oligopoly economics by thesign


									          Economic Instruction
    In this section, the Journal of Economic Education publishes articles, notes, and
    communications describing innovations in pedagogy, hardware, materials, and
    methods for treating traditional subject matter. Issues involving the way econom-
    ics is taught are emphasized.

                                                M I C H A E L WAT T S, Section Editor

Oligopoly—An In-Class
Economic Game
J. Patrick Meister

   In teaching principles of economics, I have found that a number of otherwise
high-quality textbooks do not cover oligopoly theory in a modern, yet accessible
way. For instance, the workhorse model for some chapters on oligopoly is the
kinked demand curve, even though it is not really a focal point of any higher-
level presentation of oligopoly theory. Partially to deal with this problem,I decid-
ed to let students have an opportunity to learn about oligopoly in a hands-on
manner. I have them participate in an in-class simulation based on a quantity-
competition oligopoly game (see Carlton and Perloff 1994 for a detailed discus-
sion of quantity-competition oligopoly) in which firms’products are perfect sub-
stitutes.1 (For other oligopoly games, see Joseph 1965, and Hemenway, Moore,
and Whitney 1987.)
   I typically start this game after introducing the topic of oligopoly in class and
showing students some basic game theory. I divide students into industries of five
firms (I discuss later how I handle different sizes of industries), and each person
is the manager of one firm. 2 To give students incentive to maximize profit, each
player earns extra credit on the basis of individual, average profit over the course
of the game. The game has several rounds. Students learn that the attempt to have
the greatest market share can be damaging to profits. Students perform calcula-
tions to see if, during the course of the game, they are producing anywhere near
a one-period, profit-maximizing level of output. This can help them determine if
they are producing too much or too little. Students have reported that such cal-

J. Patrick Meister is a visiting professor of economics at Butler University (e-mail:pmeister@
butler.edu). The author wishes to thank Robert Main, Michael Watts, and three anonymous referees
for their valuable comments.

Fall 1999                                                                                   383
culations help them. Participants are also required to sign an agreement not to
collude in any manner during the game, because successful collusive schemes
reduce mar ket efficiency and unfairly redistribute income toward sellers. Thus,
the government makes such schemes illegal.
   Students have written that they have learned a great deal about what it is like
to compete in a dynamic market in which they have some influence over the out-
come but not absolute control. They have generally found it a stimulating chal-
lenge to attempt to form strategies that will earn them high profits. Some people,
of course, have been frustrated by their inability to control their rivals’ actions,
especially when those actions lower profits for the whole industry, but they gen-
erally realize that this is part of business.


   Oligopoly is a game of quantity competition in which firms’products are per-
fect substitutes. Individuals (firms) simply choose how much output to produce,
and the market price is a negative function of total production in the industry.
Students do not know in advance what the market price will be. They have to
form their choices on the basis of what they predict other firms will do. Many
students learn how to make better predictions as the game progresses.
   The game has a number of rounds. Students hand in their output choices at a
class meeting, I enter the choices on a spreadsheet program I developed, and they
see the outcomes in spreadsheet format at the next class meeting. I allow them to
take the results home to contemplate what they will enter for their output choic-
es the next round (i.e., the class meeting after they see the results of the prior
round). The same players face each other for the entire game; students are not
randomly matched across rounds.3
   Extra credit is awarded on the basis of individual average profit over the course
of the game; the higher the average profit earned by an individual, the more extra
credit points are earned. Therefore, students have an incentive to maximize their
profit because the more extra-credit points they earn, the more likely their letter
grade will improve. I inform the students that I determine the course grade scale
before adding extra-credit points from the Oligopoly game—then I add the extra-
credit points. This prevents the game from having any effect on the grade scale.
   Obtaining the most profit in a given round requires producing the most output
in that round (as long as profits are nonnegative). If participants compete to pro-
duce the most output, however, the price is driven down. This causes profits to
fall, which hurts everyone’s extra credit. This has happened on occasion, but
many students learn that it is better to back off, to decrease production levels, in
such cases. To avoid the undesirable possibility of having a disgruntled partici-
pant place so much output on the market that the price is always zero, each firm
has a capacity constraint, a maximum level of output it can produce each period.
(Unused capacity does not accumulate during the game.) Furthermore, business-
es typically do not have unlimited capacities.
   It would not be usually in the interest of any firm to produce at capacity any-
way because that would, in many cases, drive price and profits very low. Players
384                                       JOURNAL OF ECONOMIC EDUCATION
typically see that their extra credit would then be very low, too. They could sim-
ply increase profit and, therefore, extra credit by producing less. Occasionally, a
student will not learn this. A few students have produced at their capacities every
round and have believed they were doing well because they had the most profit.
However, their profits and, therefore, extra-credit levels were very low. This seri-
ously undermined their chances (as well as their rivals’ chances) to improve their
grades. Alternatively, many students who have produced their capacity to start the
game subsequently reduced their output levels when they found that their profit
levels were very low. Imposing a capacity constraint limits how much punishment
one firm can impose on others by driving price down. If the instructor wishes, the
capacities could be more generous than I allow or be done away with altogether.
   Students do not know how many rounds the game will last. I tell them that I
will determine when the game is over and it will be a surprise. This way, I avoid
having strange behavior simply because the students know that the game is in its
last round. This approximates reality because businesses generally do not know
in advance when the market for their products will dry up. I make sure that
enough class periods are left at the end of the game so that students cannot pre-
dict when the game will end.
   Students know the market demand curve, their own (and everyone else’s) con-
stant marginal cost of production, all firms’ capacity constraints, and how many
firms are in the industry. There are no fixed costs in the game. All of this infor-
mation is common knowledge. Students also know the price of the product in a
given round, their own profit, and profits of each of the other firm’s after entries
are received each round. Because they also know their average profit and there-
fore extra credit, standing at any point in the game. Thus, they can tell if their
earned extra credit is increasing, decreasing, or remaining steady as the game
progresses (Figure 1).

Comments on One-Period Nash Equilibrium

   It may be of interest to note that the one-period simultaneous Nash equilibri-
um of the 5-firm industry has all firms in the industry producing 60 units of out-
put.4 (Nash equilibrium is a situation in which each participant has maximized
profit given what its rivals have done.) This will yield a market price of $50 and
individual profits of $1,800 each. Because average profit for the whole game is
divided by 360 to determine extra-credit, the one-period Nash equilibrium would
yield 5 extra-credit points. (400 points are available in my course from exams,
quizzes, papers, etc.) If this Nash equilibrium were realized each period for the
entire game, students would increase their grades by slightly more than 1 percent.
An example of the spreadsheet return a student (firm 1) would receive after one
round of everyone producing 60 units of output is shown in Table 1.
   In the tables and the following discussion, Rnd represents round number;
q(firm 1) represents the output; Q and P represent market quantity and price,
respectively; π represents profit in that round; AVG Profit represents average
profit (sum of firm 1’s profits divided by the number of rounds completed); and
E.C. represents extra credit (AVG Profit divided by 360).
Fall 1999                                                                       385
                                         FIGURE 1
                           Elements of the Game and Instructions

         The following information comes from the handout students receive:
      You are going to run your own firm in an oligopolistic industry. In your industry,
      you produce a product identical to that of your competitors. Your decision is how
      much to produce during each time period, and total industry production determines
      the market price in a given time period. Thus, your profit will depend not only on
      your own output level, but also on the output levels of your rivals.

      You have the same production technology as your rivals (i.e., the same constant
      marginal cost). You will know your constant marginal cost and the market demand
      curve, but not how much your rivals are going to produce (so you will not know
      the market price in advance). Assuming you are firm i, you have the following
      things to consider:
  Your output:                 qi
  Industry output:             Q = ∑qj          ( N = number of firms)
                                    j =1

  Output of all rivals:        Q–i = ∑ qj
                                         j ≠i

                               P(Q) = max  200 – Q,0  (for 5-firm industries)*
  Market demand:                                     
                                                 2   
  Constant MC:                 c = $20
  Your profit:                 π i = P(Q)qi – cqi
                                 = P(Q)qi – 2 0 i
  Capacity:                     q = 82 (for 5-firm industries)

         I will divide each person’s average profit (sum of an individual firm’s profits
      over the course of the game divided by the number of rounds played) in a given
      industry by 360, and that’s how many extra credit points you will receive! (I will
      set up the game in such a way that the extra credit possibilities are virtually the
      same regardless of which industry you are in.) Extra Credit will be added after the
      grade scale is determined. You will not know in advance when the game ends. (I
      will determine that, but not tell you.) (Note that for the 5-firm industry, if average
      output is 72, P = $20 and profits then would be 0.)
        The students receive the following, noncollusion agreement form to sign:
      AGREEMENT (required for participation in Oligopoly)

      I, ______________________ , promise not to communicate with others in my
      class in any manner about what is happening, has happened, or may happen in this
      oligopoly game. If any such communication is discovered by my instructor, I agree
      to allow him to deduct profit as he deems appropriate.

      Signed: __________________________
      Date: _____________
      *See end note 4 for comments on different industry sizes.

386                                                JOURNAL OF ECONOMIC EDUCATION
                                               TABLE 1
                                          Spreadsheet Example

Rnd#       q(firm 1)        Q         P         π       AVG Profit   E.C.    π=      All profits

1             60           300       50       1800          1800      5     π(1) =     1800
                                                                            π(2) =     1800
                                                                            π(3) =     1800
                                                                            π(4) =     1800
                                                                            π(5) =     1800

Note: For an explanation of column headings,see page 385.

  In my experience, some students earn more than 5 extra-credit points, and
some earn less. Typically, however, most industries (in most rounds) produce
more than the quantity that would result in a one-time Nash equilibrium.

                         CHRONICLE OF A TYPICAL GAME
   To help readers acquire a better understanding of how the game works and
how students often react in certain situations, I chronicle here an actual game in
one of my classes. This game lasted five rounds,although some semesters’ games
have lasted up to seven rounds. This game has some fairly common behavior
   In round 1, total production was Q = 339, which resulted in a price of P = 30.5
(P = 200 − 1/2 Q) (columns 2 and 3 in Table 2). Firm 2 chose to produce
q(firm 2) = 69 (column 1), resulting in profit of π(2) = (P − c) q2 = (30.5 −
20)(69) = 724.50 (reported in columns 4 and 8). (Recall that c equals constant
marginal cost of production that was equal to $20 in this game.) Avg. Profit (col.
5) is (in this case) firm 2’s average profit up to the given round and is obviously
the same in round 1 as firm 2’s round 1 profit. Firm 2’s extra-credit level (col-
umn 6) in round 1 was 2.0125 (calculated by taking firm 2’s Avg. Profit of 724.5
and dividing by 360). Other firms’ individual production levels can be calculat-
ed by looking at individual firms’profit levels (last column) and dividing by P −
c (= 10.5 in round 1) because π = (P − c)qi, where i = firm i. Thus, production
levels for firms 1–5, respectively, were q1 = 60, q2 = 69, q3 = 68, q4 = 67, and q5
= 75. Firm 2 could compute what output level would have maximized its profit
in round 1, given the production levels of the other firms. Of course, this is ex
post analysis, but it can help the participant figure out if his or her output level
was anywhere near to the one-period, profit-maximizing one. For firm 2 in round
1, this is easily shown to be q2 = 45. This would have earned firm 2 profit of π2
= 1,012.50.
   In round 2, most students kept production close to the same as round 1 except
firm 2, which reduced production from 69 to 50 and firm 1, which increased pro-
duction from 60 to 68 (Table 2). Total production was Q = 328, which yielded a
price of P = 36. Perhaps firm 2 calculated that producing 69 was too much to
maximize profit in round 1 (i.e., q2 = 45). All firms experienced higher profits in
round 2 than in round 1, and firm 2’s profit was π(2) = 800. Averaging firm 2’s

Fall 1999                                                                                   387
                                            TABLE 2
                           Results of Rounds 1–5 of the Oligopoly Game

q(firm 2)     Q              P             π        AVG Profit    E.C.     π=      All profits

                                                 Round 1
69           339           30.5          724.5         724.5     2.0125   π(1) =     630
                                                                          π(2) =     724.5
                                                                          π(3) =     714
                                                                          π(4) =     703.5
                                                                          π(5) =     787.5

                                                 Round 2
50           328            36            800          762.25    2.1174   π(1) =    1088
                                                                          π(2) =     800
                                                                          π(3) =    1104
                                                                          π(4) =    1056
                                                                          π(5) =    1200

                                                 Round 3
71           351           24.5          319.5      614.666667   1.7074   π(1) =     306
                                                                          π(2) =     319.5
                                                                          π(3) =     310.5
                                                                          π(4) =     306
                                                                          π(5) =     337.7

                                                 Round 4
60           323           38.5          1110           738.5    2.0514   π(1) =    1258
                                                                          π(2) =    1110
                                                                          π(3) =    1276.5
                                                                          π(4) =    1128.5
                                                                          π(5) =    1202.5

                                                 Round 5
57           312            44           1368           864.4    2.4011   π(1) =    1704
                                                                          π(2) =    1368
                                                                          π(3) =    1392
                                                                          π(4) =    1464
                                                                          π(5) =    1560

Note: For an explanation of column headings,see page 385.

profit levels from rounds 1 and 2 (724.50 and 800, respectively) gives firm 2 an
Average Profit of 762.25. Dividing this by 360 yields firm 2’s extra credit stand-
ing of E.C. 2.117 (rounded). Calculating individual firm production levels (as we
did for round 1) yields q1 = 68, q2 = 50, q3 = 69, q4 = 68, and q5 = 75.
   In round 3, all but firm 2 kept their production levels the same or within 2 units
of their round-2 levels (Table 2). Firm 2 increased its output from 50 to 71 (a
drastic increase). Perhaps this player was dissatisfied at having the lowest profit
in round 2. Mostly because of the increased output of firm 2, total industry out-
put increased to Q = 351 (from 328), which yielded a price of P = 24.5. All the
388                                                    JOURNAL OF ECONOMIC EDUCATION
firms’ profits dropped noticeably (firm 2’s from 800 to 319.50), as did each
firm’s average profit. Therefore, each firm’s extra-credit standings fell (firm 2’s
from 2.117 to 1.707, rounded). Production levels for firms 1–5, respectively,
were q1 = 68 (no change from round 2), q2 = 50 (increase of 21 from round 2),
q3 = 69 (no change from round 2), q4 = 68 (increase of 2 from round 2), and q5
= 75 (no change from round 2).
   In round 4, industry output declined to Q = 323 (from 351), the lowest output
yet (Table 2). Consequently, the market price hit an all-time high of P = 38.5. Firm
2 decreased production from 71 to 60, and thereby earned profit of 1,110 (notice-
ably higher than the profit of 319.50). Firm 2’s Average Profit climbed to 864.4,
and thus, its extra credit standing climbed to 2.051 (rounded) (from 1.707). Output
levels of firms 1–5, respectively, were q1 = 68 (no change from round 3), q2 = 60
(decrease of 11 from round 3), q3 = 69 (no change from round 3), q4 = 61 (decrease
of 7 from round 3), and q5 = 65 (decrease of 3 from round 3). Apparently, these
firms,especially firm 2, learned that putting large quantities on the market to obtain
higher profit than one’s rivals can actually decrease profit; it is better to decrease
production somewhat to increase the price and, in this case, profit. Perhaps firms 1
and 3 did not change output because they suspected other firms would decrease
output and cause an increase in price. By keeping their production levels constant,
perhaps they were trying to take advantage of an increase in price.
   In round 5, firm 2 produced a bit less than in round 4, 57 instead of 60 (Table
2). Total industry production declined slightly to Q = 312, from 323 in round 4,
making the price the highest of the game at 44. Output levels for firms 1–5 were,
respectively, q1 = 71 (an increase of 3 from round 3), q2 = 57, q3 = 58 (a decrease
of 11 from round 3), q4 = 61 (no change), and q5 = 65 (no change). Apparently,
firms 2 and 3 noticed that decreasing output further would still increase profit.
This is primarily why the price increased.
   In summary, we can see that when profit levels become low, students learn that
putting less on the market can be beneficial. Some decide that as long as others
do this, they will keep their output levels relatively high. Of course, sometimes,
such players seem to keep their output levels too high—lowering output could
increase their profits even more. Perhaps such players think that earning the high-
est profit in the industry means they are doing well, even if their profits are low.


   The basic game can be extended in three ways to help students understand other
aspects of oligopolistic industries. First, the instructor could allow collusion among
firms to illustrate how successful collusive schemes unfairly redistribute income
from buyers to sellers through artificially restrained output levels that cause the
market price to increase. Also, the instructor could use such an exercise to illustrate
the temptation to cheat on such collusive arrangements placing more output on the
market than the collusive arrangement calls for to take advantage of the artificially
higher price. No doubt, at least some students would perceive this incentive, and
some might well act on it. After the game is over, the instructor could discuss with
the students whether they had noticed this incentive and if anyone had acted on it.
Fall 1999                                                                          389
   Second, the instructor could use the game to illustrate the effect of industry
size on market price and firms’ profits by simply specifying identical market
demand curves and constant marginal costs across industries, but having differ-
ent-sized industries (e.g., two firms, three firms). What is expected, of course, is
that two-firm industries, for example, will generally have higher market prices
(on average) than five- or six-firm industries.
   Third, the instructor could run an experiment in which participants know
which round is the last one. The results could be compared to those cases in
which students did not know the terminal round. Then differences in the two
cases could be observed and evaluated by the instructor and/or the students.

                                 CLOSING COMMENTS

   My students write a short paper about their oligopoly experience after the
game is over, describing how they formed their strategies and what strategies
they thought their rivals had employed. Students have been enthusiastic about
their experiences. They often figure out detailed methods of attempting to maxi-
mize profit and indicate that they think very carefully about what their rivals have
done and will do. Many write that they have a much clearer picture of what it is
like to participate in a market as a producer. Also, some students become frus-
trated when other industry participants produce so much that all firms’profits are
kept low.
   It is intriguing to watch the various industries throughout the game. Players
never approach the fully collusive outcome (i.e.,the joint-profit maximum). Even
if some students in an industry produce very little, at least one other will take
advantage of it by placing high output levels on the market. Further, when all
industry participants produce large output levels so that all profits are low, I often
do not see much response from participants until profits become either negative
in a round or nearly zero.
   I find this game of great value for helping students learn some principles of
oligopoly theory. They have the opportunity to do calculations to attempt to max-
imize profit, to make predictions concerning rival behavior to evaluate those pre-
dictions, to form strategies, and to evaluate their rivals’strategies.


1. Perfect substitutes means that the goods are identical in the eyes of buyers. Therefore, all firms
   will char ge the same price. Perfect substitutes in quantity competition also means that market
   price is a function of market quantity.
2. My classes typically are between 24 and 30 students. This game could work for larger classes if
   the instructor either uses more industries (see note 4),pairs students up to run a firm,or has teach-
   ing assistants run the game in smaller discussion sections.
3. Students may be able to tell who their rivals are when I hand back data from each round. How-
   ever, I have not noticed any suspicious reductions in quantities to increase the market price.
4. For the setup in this game, and with the slope of the inverse demand curve being negative 1/2 and
   the constant marginal cost being $20, it is relatively straightforward to show that one-period
   Cournot-Nash equilibrium profits would remain at $1,800 as long as each time the industry has
   one more firm,the P intercept of the demand curve increases by 30. If we have a 6-firm industry,
   using an inverse demand curve of P = 230 − 1/2 Q would keep one-period Cournot-Nash equi-

390                                                 JOURNAL OF ECONOMIC EDUCATION
   librium profits at $1,800. Thus,I use P = 230 −1/2 Q as the market demand curve whenever I have
   a six-firm industry.

Carlton, D. W.,and J. M. Perloff. 1994. Modern industrial organization. 2nd ed. New York: Harper-
Hemenway, D., R. Moore, and J. Whitney. 1987. The oligopoly game. Economic Inquiry 25 (Octo-
  ber): 727–30.
Joseph, M. 1965. Role playing in teaching economics. American Economic Review Proceedings 55
  (May): 556–65.

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