid their value and pay the highest
losing bid
•In 1
st
price they shade their bid and pay what they bid
•In any particular case any given auction can give results that
are better (worse) then any other auction
•Revenue Equivalence: All auction that allocate the item to
the highest bidder and lead to the same bidder participation
yield the same expected payoff.
nPrivate values
nRisk neutrality
niidvaluation
nNo collusion
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18. MIT Center for
Transportation & Logistics
Winner’s Curse

19. Auction Theory
Common Value Auctions
•After the auction the value is clear –same for all
•Before the auction, each bidder “guesses” or has
some signal to help estimate the (hidden) value
•The winner is the bidder with highest signal.
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20. Auction Theory
•But:Winning means that everybody else had
a lower estimate (“adverse selection bias”)
•So winning is “bad news” (cold feet make
sense…)
•If bidders do not correct for this, the winner
will overpay
•Bidders have to “shave” their bids further (1
st
price “shave” + WC “shave”)
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Winner’s Curse (CV Auctions)

21. Auction Theory
•Carolina Freight 1995 bid for K-Mart freight
•Overbid (lowestbidder in this case) and
went bankrupt
•Bought by ABF, who probably overbid to
acquire it
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Winner’s Curse –A Case Study

22. Auction Theory
Winner’s Curse -Getting the Correct
Exp. value
•Essentially, a bidder should realize a-piorithat if
he wins, it is likely that his signal was unusually
high and his true value is lower.
•Thus, WC results strictly from judgment failure
•Note: the shading for WC is larger (lower bids)
with more bidders. This is the opposite of the
1
st
price shading which is smaller (higher bids)
with more bidders.
•Note: the existence of WC in practice is hotly
debated among economists since it implies
irrationality
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23. MIT Center for
Transportation & Logistics
Practical Considerations

24. Auction Theory
Practical considerations -Asymmetric
Valuations
•Asymmetric valuations –“strong” and “weak”
bidders (valuations drawn from different
distributions)
•Strong bidders prefer English –usually win in an
open format
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•Weak bidders have a chance in
sealed bids (1
st
price); it gives them
some probability of winning
•So: weaker bidders may bid more
aggressively (closer to their
valuation) in sealed bids

25. Auction Theory
•English auctions are more susceptible to predatory
behavior since strong bidders can bid aggressively in early
rounds causing others to drop too early and win with a
price that is too low.
•English auctions are more susceptible to collusion. In
particular with multiple items bidders may signal each
other in the early rounds, dividing the pie without driving
the price too high. Also bidders can “punish” aggressive
behavior by bidding high on something small that the other
bidder really wants
Practical considerations
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26. Auction Theory
•Auctioneers should make sure that there are enough
bidders
nMore bidders –higher bids
nToo few bidders –opportunities for collusion
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For n bidders with PV
and V~U(0,100):
Practical considerations -# of Bidders

27. Auction Theory
Procurement Auctions
•Typically does not end up with a one-time
transaction (as in many consumer auctions)
nTypically last for a long period
nExample: transportation; automotive parts
•Important characteristics:
nEfficiency (future services)
nRobustness (supplier failure)
nSimplicity and speed (supplier burden)
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28. Auction Theory
Summary
•There are many auction formats
•Under general conditions many yield the same results
•Auction strategy:
nIn English auction –bid your value
nSealed bid first price –require “shaving” (less with more bidders)
nWinner’s curse –requires further “shaving” (more with more
bidders)
•Auctioneer:
nGet the highest number of bidders
nContinue developing suppliers
nKeep the auction process simple

29. Auction Theory
Thank you for listening
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