Imperfect
Competition and Game Theory
Imperfect Competition and Game Theory
Product Differentiation
The Effect of Advertising on Consumer Choice
Robert M. Kenney, Miami‑Dade Community College
To help my students understand how consumer choice is influenced by television advertising, I ask them to name the worst commercial they remember. As each student answers, he almost invariably names the product being advertised. If he doesn't, I ask what it is. Without exception he is able to do so. When the last student has answered I point out that even though I asked for the worst commercial, each student responding was able to recall the product which, after all, was the purpose of the advertisement.
Visual Aids for Industrial Organization
Josef M. Broder,
Economics instructors often get more excited by industrial organization than many of their students. Graphical and mathematical descriptions of monopolies, oligopolies, etc., are challenging but tend to overwhelm beginning students. To supplement textbook presentations of industrial organization, I bring to class visual aids or actual commodities produced by firms in a given industry.
For
competitive firms I use samples of undifferentiated corn from several corn
producers. For the monopolistically competitive local fast food market I use
the Burger King Whopper and McDonald's McDLT. Oligopolies can be illustrated by
samples of Coke and Pepsi; packages of Lipton, Luzianne, and Tetley teas; or
boxes of 35mm film from Kodak and
These consumer products can readily be used to explore questions of structure, behavior, and performance in various industries. Specific pricing strategies of monopolists can be illustrated by identical bottles of Heinz ketchup, one originating from the local grocer, the other used in a local restaurant. A comparison of prices for identical products sold by full‑service grocers to those sold in convenience stores is also a valuable teaching aid. A visual inspection of the colorful, cleverly designed, and extensively researched packages of differentiated products give the students a better understanding of oligopolistic behavior. With time, the instructor may be able to structure his/her entire lectures around particular consumer products.
Product Differentiation and Consumer Illusions
James Angresano, Hampden‑Sydney College
When introducing monopolistic competition to my principles students, I seek to impress upon them that the main characteristic of this industry structure is that consumers perceive that products are different. That is, many products may be differentiated in the minds of consumers where no substantive differences exist.
I begin by asking who can discern differences between Coca Cola and Pepsi Cola. At least 10 students quickly raise their hands. I then ask five of them to come to the front of the room. I place 10 glasses on a table, each of which contains some cola. I place an empty Coke and an empty Pepsi bottle on the table and tell the students that five of the glasses (say row A) contain Pepsi and five of the glasses (Row B) contain Coke. Each student is asked to drink from a glass in row A, eat a cracker, and then drink from a glass in Row B. No one in the class, including the tasters, is permitted to talk during this test. After they have tasted the soda I ask them which row contained Pepsi and which row contained Coke. In nearly every case some students will believe that Row A was Coke, while others will insist that Coke was in Row B. I then inform the class that all glasses contained RC Cola (or some cola other than Coke or Pepsi). This demonstrates to them (in addition to the lesson that they should be wary of authority figures) that goods have images and that differences between them may be more imaginary than real.
G. Michael Sher, University of Minnesota and
S. Gupta, Jackson Energy Cooperative
1. Aspirin. Bristol Myers makes:
a. Excedrin b. Bufferin
2. Toothpaste. Proctor and Gamble makes:
a. Crest b. Gleem
3. Drain cleaner. Bristol Myers makes:
a. Drano b. Vanish
4. Laundry detergent. Proctor and Gamble makes:
a. Tide d. Oxydol
b. Cheer e. Bold
c. Gain
5. Furniture polish. Johnson Wax makes:
a. Klean and Shine b. Favor
6. Soap. Proctor and Gamble makes:
a. Zest d. Camay
b. Lava e. Safeguard
c. Ivory
7. Aspirin. Sterling Drug makes:
a. Bayer c. Midol
b. Cope d. Vanquish
8. Dishwashing liquid. Proctor and Gamble makes:
a. Joy c. Thrill
b. Ivory
9. Household cleaner. Texize makes:
a. Fantastic c. Grease Relief
b. Janitor in a Drum
10. Cleaner. Proctor and Gamble makes:
a. Spic and Span b. Top Job
11. Sugar. Amstar makes:
a. Domino b. Spreckels
NOTE: All answers to all the preceding questions are correct.
The Seemingly Irrational Consumer
Josef M. Broder,
Many students pride themselves as being wise consumers, often going to great lengths to find bargains. Similarly, economics professors reinforce these beliefs in their lectures on consumer demand. In theory, consumers are assumed to be rational, i.e., that consumers be able to choose among bundles of goods, that consumer choices be transitive or consistent, that consumers prefer more to less, etc. Central to the consumer choice process is consumer product information which often leaves much to be desired. The absence or distortion of such information may lead to the seemingly irrational consumer.
To demonstrate the practical pitfalls of consumer choice, I have the class participate in consumer taste panels. First, I select three competing, yet similar, food or beverage products. Next, I ask students to rank these competing brands on the basis of (expected) quality and price. Then, students participate in blind taste tests where products are disguised as brands A, B, or C. Next, the blind taste test is repeated with the same brands labeled X,Y, and Z. Finally, I collect taste panel questionnaires used in the exercise and compile the results. Questions addressed by exercise include, but are not limited to, the following:
1. Do students associate quality with price?
2. Are students' prior expectations consistent with taste panel results?
3. Are student preferences similar in repeat taste panels?
4. Are student purchase choices rational?
Previous applications of this exercise have found that students often confuse quality and price, that lower priced brands are often preferred over more expensive brands, that many students cannot distinguish between competing brands, that many students overinvest in high‑priced brands which they later judge as being inferior to cheaper brands, and that the use of taste panels in advertising, as well as advertising itself, can be misleading.
Students find the taste panel exercise to be both informative and challenging. I use the exercise to introduce and critique consumer economics. The questionnaire used in the taste panel exercise is shown below:
TASTE PANEL
Please rank the following on the basis of what you know or expect from these brands (where 1 = most preferred or most expensive and 3 = least preferred or cheapest):
Product Preference Price
Brand Ranking Ranking
Lipton _____ _____
Luzianne _____ _____
Tetley _____ _____
Blind Taste Tests
Test One (A, B, & C) Test Two (X, Y, & Z)
1st Preference_____ 1st Preference_____
2nd Preference_____ 2nd Preference_____
3rd Preference_____ 3rd Preference_____
Is Beer Artificially Differentiated?
Craig Nauman,
My idea is designed to illustrate non‑price competition in oligopoly. Students are asked to find the average price of a six‑pack of their regular beer. Beers are then grouped according to type (regular, premium, super premium, light). To illustrate the non‑price competition, a sample of each type of beer is brought to class for a blind taste‑testing. Students are asked to name the type, and, if possible, the brand. Invariably they cannot tell either, and find that the price of beer has little to do with their taste favorite.
Monopolistic Competition
Joseph Phillips, Jr.,
To crystallize the concept of a monopolistically competitive industry model, I utilize one of the hottest consumer products today, VHS format videotapes. The casings found on the tapes are identical in every respect except for brand names which makes them compatible with all brands of VHS tape decks, the "competitive" nature of the model.
However, differences in quality, though subtle (color definition, picture detail and dropout tendencies, for example) give each brand a uniqueness of its own, the "monopolistic" element of the model.
It is pointed out that absent a special sales price, videotapes are generally sold within a very tight price range and that because the consumer has numerous alternatives, one brand could lose its entire market if it unilaterally increases price dramatically. The current video craze is a major source of examples which effectively maintains the student's interest.
The Benefits of Product Differentiation
Ralph T. Byrns
Poll your class about the percentage price cuts, percentage increases in safety, and percentage increases in miles per gallon that would be necessary before they would all be willing to drive identical cars. You may be surprised at how much even impoverished students are willing to pay for product differentiation in automobiles when you discuss this feature of monopolistically competitive markets.
Discuss the benefits of product differentiation, and suggest to your class that savings might be as high as 20 percent if we would all buy standardized cars, clothing, homes, or whatever. Ask how many would acquiesce to majority rule to consume these standardized items at such savings. You may be shocked to discover that most are willing to pay very high amounts for product differentiation. Remind them that the negatively sloped demand curves associated with differentiation lead firms to follow inefficient policies. Use this to emphasize the analytics of the (in)efficiency of monopolistic competition. Then challenge your students to rationalize differentiation as an efficient production device. (This may be impossible {unless price discrimination is perfect}, but it will stimulate a lot of thought among your better students.)
Imperfect Competition
Josef M. Broder, University of Georgia
The concept of the "oligopolist's dilemma" is a graphical extension of the kinked demand curve and can be used to complement intuitive explanations of oligopolistic pricing behavior. Consider the case of the duopoly. The uncertainty of competitor reaction to price changes leads to price rigidity and non‑price competition. The possibility that competitors may or may not follow suit in a price change leads to two separate demand curves facing the oligopolist: the matched and unmatched curves. The matched demand curve results when competitors match all price changes while the unmatched demand curve results when competitors fail to match these price changes.
The oligopolist's dilemma can be shown graphically by assuming that the oligopolist is currently selling at the intersection of the matched and unmatched demand curve and by examining the total revenue consequences which might result from a price change. This dilemma is best summarized in Figure 26‑2. where any price change by the risk averse oligopolist could lead to a loss in market shares and a loss in total revenue as shown by movements along the truncated or solid lined total revenue curve.
For example, the oligopolist selling four units of quantity at a price of $2 explores the potential for increasing total revenue by changing price. Company analysts estimate that total revenue may be increased by either increasing or decreasing price toward the point of unitary elasticity. Since our firm cannot predict how competitors will react, a price change involves risk. The possible reactions to price changes are as follows:
(a) Our firm increases prices to $2.50, competitors match price increases and total revenue increases from $8 to $8.75.
(b) Our firm increases price to $2.50, competitors do not match price increase and total revenue declines from $8 to $5.
(c) Our firm decreases prices to $1.50, competitors do not match price decrease and total revenue increases from $8 to $9.
(d) Our firm decreases prices to $1.50, competitors match price decrease and total revenue declines from $8 to $6.75.
With these options, firms avoid price competition and attempt to engage in tacit collusion on price increases (price leadership). Translating the kinked demand curve into total revenue and using real numbers in these graphs gives students a better understanding of the oligopolist's behavior.
Figure 26‑2 The Oligopolist's Dilemma
Variations in Demand Elasticity and Firm Behavior
Eric K. Steger,
To help my students better understand profit maximizing behavior, I assume that I approach the ticket window at a local movie theater immediately after the movie begins. I know that there are vacant seats because I counted the number of people buying tickets. Therefore, I offer the cashier half of the regular ticket price to let me see the remainder of the movie. I assert that I will not purchase the ticket at the regular price. I explain to the students that I really don't expect the seller to give me a 50 percent discount but it would be in the theater's interest to do so because the marginal revenue generated would exceed the marginal cost of this decision. The firm has excess capacity and can provide to me a slightly differentiated service (I don't see all the movie) without increasing its marginal costs.
Typically, students ask, "If my reasoning is accurate why don't we see theaters offering different quality tickets at different prices?" My response is that they do recognize different demand elasticities among their customers by offering price discounts for matinees and other off‑peak showings. However, theater management does not recognize that another market may exist that is responsive to movie quality differentiation (not being able to see the entire film) in return for price discounts. As an example of this type of pricing, I explain that the airlines have offered `standby' discounts for customers who are willing to bear uncertainty.
Collision, Cooperation, and Collusion
Anthony J. Greco,
I speak in terms of "Collision v. Collusion." The collision course is followed when firms act independently relative to price and/or other facets of competition. They can be said to be traveling in different cars rushing toward the same customers. The collusive course, on the other hand, avoids run‑ins among firms. The firms are essentially traveling in the same car moving toward customers.
Pedagogic Reasons for Kinked Demand Models
Ralph T. Byrns
In an address after being awarded the Nobel Prize, George Stigler disparaged the continued appearance of kinked demand curves in economics textbooks because empirical testing does not seem to confirm the price stickiness predicted by this model. Nevertheless, the kinked demand curve model excels in conveying the idea that oligopolistic decision making is interdependent. Thus, going over this model in class is usually time well spent.
Edward
Two groups of three students each are selected and directed to stand at opposite corners in front of the class. (Try to make sure at least one bright student is in group I.) All the students are told that each of them has a widget to sell, that they each should submit a slip of paper showing their name and the lowest amount they will accept for the widget (maximum $1), and that I will buy one widget from each group. The following conditions are imposed:
Group I ‑ three persons ‑ can talk between themselves.
Group II ‑ three persons ‑ can't talk (I stand with them during the few minutes the students have to fill out this paper).
Group III ‑ the rest of the class ‑ can talk.
Usually I pay $1.00 to someone in Group I (which they split), about 50 cents to someone in Group II and 2 cents to someone in Group III, showing that collusion pays off (I vs. II), but that collusion in a large group is difficult (I vs. III).
Gary Galles,
I have used an extortion example in class which helps students to understand sunk costs, post‑contractual cheating (or appropriable quasi‑rents), and how one can be induced to overpay for something.
Extortion or kidnapping cases involve some sort of payment for silence about some "secret" or for return of the kidnapped. The problem with paying extortion or blackmail is that once a payment is made, that cost is sunk and the payer is still in the position of being held up (again) for a marginal ransom payment just less than the value of what is being ransomed. Furthermore, by revealing that he is willing to pay at least what was previously demanded, the payer may induce the extortionist to ask for more each time his demands are met (without this, we wouldn't see any crime dramas about extortion on TV). In this way, paying extortion not only doesn't improve your position, but it can make it worse and actually lead to payments in excess of the total value of the item taken (incidentally, this is a true case of throwing (away) good money after bad (already thrown away), but sometimes throwing good money (profitably) after bad (unprofitably spent) is rational. An example would be a factory that cost $10 million more than the present value of its net revenue stream, but which needs $1 million worth of repairs to stay open: as long as the present value of the remaining net revenue stream exceeds $1 million, it is economic to throw good money after bad).
The only time payment of extortion should be made is when the ransomed item can reasonably be expected to be recaptured (e.g., never for photographs or other reproducible items, for which no assurance that "this is the only set of negatives" can be had) or the extortionist caught in a trap (this is why the extortionist holds out the hope of providing an exchange, while not intending to let it happen, and why payments so often involve a trap).
Another thing to note is that successful trades involving kidnapped people or things are almost always simultaneous (also often true for drug transactions) rather than sequential. The reason is post‑ contractual cheating. Once we agree to trade, if the extortionist gets the money first, he will be tempted to renege on his end of the bargain; similarly, if the payer gets back the hostage first, he will renege. This is not a major problem in most of the business world, because the negative impact of a bad reputation on future sales gives them a profit incentive not to engage in such behavior, but it may be where repeat sales are unlikely and information may be slow to get out (e.g., buying something from Midnight Auto Sales, out of somebody's trunk).
Grade Collusion in the Classroom
Richard C. Schiming,
Students sometimes find it difficult to imagine the problems of a small group of firms acting in collusion. While the profit maximizing possibilities are obvious, the forces tending to disrupt collusive activities are not. To demonstrate these disruptive forces, I discuss an example common to all students. When students receive a take‑home examination, students together usually decide on a limit to the time to be devoted to the test. The hope is that such a limit will prevent the problems of uncertainty and excess competition. But, this form of collusion quickly disintegrates as each student believes others will violate the agreement and thus, each student decides to violate this agreement to protect his or her grade. Only if the class size is small and enforcement costs are low can such an agreement ever hold together. The students then see how cartels, in spite of the potential for gain, can be short‑lived.
Collusion and the Creation of an Exam
Carl E. Enomoto,
The prisoners' dilemma has always been one of the more fascinating topics in microeconomics. It is usually demonstrated with a profits‑payoff table for two firms or for two criminal suspects. One way to show how this theory works is to conduct the following experiment. For your first class exam, have each student submit one question covering any of the course material you have already gone over. Tell the class that you will select a small sample of these questions for the test. You will probably find that many of these questions are extremely difficult and you would not have asked such questions if you had made up the exam. For the second exam, let the student discuss among themselves the questions they will submit for the exam (leave the classroom when they do this). When you select questions from the list this time, you will find that the questions are usually easier to answer and concentrate less on the fine details of the course. By keeping both lists of questions submitted by the students and then returning them to the students later on, the class will see how beneficial collusion can be. One variation to this occurs if you have a particularly large class. In this case, the students cannot easily collude and usually a few students will come up with difficult questions that only they can answer. This will still allow you, however, to talk about game theory and strategy in microeconomics.
Steven W. Jones,
After explaining the concept of collusion and citing examples such as the OPEC cartel, ask for volunteers to help you illustrate some elements of successful collusion through a simple experiment.
Select five students for the experiment. Group four of them into two pairs and send them out of the room. Have the fifth student go to the board and turn his back to the class. Show the class a picture composed of several simple geometric designs. (An example is shown in Figure 26‑5.) Then ask the student to draw this diagram. The response is obvious‑‑he can't recreate the design because he has never seen it and doesn't have the specific information needed to reproduce the drawing. Without collusion, he lacks vital information of which his classmates are aware.
Invite Pair A inside and instruct them to go to the board. One member faces the board, the other faces the class. They have their backs to each other and neither may turn around. Show the student facing the class the same drawing. Instruct the student that his task is to get his companion to reproduce the drawing. The student seeing the picture can talk to his partner but cannot monitor his partner's progress. Time the process. Record the time to complete the task. This represents imperfect information about industry operations ‑ but is better than no information at all.
Finally, have Pair B enter and go to the board. One member is assigned the responsibility of reproducing the drawing; the other is actually shown the drawing. However, this pair may work together in any manner necessary to achieve their objective but only the student who did not see the picture can actually draw the designs. Time the process. Two way communication will develop, and the time to complete the process will be considerably less due to a more effective exchange of information.
Figure 26‑3
Henry G. Demmert,
My idea is an effective method of illustrating the inherent instability of a cartel (or of collusion in general).
I present the class with a reading assignment which, I emphasize, they will be responsible for on the next exam. I then ask them to imagine what would happen if they all got together and agreed not to read the assigned material. I point out that, because I grade on a curve, their grades would not be affected and they would all have more time to party, study for other exams, etc. In other words, there are potential collective benefits to be gained by all members of this hypothetical "student cartel." I then ask them what their best personal strategy would be, given that all of their classmates have agreed not to do the assigned reading. It is immediately obvious to them that they would clearly gain by cheating on their fellow cartel members: Their classmates' failure to read the assigned material would result in a lower grading curve, and they can take advantage of the lower overall curve to increase their own grade by doing the assigned reading. In fact, I note, their payoff from doing the reading is even greater in the cartel environment than under normal circumstances. Finally, I ask them if they would have enough faith in one another's "integrity" to abide by their agreement. Most concede that they would find it almost impossible not to take a peek at the assigned reading as the exam draws near.
I then draw a parallel between the incentives at work in this case and those at work in an economic cartel whose members agree to fix prices and restrict output.
Cartels and the Incentive to Cheat
Daniel R. Marburger,
To illustrate how cartels may break down because of incentives for members to cheat, I use the following analogy. Suppose that on the first day of class, the instructor announces that his course will consist of four multiple choice exams. Further, he intents to curve the scores on each of the exams (i.e., the average score on each exam is a 'C').
Several days later, an enterprising young student (whom we will call Joe) devises a way to beat the system. If all of the students agree not to take the exams, then everyone's score will be zero, which means that everyone will earn a 'C' according to the instructor's grading system. Of course, if no one takes the exam, there is no reason to study, purchase the text, or attend class. All one need do is enroll. Assuming that the promise of something for nothing is inherently appealing, the class agrees to form those non-exam taking cartel.
For the first two exams, the cartel, works like a charm. No one shows up for the exams, and all students receive a 'C'. Prior to the third exam, however, Joe, no longer satisfied with a free 'C', invents a means of beating his own system. Joe decides to show up at the exam and randomly guess the answers. Since the instructor gives multiple choice exams, the law of averages suggests that Joe will earn a score of roughly 20%. Since the rest of the cartel members do not take the exams, a score of 20% should be at the top of the class. In other words, whereas the remainder of the class earns 'Cs' for nothing, Joe will earn an 'A' with an equal lack of effort. And since none of the other cartel members will be in the classroom during the exam, there is no way for him to get caught.
Soon, the exam date arrives. With a rather cocky air about him, Joe strolls into the classroom--only to find 10 other students already taking the exam. As he scans the room, two questions cross his mind: 1) Have these people been here for the previous exams? After all, Joe didn't show up for the first two exams. 2) Did they study? If these people know the answers while Joe randomly guesses, he's going to fail the exam!
It doesn't take a genius to figure out what happens for the fourth exam. All of the students show up for the exam, and all of them study. When the final curve is announced, Joe, who organized the cartel in an attempt to get something for nothing, earns a 'D' for the course; a 'D' that he worked to earn.
Dollar Bills and Cartel Stability
Mark Mitchell,
An experiment that illustrates the difficulty of maintaining a stable cartel is to cut a dollar bill into quarters and distribute them to four willing students. The experiment is more interesting if you use a larger bill. The rules are 1) each part is worthless alone, 2) the bank only requires three parts in return for a crisp clean undamaged bill (you are the bank), and 3) communication among the students is encouraged at all times. Two options are readily available. All four may go to the bank together and receive twenty‑five cents each or three students could form a cartel and split the money three ways instead of four. If the students choose the first option, remind them that forming a cartel of any three will increase their wealth. Once a cartel forms, (whether spontaneously or by your prodding) and begins to exchange with you, remind the excluded student that the value of her part falls to zero once the exchange is made. Unless she begins trying to break the cartel on her own initiative, suggest going to two cartel members with an offer to make them better off than their current arrangement. For example, she could agree to accept only twenty cents, leaving forty cents each to her two co‑conspirators. All three parties will be better off, so a new cartel is formed. Naturally, while the new cartel is on the way to the bank, the entire scenario is repeated. The ejected member, finding the value of his part threatened, will bargain with two current cartel members and a new cartel will form. Students eventually realize that bargaining could continue forever, so the likely final solution is that all four students go to the bank. Competition prevails, and the stability of the cartel has been proved unsustainable.
Curt L. Anderson,
Sometimes it is difficult for students to understand why individual firms of a cartel would "cheat" on a cartel agreement that supposedly makes them all better off. To illustrate why this occurs, I inform the class that the grades on the next test will be given out on the following basis: if one scores within 10 points of the top score in the class, an A will be received; if within 11‑20 points, a B; and so on. I then point out that the class perhaps should consider forming a cartel with each individual student as a member. By making the agreement that each individual will not study at all for the test, the top score would be held way down and all students would receive a decent grade without any effort. Thus, the agreement is generally perceived as beneficial. Quickly, however, the students begin to realize that if everyone else in the class abides by the cartel arrangement of no studying, they could ensure themselves an A (a greater benefit than just a "decent" grade) with just a little studying. So, because the benefit from cheating on the cartel arrangement is greater than the benefit from following it (assuming everyone else does), cheating occurs. Everyone of course, faces the same situation and so soon everyone begins to study and the cartel falls apart.
Supermarket Coupons and Noncollusive Oligopolists
Joseph Phillips, Jr., Creighton Uniersity
To illustrate clearly the concept of the "kinked" demand curve faced by a noncollusive oligopolist the following example based on actual real life occurrences can be utilized:
In the city
of
In September of the next year, Supermarket B announced that it was eliminating double coupons. No other market announced that it planned to do likewise. This proposed policy change never was implemented by Supermarket B. This is illustrative of the demand curve above the kink where competing firms are not as likely to match a price increase and thus the firm tends to face a relatively elastic demand curve above that point.
Discouraging Shirking in Group Projects
John J. Gregor,
The problem of what to do about an individual member(s) of a group who does not fully participate in the work load (shirking) is handled in a very efficient fashion by providing each group with a budget of $10,000 which they allocate among the members of the team by vote. These dollars are then used to purchase additional points on the project grade or on an exam. The price of points is determined by the instructor before the beginning of the course. It could, however, be determined by class auction.
Peter D. Adelsheim,
1. This game is designed to simulate the dynamics of oligopolistic competition. The goal of individual profit seeking takes the student from competition to collusion and eventually back to competition (after the cheating on the cartel begins).
2. The game is played in six rounds. In each round, each individual student will decide whether he/she wishes to "compete," i.e. lower prices, or "collude," i.e. raise prices.
3. After deciding, each student indicates his/her decision by raising an open hand for competition or a fist for solidarity. Your "profits" in each round are determined by what the majority does in conjunction with what you do, as indicated in the table below.
What you do
Compete Collude
What Compete 10 0
the
Majority Collude 40 20
Does
Table 26‑1
4. We will play one game of six rounds for practice and then discuss the simulation. I suggest that we then play the game another time which will then count for 10% of the student's final course grade.
5. Grades are determined as follows:
over 120 = A
120 = A‑
100‑120 = B
80‑90 = C
60‑70 = D
below 60 = F
Jerry McElroy,
In order to clearly demonstrate the meaning of interdependence in oligopolistic price and quantity decision‑making, I use two applications of game theory. The first is a basketball analogy whereby I demonstrate that one team's offensive posture will depend on the defensive position taken by the opponent. Following along with this example, I diagram on the board different offensive strategies against two common zone‑type defenses, showing, e.g., the 1‑3‑1 offense (Figure 26‑4A) against a 2‑1‑2 zone defense; similarly the shift to a 2‑3 offense (Figure 26‑4B) against a 3‑2 zone defense.
In the same fashion, to use a more experiential example, I explain some of the varieties of strategies used by poker players depending on who the competition is, i.e., who is playing against whom. These include conservative play against, say, an unknown player, bluffing against the more inexperienced, and so on.
Both types of examples tend to solidify students' intuitive grasp of the essential characteristics of oligopolistic decision‑making, i.e., taking rivals' reactions and strategies into account.
Figure 26‑4
David Hemenway,
Oligopolistic behavior is usefully explained in game theoretic terms. Most of my time devoted to game theory is spent ensuring that students understand the prisoner's dilemma game. Understanding the prisoner's dilemma also improves discussions of externalities and the moral hazard problems of insurance. The best way to understand game theory is to play games. Using a number of real world examples, I carefully describe payoff matrices and how to read them. We also go over the classic bank robber scenario of the prisoner's dilemma game. Then I tell the class that we are going to play a serious game for something that counts to them‑‑10% of the grade.
We play the game reflected in Figure 26‑5 five times. A few students are selected as "Column." All students must make a simple simultaneous choice‑‑put up a hand (for competition) or a fist (for solidarity). The rest of the class is "Row." Thus if student A puts up a fist, but the majority of the class puts up a hand, student A receives 0 points. The grading scale is also given. I spend some time making sure everyone understands the rules. No talking is allowed.
The class becomes very involved. They have never won. While all could easily get A‑'s (or better), they usually all get C's and lower. Even when the majority begins by putting up fists, they become so enraged at the ones "competing" and receiving 30 points that the implicit coalition breaks down. And once the coalition breaks, it seems impossible to reform if without communication.
After the five rounds they determine their own grades. I then ask if they would like to play the game again, for another 10% of their grade‑‑under the condition that I first leave the room for five minutes and they can talk. At the end of the class we discuss the type of variables which affect the likelihood of successful coordination or collusion (e.g., number of players; the existence of a strong trade association, etc.). I don't count the grades, but it is important for them to believe that I might.
Figure 26‑5
Attending Class as a Prisoner' Dilemma
Josef M. Broder,
Maintaining class attendance is a perennial challenge for all levels of instruction. After midterm examinations, class attendance often drops to discouraging levels. Popular techniques for maintaining attendance are often time consuming (roll‑calling) and/or are demeaning to many students (seat assignments). In place of, or in addition to, these conventional attendance techniques, the instructor can use game theory to encourage attendance.
This attendance experiment assumes that a certain amount of class attendance is important to the learning process and that students should have some options, and thus bear some responsibility, for attending class. The experiment is initiated after the midterm exam. The rewards of the experiment are simple: the class as a whole receives points for class attendance. Specifically, each student in the class receives one point on his final grade for each day that class attendance exceeds a predetermined level, i.e., 90 percent. University guidelines for attendance make a good starting point. When this attendance level is reached, all students receive the bonus points, including those who were absent on that particular day. A simple head count is sufficient to monitor daily attendance. The class is not penalized for poor attendance; they lose the opportunity to improve their final grades.
The experiment is useful in teaching game theory and the prisoners dilemma, or in this case, the student's dilemma. Students have the option to attend class (cooperate) or cut class (defect). Each option has two possible outcomes such that attending class may or may not ailed bonus points, while cutting class may or may not result in a loss of points.
The dynamics of the experiment are enjoyable to the students and tend to vary with class size. In small classes, students are quick to see the advantages of cooperation and will encourage attendance among the would‑be defectors. Student generated lists of rationed cuts have also emerged in small classes. In large classes the results are less predictable. Attendance standards may have to be reduced in large classes to maintain student interest and participation. Also, attendance standards can be lowered during the experiment if necessary.
Despite the generous appearance of the attendance experiment, the total bonus points awarded tend to be less than the arbitrary "curve" which is often given at the end of the term. When used in place of the curve, these attendance points may represent a more objective factor in assigning final grades.
Simple Game Theory and Oligopoly Models
Paul Temple,
First year micro‑students are often told that, unlike perfect competition and monopoly, oligopolistic market situations are quite common in modern industry. Yet the analysis of oligopoly receives scant attention at most levels of undergraduate study. Game theory provides the most general set of tools in the analysis of oligopoly, but is generally considered to be outside the scope of introductory classes. Nevertheless, I have used a very simple pay‑off matrix that, besides providing an introduction to game theory, also illustrates some of the important aspects of oligopolistic markets.
Consider the very simplest kind of game; there are two players (firms) and each firm can choose between two prices, "high" or "low". The outcome, in terms of profitability, can be illustrated in a simple matrix, as in Table 26‑2.
Profit
($) per period (firm 1's first)
FIRM
1
F High Price Low Price
I
R High Price 1,000; 1,000 1,500; 200
M
2 Low Price 200; 1,500 800; 800
Table 26‑2
Most people intuitively understand the nature of such a simple game, but it illustrates some important principles:
(a) Interdependence: each firm's profit depends not only upon its own actions, but also those of its rival.
(b) Collusive solution (joint profit maximization): If each firm charges a high price, then joint profits are at a maximum. Such a solution may be reached by either overt collusion or a more tacit procedure such as price leadership. It represents the "cooperative" solution, and involves a superior outcome for both firms.
(c) Competitive solution at "low‑low": Such a solution is likely to be found in games where, for one reason or another, each firm plays a very cautious, safety‑first policy. We can see this because charging a low price provides the best outcome when one assumes that one's opponent adopts a strategy likely to do you the most damage (i.e. by setting a low price). Setting a low price can also be seen to be the strategy when "maximizes one's minimum gain" (maximin).
(d) "Chiseling": it is often contended that there is an incentive for individual firms to cheat on a collusive agreement, because for each firm marginal revenue is greater than marginal cost. Such a possibility can be seen by a movement from "high‑high" to "low‑low". But such a movement cannot, it seems, persist. For, at a "low‑high" outcome, the firm with the high price can do better, regardless of his opponent's reaction, by setting a low price. Thus the ultimate effect of chiseling would almost certainly be to make all parties worse off. The "chiseller" is thinking in "marginal" terms, but not "strategically".
(e) Changing values: by altering the figures somewhat, it is possible to illustrate other propositions. We can introduce the notion of "bargaining power" or "threat strength" by making one firm's profits considerably lower than the others at the competitive solution ("low‑low"). In that case one firm stands to lose much more by failing to co‑operate, giving the other firm much greater "threat strength" and consequently bargaining power.
(f) Kinked demand: A kink in the demand curve is much more likely to occur at the "high‑high" solution, where an increase in price by both parties is likely to make both worse off. At the "low‑low" solution, on the other hand, is it rational for a firm not to follow a price rise?
Jim Ford,
Two men hate each other, and with good reason. John has had a very long‑standing and passionate affair with Fred's wife, Rita. Now Fred loves Rita very much. Worse than this, however, John wants the affair to continue although Fred demands that it be ended. Fred would like to kill John, being, among other things, a righteous and indignant husband. John feels the same way about Fred; John would have Rita if Fred were not alive.
For no reason other than for illustration, and perhaps because of a bit of sadism within us, we are going to place these two bitter enemies, Fred and John, in a room that is totally dark. We hand each man a similarly deadly knife; machetes of the same length and design would be appropriate. Letting our imaginations run rampant, we then tie their left hands together, being certain beforehand that they were both right‑handed. Finally, we would leave the room, locking the door as we departed.
Now, what options do Fred and John have? First, either one may attempt to kill the other by slashing blindly into the air. This might be called the direct means to murder. On the other hand, this could be attempted craftily, the more indirect approach. Fred might make overtures of peace to John hoping to lull the victim into believing he is safe until it is too late. After all, if John feels safe, he will stand still. He will be easier to hit with one deadly blow with a machete.
Secondly, another option is fairly obvious. If one is not hell‑bent on absolute retribution‑‑killing would be psychically optimum‑‑perhaps a compromise would be advisable. Even losing one's leg is not palatable, although it is better than losing one's head. Furthermore, there is the ultimate question of who is killing whom. John may be the victim instead of the victor. The goal may be sweet, but the odds may be frightening. A truce may be the better option because the situation may be simply too dangerous for either John or Fred. Survival at all may be preferred to being entirely free of one's enemy. Sometimes two can make a comfortable peace.
If these were the only options open to you if you were Fred or John, which would you choose? Would you go for the big one, or would you allow your enemy‑‑and maybe yourself‑‑to exist? Now, put yourself into another situation. We are going to allow you to become either president or chairman of the board of a very large company, and your name is Fred. Furthermore, someone named John is in the same position with your only competitor. There are no other firms in the industry in which you operate, although one or two more would make little difference. Such an industry is defined as an oligopoly ‑ one with few firms making it up.
Compare Fred and John, husband and lover respectively, with Fred and John, corporate movers. Both are desperate because the stakes are high. Both are in the dark. The husband and lover are literally so; the corporate chiefs are in the dark about what each other is doing. Furthermore, corporate power is great. The problem is that both have equal power in this respect. Remember that Fred and John in that dark room had machetes, but they were deadly and equal too. They were tied together with a rope; the business competitors are tied together by trying to sell the same product. Everything appears to be equal, similar, and locked into position.
Now what about the options between the two corporate giants, Fred and John? They too may attempt to kill each other. Each may cut its prices below its costs and await the opponent's demise. The trouble is that Fred may try to destroy the company John directs only to find that John's firm had more than anticipated resources with which to do battle. Fred's attempt killed Fred's company. That was not the way the plan was supposed to work. Besides, there is the other problem. Cutting prices to force closure of a competing firm is unlawful. The Antitrust Division is not fun to fight. Even if a company wins, the costs can be ruinous.
Peacemaking may be preferred to direct murder. After all, blessed are the peacemakers. Besides, if one cooperates with a competitor long enough, he will be easier to kill. Just like with machetes, when the enemy stands still, he is easy to hit. Waiting is better anyway. Presently, the plan is to survive, and to allow the opponent to do the same. Fred ‑ husband ‑ can cut John's ropes, and John can cut Fred's, probably at the same time. Then both may relax. The situation is even rosier with the two companies. Provided Fred and John do not raise suspicion in the Antitrust Division, they may share information. Being in the dark as to one's competitor is not welcome. Furthermore, this development would be like throwing down their counterpart's machetes. Now our two competitors are no longer locked together in a deadly duel. They are where they desire to be. Fred's company may pass its cost data and prices along to John's company. John's firm will reciprocate. No other corporation makes the same product. By joining forces, the two can operate like a monopoly. (One and one does not necessarily make two here.) The two can raise prices and profit margins. Fred's and John's companies can get rich by acting together. What is so bad about that? In both situations, peace is probably preferable to war.
Cost Analysis of the Multiproduct Firm
Mark Jelavich,
In analyzing the costs of a multiproduct firm, two concepts arise that do not show up in most microeconomic texts. The first concept is the idea of "scope economies". Say we have a multiproduct firm producing two goods: minivans and light trucks. Scope economies are said to exist if the cost of producing some particular number of minivans and some particular number of light trucks together is less than the cost of producing each product separately (using the same technology). If some economies exist, then it is rational to have a multiproduct firm. For example, say the cost of producing one million minivans and two million light trucks together is $15 billion. However, the cost of producing one million minivans alone is $8 billion, while the cost of producing two million trucks alone is $9 billion. In this case, scope economies exist. Some reflection would show that such economies can arise from shared fixed costs as well as "cost complementarities" (e.g., sharing specialized labor or distribution costs).
A second concept is the idea of average incremental costs. The concept of average cost is often indefinable in a multiproduct firm context: If you add one million minivans and two million light trucks together, what do you have? The concept of average incremental cost (AIC) is used in place of average cost. The AIC of a minivan in the above case would be the total cost of producing one million vans and two million trucks together, minus the cost of producing the two million trucks along; the difference is divided by one million minivans. Thus if the cost of producing both products together is $15 billion, and the cost of producing trucks alone is $9 billion, the AIC for vans is $6000.
The concept of marginal cost for each product still holds in a multiproduct firm. By comparing the marginal cost of producing a (say) minivan to its AIC, you can determine if there are scale economies in minivan production. If the marginal cost is less than the AIC you have increasing returns to scale in minivan production. The same analysis can be performed on light truck costs.
A good "primer" on this topic is E.E. Bailey, A.F. Friedlaender, "Market Structure and Multiproduct Industries", Journal of Economic Literature, September 1982.