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CHAPTER SEVENTEEN
AUCTIONS AND
COMPETITIVE BIDDING
OBJECTIVES
1. To demonstrate the potential advantages of auctions compared to posted
prices, on the one hand, and to unconstrained negotiation, on the other,
and to show how auctions can enhance revenue.
2. To analyze bidder strategies under various auction mechanisms including
English auctions, Dutch auctions and sealed-bid auctions.
3. To examine the phenomenon of the winner’s curse and how it affects the
bidding process.
4. To analyze the auction process from the auctioning party’s perspective
and to determine which types of auctions produce the best terms for the
auctioning party.
5. To discuss competitive procurements.
TEACHING SUGGESTIONS
I. Introduction and Motivation
A. Guinea Pig Question
Bidding for an Item of Unknown Value. Tell the class that you will
conduct a sealed-bid auction for a valuable item. The high bidder will pay
his bid and win the item. The item is a jar of pennies. Actually it’s easier
to
fill a glass pickle jar with colored plastic Christmas ornaments (little
pinwheels about penny size) to spare the bother of dealing with pennies.
Fill the jar with a predetermined number of trinkets. (For instance, set the
number at 463 by using two packs of 250 trinkets minus 17.) Tell the
class that the winning bidder will receive the value of the jar where each
trinket is redeemable for a penny. Thus, though the students don’t know it
the jar is worth $4.63. A buyer with a winning bid of $3.50 would make a
profit of $1.13. If the winning bid were $6.00, the “winner” would lose
$1.37.
Ask each student to write down 4 items: 1) an estimate of the value of
the jar (i.e. the number of trinkets translated into dollars); 2) a sealed bid
for the jar; and 3) upper and lower bounds constructed to form a 90%
confidence interval around the true value. (Remind students what a
confidence interval is.)
B. Guinea Pig Question, Discussed
Bidding for an Item of Unknown Value. This example introduces
complications posed by uncertainty. Each bidder is uncertain about the
value of the jar and also about the level of competitors’ bids. Before
revealing the true value of the jar, ask a number of students to reveal their
estimates. Students will be surprised by the wide dispersion of estimates.
Ask the class what the distribution might look like if it were plotted. A
number of students are sure to suggest a bell-shaped normal curve. By
shows of hands, find roughly the median of the class estimates and sketch
a normal curve with this mean. Then ask students how they bid. Compare
bids to estimates to emphasize the logic of placing bids below estimates.
Note that the optimal degree of shading involves a tradeoff between the
chance of winning and the profit from winning. (Finding an optimal
solution is a complex problem.) Superimpose the bid distribution next to
the estimate distribution. Your graph should resemble Figure 17.2.
Now is the time to suggest the possibility of the winner’s curse by
raising two hypotheses. First, suppose estimates are unbiased, i.e.
centered around the true value of the item. (This seems reasonable.)
Second, suppose that the estimates and bids are quite disperse. (Also
reasonable.) These two points imply that the highest bids (the shaded tail
in Figure 17.2) are above the true value of the item. On average, the
winning bidder loses money on the acquisition. At this point, you may ask
some of the high bidders in the class, whether this argument worries them.
(Do they still want to play for real or only for fun?) Find the highest bid.
Then, reveal the value of the item. With 20 or more students in the class,
nine times out of ten, the winning bidder will fall prey to the winner’s
curse, i.e. pay more than the item’s value. The only exceptions occur if
the class estimates are biased well below the true number of trinkets. (To
avoid this problem, try the trinkets in different shaped jars, and see that
the jar is 75% or more full.)
Having made the main point, you can raise some other questions.
What factors increase the likelihood and magnitude of the winner’s curse?
As discussed in the text, the winner’s curse increases with the degree of
uncertainty and the number of bidders. Does the winner’s curse happen in
real life? Yes, bidding for off-shore oil leases, competitive tender-offers,
and free-agent bidding for athletes are just three examples. How well did
you (the student) gauge your degree of uncertainty? Most individuals are
overconfident of their estimation abilities. Ask students if the true estimate
fell between their lower and upper bounds. Typically, less than half the
students answer in the affirmative by a show of hands. By construction,
the intervals should bracket the true value 90 percent of the time.
Students are surprised that their knowledge is so uncertain.
II. Teaching the “Nuts and Bolts”
This optional chapter contains a good deal of advanced material.
Accordingly, the instructor has a number of decisions concerning teaching
strategy.
A. In our view, the most important points include:
1. Optimal sealed-bids against a BCB distribution;
2. The winner’s curse;
3. The benefits of auctions.
B. A number of advanced topics can be omitted without loss of continuity:
1. Equilibrium bidding strategies; and
2. Revenue Equivalence
Teaching Hint: The formulas and intuition for equilibrium bidding strategies
in the uniform case are greatly simplified if the lower bound is taken to be
zero, L = 0. For instance, suppose values are uniformly distributed between
0 and 100. It follows that:
E(vmax) = [n/(n+1)]100, E(v2nd) = [(n-1)/(n+1)]100, bi = [(n-1)/n]vi
E(bmax) = [(n-1)/n]E(vmax) = [(n-1)/n][n/(n+1)]100 = [(n-1)/(n+1)]100.
This is a direct confirmation of revenue equivalence:
E(bmax) = E(v2nd).
\
C. Recommended Problems
Problems 3, 4, 5, 6, 7, 8, and 11.
D. Exercise: Bidding for Film Exhibition Rights
In this exercise, student teams representing movie chains bid for the
right to show actual feature films. (The accompanying student information
sheets provide full details.) For instance, suppose a student team wins the
right to show a blockbuster film for a four-week run by placing a high bid of
$6,000 per week. If the actual gross revenues for the run turn out to be
$10,000, $8,000, $5,000, and $4,000, its overall profit would be 27,000 -
24,000 = $3,000.
The great virtue of this exercise is that bidding is for real films and
profits are based on actual theater revenues (as reported each week online at
Variety.com). To conduct the exercise, the instructor should carry out the
following steps. (The illustration is for a class of 25 students. Larger classes
would mean more teams and more films up for bid.)
1. Divide the class into 5 teams.
2. Select 8 films that are about to open nationwide. Consult Variety.com
or other entertainment websites or publications for about-to-open or
recently opened films.
3. Have teams bid for these films in class. Use the conventional English
auction (higher and higher bids) for the first 5 films. Use sealed bid
auctions for the final 3 films. (No team can acquire more than two
films. Some teams will acquire one or no films.)
4. For each of the next four weeks, look up the revenue for each film in
Variety.com or other websites. To compute weekly revenue per theater,
divide the total “Gross” by the number of screens. Report the teams’
cumulative profits. Students usually take a strong interest in how they
are doing.
Optional tasks:
5. Update the information on page 3 of the handout. (That information is
drawn from Summer 2012.)
6. Provide movie reviews or other information on the films up for bid.
Remarks.
1. Based on past history, an average top-25 film in weeks 1 to 4 of release
can expect to earn typical weekly grosses of $6,000, $4,500, $3,000, and
$2,000. A block-buster could earn grosses twice as large, a box-office
bust grosses half as large. Weekly revenues also depend on the time of
year (see the chart on page 3 of the handout) and the breadth of the
release. Frequently, “art” films or foreign films have a narrow release
(less than 100 theaters nationwide) and can earn $10,000 or more per
theater. (To get some benchmarks for potential film values, the astute
student should compute gross revenues per screen for the films reported
on page 3 of the handout. To arrive at a final value estimate for a
particular film up for bid, the student can then adjust these benchmarks
based on any of a variety of subjective factors.
2. The winner’s curse is definitely present in this exercise. Dreaming of
blockbusters (and forgetting that weekly revenues decline as weeks go
by) leads many student teams to overbid for films. (Remember, each
team submits a fixed bid to apply for all 4 weeks, even though weekly
revenues typically fall over time.) Though there is a wide variance, the
typical team makes a zero profit on average. (This is worse than if a
team were to win no films, in which case its total profit for the 4 weeks
would be $4,000; see page 2 of the handout.) Some 40% of all teams end
up making losses. Earning a final profit of $10,000 or more is a strong
performance accomplished by only about one team in four.
Bidding for Film Exhibition Rights
Many of the motion pictures released by major film companies are
distributed via blind bidding. Theater owners bid for the exhibition rights to
a film without having seen it (often in advance of the film’s completion).
The merits of this practice are hotly disputed by theater owners and
distributors alike. Theater owners contend that under the system they
frequently overpay for movies that are flops and that they shoulder a
disproportionate share of the risk inherent in film rentals. For their part,
movie companies insist that blind bidding is necessary. Big budget
blockbusters will be produced, they insist, only if solid play dates in prime
time (summer, Christmas, and Easter) can be assured. Advertising
campaigns (especially television) must be planned as much as a year in
advance. They add that theater owners should bear some share of film risk.
About 25 states have passed laws banning blind bidding. Exhibitors
in these states bid for films after regional screenings -- a process which
delays film openings two to three weeks behind states that do not prohibit
blind bidding.
The Bidding Competition
Members of the class will be divided into teams and bid to obtain the
exhibition rights to a number of films. Each team represents a theater chain
seeking to acquire the rights for up to two films. The major film companies
that distribute the films have specified a “standard” contract with the
following provisions:
1. The film will be shown for a minimum play period of four weeks.
This period begins following the film’s nationwide release date.
2. The EXHIBITOR will guarantee the DISTRIBUTOR a weekly
payment of $ _______.
Bidding
In all, 8 films are up for bid. The first five films (A-E) will be sold in
order by English auction. The last three films (F-H) will be sold by
successive sealed bid auction.
If a chain fails to acquire a film to play in its theaters, its fall-back
option is to play a previously released film (in which case it earns $500 a
week in net revenues).
Calculation of Payoffs
A chain’s return from film exhibitions is calculated according to its
average gross revenue per theater during the four week run. For example, if
a particular film were playing in five theaters and earned a total revenue of
$24,000 in a given week, then the average gross revenue per theater is
$4,800. Therefore, the chain receives net revenue equal to $4,800 minus its
bid. (For example, if its bid were $3,200, the chain’s net revenue on the film
would be $1,600.) Each chain seeks to maximize its total net revenues over
the four-week movie run. At the end of the competition, your team’s total
net revenue payoff will be converted into a grade equivalent.
Pre-Bid Information
Prior to bidding, each team should review its packet of materials.
These describe the films up for bid (including reviews by critics) and
provide historical statistics on film rentals. In class, your team will bid for
the films. At that time, you should indicate on the data sheet your best
estimate of each film’s weekly gross revenues and your bid (if any) for the
film. Describe briefly the method (if any) used to arrive at your estimates
and bids.
Box Office Gross Revenues
Selected Summer Films 2012
Spiderman 4 (7/6) Ice Age (7/13) Bourne Legacy (8/10) That's My Boy (6/15)
Wk Revenue Screens Revenue Screens Revenue Screens Revenue Screens
1 90.8 4318 61.4 3881 52.6 3745 20.3 3030
2 51.8 4318 33.1 3886 23.6 3753 11.9 3030
3 17.5 3753 21.9 3869 12.8 3654 3.3 822
4 11.1 3160 13.9 3452 10.66 3131 0.94 400
5 7.0 2425 9.87 2847 5.28 2766 0.31 172
6 3.33 1395 4.6 2274 3.9 2170 0.072 84
7 1.2 542 2.6 1211 2.1 1431
Closed
8 0.736 368 2.0 1036 Still Playing
9 1.4 501 1.0 763 Ruby Sparks (7/27)
10 0.57 416 0.7 541 Revenue Screens
11 0.36 328 0.7 420 0.203 13
12 0.25 253 Still Playing 0.555 64
Still Playing 0.700 252
0.45 182
0.238 119
0.138 78
0.076 76
0.064 70
Closed
Top Grossing Films
Week of 9/21 - 9/27
Weeks in
Ran
k
Film Title
. Release
Revenu
e Screens
1End of Watch 1 18.2 2730
2Trouble w/ the Curve 1 16.2 3212
5Resident Evil 2 8.9 3016
10 Bourne Legacy 7 2.1 1431
15 The Campaign 7 1.6 1250
20 Last Ounce of Courage 2 0.84 1064
30 Perks of Being Wallflower 1 0.32 4
40 Step Up Revolution 9 0.174 182
50 To Rome w/ Love 14 0.083 50
Revenue = Gross Box Office Revenues in $ millions
