AUCTIONS
By: Jessica Wisler
“The foundation of trade is mutual gain, people make exchanges because they expect them to
improve their well-being, although sometimes one of the counter parties is later disappointed
(Koch, P.99).”
An auction entails a potential buyer competing for the right to own a good, service or anything
of value . The auctioneer is either seeking bids to sell a service/item to a purchaser for its
highest price or is seeking bids to purchase a service/item from a supplier for its lowest price.
Either way an auctioneer will benefit from having many bidders as competition leads to better
terms for the auctioneer. Companies can act as either the bidder or the auctioneer for goods or
services they want to purchase or sell. Thus it is important for managers to understand auction
models, bidding strategies and revenue expectancies to make optimal selling and purchasing
decisions for their company (Baye, p. 456).
TYPES
Types of auctions differ by the timing of the bid (whether it is sequential or simultaneous) and
the amount the bidder is required to pay. There are four main types of auctions: English
(ascending bid) auctions; First-price, sealed bid auctions; Second-price, sealed bid auctions; and
Dutch (descending bid) auctions.
The English (ascending bid) auction is the most common type of auction. In an English auction a
single item is being sold to a highest bidder. The auction begins with an opening bid then the
auctioneer will ask if anyone is willing to pay a higher price. The auctioneer will take higher
prices (bids) in sequentially until no one is willing to pay a higher price. The purchasing price is
the price at which the last competitor drops out (Baye, P. 457). The English auction is the only
auction type that the bidder has knowledge of bids made by others. An example of an English
auction can be watched on BBC America’s Cash in the Attic. The television show works with
families who want to raise money for a specific project. The show's experts help them go
through their possessions, looking for potential items of value. Anything that is found then goes
to auction (BBC America-Cash in the Attic).
In a first-price, sealed bid auction the highest bidder wins the item just as in an English auction
but all bids are simultaneously written down and handed to the auctioneer. The auctioneer
awards the item to the person with the highest bid and no one knows one another’s bids (Baye,
P. 457). The bidder pays what s/he bid for the item. Fish auctions use first-price, sealed bid
auctions (McConnell, 2000).
Second-price, sealed bid auctions also consist of bidders simultaneously submitting bids,
without the knowledge of the other bidders, to the auctioneer and the highest bidder wins. The
difference from the first-price sealed bid auction is that the winning bidder only has to pay the
second largest-bid. eBay’s proxy bidding system is mimics a second-priced auction. The system
permits a bidder to submit their maximum price “reservation price.” This amount is kept secret
by the system which automatically updates the bid using the smallest increment possible above
the previous bid until the previous bid is higher then the reservation price. The winner pays the
price of the second highest bid plus the bidding increment (Baye, P. 458).
A Dutch (descending bid) auction is where the seller sets a very high price for an item (higher
than it is believed anyone will pay) and the auctioneer starts at this price then sequentially
lowers the price until a bidder is willing to pay the last price announced. In a Dutch auction
bidders do not know the bids of the other players and the bidder pays what s/he bid for the
item (Baye, 458). This type of auction is convenient when it is important to auction goods
quickly, since a sale never requires more than one bid. An example is the Dutch Flower Auction
which is where the auction type received its’ name. First-price, sealed bid auctions and Dutch
auctions are identical in terms of optimal bidding behavior and profits earned by the auctioneer
(Baye, 457).
VALUATIONS
Merriam-Webster defines Valuation as “the act or process of valuing; specifically: appraisal of
property” as well as “the estimated or determined market value of a thing” (Merriam-Webster
Online). What information is available to bidders for their valuation of an item in an auction is
known as the information structure.
When all bidders know for certain the worth, valuation, of an item the information structure is
called perfect information (see table 1 for example). Perfect information is rare in that there are
very few items that have a true consensus of their worth both in the intrinsic value of the item
and the additional value one may put on the item due to personal taste.
More common is an estimation of worth by bidders to determine their valuation of the item.
When each bidder’s valuation of the item being auctioned off is not known by themselves
and/or other bidders, asymmetric information within an auction occurs. When personal taste
exists as part of the valuation this is known as private value. When personal taste is not
dependent on the valuations of other bidders this is known as independent private value (Baye,
P.459).
A correlated (affiliated) value estimate is where a bidder does not know their own or others
valuation of an item. They must estimate the value for the item through research. This estimate
of worth is also correlated with other bidder’s valuations. If one bidder has a high value
estimate, then others bidders are more likely to have high value estimates.
When a correlated value estimate exists with no personal/individual taste involved then a
special case arises called a common-value auction. Again, all bidders will have different
estimates based on their research and tests (Baye, P.460).
Table 1, below, provides the information structures discussed above and examples of items that
lend themselves to these information structures.
Table 1: INFORMATION STRUCTURES
Information
Structures
Defined
Perfect Information
Private Value*
Exact worth of item is
known by all bidders
Personal taste is part of the
bidder's valuation of an item
Independent Private
Value*
Bidder's valuation is
dependent on personal
taste known only to the
bidder and not other
bidder's valuations
Correlated (affiliated)
Value* Estimate
Bidder does not know their
own or others' valuation of
an item
Common Value*
Special case of correlated
value estimates; no
personal taste is added to
the valuation; true worth
exists but not known to
bidders
Example
current $10 bill
a collectible (antique
furniture)
Valuation of art at $200
because it matches the
bidder's home décor vs. Art
Reseller’s valuation at $75
based on the quality and
resale value of the art piece.
Real Estate (must research
the local market & estimates
of worth vary based on
research done)
Oil Deposits (finite amount in
ground & estimates of how
much oil vary depending on
research done)
* Asymmetric information exists within the auction.
AUCTION THEORY
Auctions, in general, may be viewed as games with incomplete information (Harsanyi, 1967).
Thus one can apply game theory to assess auction bidding strategies and revenue. Within game
theory is the Nash Equilibrium. A Nash equilibrium, defined by Baye, is, “ A condition describing
a set of strategies in which no player can improve her payoff by unilaterally changing her own
strategy given the other players’ strategies (P.357).” All auctions have a Nash equilibrium, a bid
that perfectly balances the risk of losing to a higher bidder where no profit is made against the
possibility of greater profits where the lower the bid, the greater the profit (Holt, 2004). The
following describes the appropriate bidding strategy to obtain the highest expected profit for
risk neutral bidders which are bidders that are indifferent between a risky prospect and a sure
thing as well as revenue expectancies for both risk neutral and risk-averse bidders.
BIDDING STRATEGIES for NEUTRAL BIDDERS:
An English auction bidder with Independent private values should continue bidding until the
price exceeds their valuation of the item. If the player were to drop out with a bid lower than
their valuations, they lose the chance of winning at the value they placed on the item. If they
continue bidding higher than their valuations, they pay higher than they already valued the
item.
A second-price, sealed bid auction bidder with independent private values has an incentive to
bid exactly their own valuation of the item since they pay the second-highest bid and not their
own. If the player were to bid lower than their valuations, they reduce the chance of winning. If
they were to bid higher than their valuations, they increase their chance of winning but only in
so much that they pay higher than they already valued the item. So the dominant strategy is to
bid their valuations.
A first-priced, sealed or Dutch auction bidder does not know the valuations of their fellow
bidders. Since the highest bid wins the bidder wants to lower their valuation down to avoid
having a substantially higher bid then the rest of the bidders. This is known as Bid Shading. The
profit earned by doing this offsets the reduced chance in winning. The more bidders there are
in the auction the more competition their will be and the closer the bid needs to be to the
bidder’s valuation. The following formula uses the bidder’s own valuation (v), the total number
of bidders (n), and the assumption that bids have an evenly distributed range between the
lowest (L) and the highest to compute the player’s optimal bid (b).
b v
vL
n
A correlated values auction bidder has the most complex information structure in that they do
not know their valuation or the other bidders’ valuations of the item. In this case the lack of
information on the valuation of the item lends towards a higher tendency to over bid and in the
case of English Auctions and correlated values the bidder must adjust their valuations as others
bid to put forth an optimal bid.
The common values auction exacerbates the tendency to over bid in that the winner is the one
who has the highest estimate of the true worth of the item (i.e., oil) while all other estimates
are lower. Logic follows that the true value is problem an average of all the estimates and not
the highest estimate. This is known as the winner’s curse. The winner’s curse is most
pronounced in sealed bid auctions because no information can be gathered on the estimates of
other bidders.
Table 2: BIDDING STRATEGY
Auction type
Information Structure
Bidding Strategy
English
Independent Private Values
continue bidding until the price
exceeds your valuation of the
item
Second-price
Independent Private Values
bid your valuation of the item
Firstprice/Dutch
Independent Private Values
b v
vL
n
English
Affiliated Value Estimates
Sealed Bids
Affiliated Value Estimates
adjust estimate of valuation on
other bidders' estimates;
continue bidding until the price
exceeds your valuation of the
item
revise downward your private
estimate
REVENUE:
One of the major findings of Auction Theory is the Revenue Equivalence Theorem, which states
that the auctioneer’s expected revenues are the same for all four auction types. All
independent private value auctions’ bidders already know their independent private valuations
and learn nothing more about the worth of the item from the auction. Thus the revenues are
equal. English and second-price auctions each result in the bidder paying the second highest
valuation and the first-price and Dutch auctions encourage bid shading by all in which the net
effect is an overall equal reduction in valuation. Thus the highest bid after Bid Shading is the
equivalent of the second highest valuation. This is illustrated below in Table 3.
Due to the asymmetric information of correlated values revenue equivalency does not hold
and bidders shrink their bids based only on their private value estimates to avoid the Winner’s
Curse. In English auctions bidders gain the post information of other bidder’s value estimates
and can adjust their values acccordingly. This gives them more confidence in their estimates
and they shrink their bids less. In First-price and Dutch auctions bidders learn nothing of each
others estimates and thus shrink their bids accordingly (greater than the English auction). In the
second-price auction bidders know they will only have to pay the second highest bid thus they
do not shade their bid as much as in the English auction. The results are illustrated in the
affiliated value estimate row in table 3.
Table 3: EXPECTED REVENUES (Risk-Neutral bidders)
Information Structure
Expected Revenues
Independent Private Values
English = Second-price = First-Price = Dutch
Affiliated Value Estimates
English > Second-price > First-Price = Dutch
(Baye, P. 465)
Risk-averse bidders are those that prefer a sure amount of profit to a risky prospect with a
greater expected value. Surprisingly risk aversion players bid more aggressively in first-price
auctions with independent private values because they are less willing to accept the risk of
being outbid by shading down their bids so they shrink their bids by less. Lastly, the affiliated
value estimates for these bidders’ results is more aggressive bidding for English auctions as
well. The English auction provides bidder information which lessens the Winner’s curse thus
making the risk-averse bidder more confident in not Bid Shading. Thus the English auction
always results in greater revenue than second-price and maybe even first- price. The results are
below in table 4.
Table 4: EXPECTED REVENUES (Risk-Averse bidders)
Information
Auction
Structure
type
Expected Revenues
Independent
Private Values
Independent
Private Values
Independent
Private Values
Affiliated Value
Estimates
English
Secondprice
Firstprice
English = Second-price = First-Price = Dutch
ALL
English > Second-price < First-Price = Dutch
>
English = Second-price = First-Price = Dutch
First-Price = Dutch > Second-price = English
MARKET-BASED MANAGEMENT APPLIED
Koch Industries follows a Market-Based Management (MBM) approach. Within this approach
are five dimensions with the first dimension described as the vision. The vision is “Determining
where and how the organization can create the greatest long term value (Koch, P.26).”
Throughout Koch’s book, “Science of Success”, Koch addresses the importance of value driving
profit. Subjective value is discussed in the sense that value is subjective and not directly
measurable. The only way to properly measure value is through the actions of the market (the
purchasers). Understanding what drives value and the need for value creation aids Koch
Industries in maintaining their competitive advantage.
Furthermore, because Koch is a leader in natural resource-based products Koch must properly
assess the correct bidding strategy for their natural resources. They must understand that if
they are attempting to procure a natural resource from the government they will be dealing in
a common value (correlated) auction and will need to engage in Bid Shading to avoid the
Winner’s curse and to get the natural resources at a price for which they can still create true
value and profits. As Koch puts it, “An effective business vision begins and ends with value
creation (P. 55).”
QUESTIONS
Question 1: When the Government auctions off oil rights bidders are using an information
structure of…
a) perfect information
b) independent private value
c) correlated value estimates
d) both a and b
Question 2: You’re participating in an auction where all the 10 bidders have independent private
values of 5, 7, 9, 11, 12, 12, 17, 19, 21 and 23. Your own valuation is 12. Determine your own
optimal bidding strategy in a first price, sealed bid auction.
a) $11.30
b) $12
c) $12.78
d) $12.16
Question 3: Koch,” seeking the highest valued alternative for every resource,” wants to auction
off one of his asphalt plants. The bidders are risk neutral and have affiliated value estimates.
What auction type will maximize his revenue from the sale?
a) All four auction types will lead to equal revenue
b) First-Price
c) English
d) Both b and c
Question 4: A bid that perfectly balances the risk of losing to a higher bidder where no profit is
made against the possibility of greater profits (where the lower the bid, the greater the profit)
is…
a) not possible
b) an audit’s Nash Equilibrium
c) an example of perfect information
d) the result of subjective value
Question 5: Auctions can be viewed in terms of games with incomplete information.
a) True
b) False
ANSWERS
Answer 1: c; Answer 2: a; Answer 3: c; Answer 4: a; Answer 5: b
REFERENCE:
Baye, Michael. R. (2009). Managerial Economics and Business Strategy, 6th Edition. St. Louis:
McGraw-Hill Irwin.
“Cash in the Attic.” BBC America . 2009. Worldwide Americas Inc. 26 Apr. 2009
<http://www.bbcamerica.com/content/74/index.jsp>.
Engelbrecht-Wiggans, Richard (Feb., 1980). Auctions and Bidding Models: A Survey.
Management Science, Vol. 26, No. 2, pp. 119-142.
Harsanyi, J. C. (1967). "Games with Incomplete Information Played by 'Bayesian' Players, Part I.
The Basic Model, Management Sci.
Holt , Charles A. &, A.E. Roth (2004): The Nash equilibrium - A perspective. PNAS vol 101, no12
p. 3999-4002.
Koch, C.G. (2007). The science of success: How market-based management built the world's
largest private company. John Wiley & Sons, Inc.
McConnell, Kenneth E. & Strand, Ivar E. (Feb., 2000). Hedonic Prices for Fish: Tuna Prices in
Hawaii . American Journal of Agricultural Economics, Vol. 82, No. 1 (pp. 133-144).
“Merriam-Webster Online” (2009). Merriam Webster Inc. 26 Apr. 2009. <http://www.merriamwebster.com/dictionary/valuation>