978-1118808948 Chapter 17 Lecture Note Part 1

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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

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

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