posted by bhawna bhardwaj

1. Prisoner’s Dilemma
LEARNING OBJECTIVES
 Explain the role of game theory in understanding the behavior of oligopolies
Because of the complexity of oligopoly, which is the result of mutual
interdependence among firms, there is no single, generally-accepted theory of how
oligopolies behave, in the same way that we have theories for all the other market
structures. Instead, many economists use game theory, a branch of mathematics
that analyzes situations in which players must make decisions and then receive
payoffs based on what other players decide to do. Game theory has found
widespread applications in the social sciences, as well as in business, law, and
military strategy.
A key element of game theory is the concept of Nash equilibrium. The concept was
developed by John Nash, an American mathematician who was awarded the 1994
Nobel Prize in economics for this work. A Nash equilibrium occurs when no player
has an incentive to change their decision, taking into account what the players have
decided and assuming the other players don’t change their decisions. Thus, all
players have made an optimal decision, given the decisions of the other players.
The prisoner’s dilemma is a scenario in which the gains from cooperation are
larger than the rewards from pursuing self-interest. It applies well to oligopoly. The
story behind the prisoner’s dilemma goes like this:
Two co-conspiratorial criminals are arrested. When they are taken to the police station, they
refuse to say anything and are put in separate interrogation rooms. Eventually, a police
officer enters the room where Prisoner A is being held and says: “You know what? Your
partner in the other room is confessing. So your partner is going to get a light prison
sentence of just one year, and because you’re remaining silent, the judge is going to stick
you with eight years in prison. Why don’t you get smart? If you confess, too, we’ll cut your jail
time down to five years, and your partner will get five years, also.” Over in the next room,
another police officer is giving exactly the same speech to Prisoner B. What the police
officers do not say is that if both prisoners remain silent, the evidence against them is not
especially strong, and the prisoners will end up with only two years in jail each.

2. Figure 1. The Prisoner’s Dilemma. Alternative text for the Prisoner’s Dilemma can be accessed here.
The game theory situation facing the two prisoners is shown in Table 1. To
understand the dilemma, first consider the choices from Prisoner A’s point of view. If
A believes that B will confess, then A ought to confess, too, so as to not get stuck
with the eight years in prison. But if A believes that B will not confess, then A will be
tempted to act selfishly and confess, so as to serve only one year. The key point is
that A has an incentive to confess regardless of what choice B makes! B faces the
same set of choices, and thus will have an incentive to confess regardless of what
choice A makes. Confess is considered the dominant strategy or the strategy an
individual (or firm) will pursue regardless of the other individual’s (or firm’s) decision.
The result is that if prisoners pursue their own self-interest, both are likely to confess,
and end up doing a total of 10 years of jail time between them. You should note that
this result is a Nash equilibrium.
The game is called a dilemma because if the two prisoners had cooperated by both
remaining silent, they would only have had to serve a total of four years of jail time
between them. If the two prisoners can work out some way of cooperating so that
neither one will confess, they will both be better off than if they each follow their own
individual self-interest, which in this case leads straight into longer jail terms.
Oligopoly Version of the Prisoner’s Dilemma

3. Figure 2. A Prisoner’s Dilemma for Oligopolists. Alternative text for a Prisoner’s Dilemma for
Oligopolists can be access here.
The members of an oligopoly can face a prisoner’s dilemma, also. If each of the
oligopolists cooperates in holding down output, then high monopoly profits are
possible. Each oligopolist, however, must worry that while it is holding down output,
other firms are taking advantage of the high price by raising output and earning
higher profits. Table 2 shows the prisoner’s dilemma for a two-firm oligopoly—known
as a duopoly. If Firms A and B both agree to hold down output, they are acting
together as a monopoly and will each earn $1,000 in profits. However, both firms’
dominant strategy is to increase output, in which case each will earn $400 in profits.
Can the two firms trust each other? Consider the situation of Firm A:
 If A thinks that B will cheat on their agreement and increase output, then A will
increase output, too, because for A the profit of $400 when both firms increase
output (the bottom right-hand choice in Table 2) is better than a profit of only
$200 if A keeps output low and B raises output (the upper right-hand choice in
the table).
 If A thinks that B will cooperate by holding down output, then A may seize the
opportunity to earn higher profits by raising output. After all, if B is going to hold
down output, then A can earn $1,500 in profits by expanding output (the bottom
left-hand choice in the table) compared with only $1,000 by holding down
output as well (the upper left-hand choice in the table).
Thus, firm A will reason that it makes sense to expand output if B holds down output
and that it also makes sense to expand output if B raises output. Again, B faces a
parallel set of decisions.

4. The result of this prisoner’s dilemma is often that even though A and B could make
the highest combined profits by cooperating in producing a lower level of output and
acting like a monopolist, the two firms may well end up in a situation where they
each increase output and earn only $400 each in profits. The following
example discusses one cartel scandal in particular.
WHAT IS THE LYSINE CARTEL?
Lysine, a $600 million-a-year industry, is an amino acid used by farmers as a feed additive to
ensure the proper growth of swine and poultry. The primary U.S. producer of lysine is Archer
Daniels Midland (ADM), but several other large European and Japanese firms are also in
this market. For a time in the first half of the 1990s, the world’s major lysine producers met
together in hotel conference rooms and decided exactly how much each firm would sell and
what it would charge. The U.S. Federal Bureau of Investigation (FBI), however, had learned
of the cartel and placed wire taps on a number of their phone calls and meetings.
From FBI surveillance tapes, following is a comment that Terry Wilson, president of the corn
processing division at ADM, made to the other lysine producers at a 1994 meeting in Mona,
Hawaii:
I wanna go back and I wanna say something very simple. If we’re going to trust each other, okay, and if I’m
assured that I’m gonna get 67,000 tons by the year’s end, we’re gonna sell it at the prices we agreed to . . .
The only thing we need to talk about there because we are gonna get manipulated by these [expletive]
buyers—they can be smarter than us if we let them be smarter. . . . They [the customers] are not your
friend. They are not my friend. And we gotta have ’em, but they are not my friends. You are my friend. I
wanna be closer to you than I am to any customer. Cause you can make us … money. … And all I wanna
tell you again is let’s—let’s put the prices on the board. Let’s all agree that’s what we’re gonna do and then
walk out of here and do it.
The price of lysine doubled while the cartel was in effect. Confronted by the FBI tapes,
Archer Daniels Midland pled guilty in 1996 and paid a fine of $100 million. A number of top
executives, both at ADM and other firms, later paid fines of up to $350,000 and were
sentenced to 24–30 months in prison.
In another one of the FBI recordings, the president of Archer Daniels Midland told an
executive from another competing firm that ADM had a slogan that, in his words, had
“penetrated the whole company.” The company president stated the slogan this way: “Our
competitors are our friends. Our customers are the enemy.” That slogan could stand as the
motto of cartels everywhere.
How to Enforce Cooperation
How can parties who find themselves in a prisoner’s dilemma situation avoid the
undesired outcome and cooperate with each other? The way out of a prisoner’s
dilemma is to find a way to penalize those who do not cooperate.
Perhaps the easiest approach for colluding oligopolists, as you might imagine, would
be to sign a contract with each other that they will hold output low and keep prices
high. If a group of U.S. companies signed such a contract, however, it would be
illegal. Certain international organizations, like the nations that are members of
the Organization of Petroleum Exporting Countries (OPEC), have signed
international agreements to act like a monopoly, hold down output, and keep prices
high so that all of the countries can make high profits from oil exports. Such

5. agreements, however, because they fall in a gray area of international law, are not
legally enforceable. If Nigeria, for example, decides to start cutting prices and selling
more oil, Saudi Arabia cannot sue Nigeria in court and force it to stop.
LINK IT UP
Visit the Organization of the Petroleum Exporting Countries website and learn more
about its history and how it defines itself.
Because oligopolists cannot sign a legally enforceable contract to act like a
monopoly, the firms may instead keep close tabs on what other firms are producing
and charging. Alternatively, oligopolists may choose to act in a way that generates
pressure on each firm to stick to its agreed quantity of output.
One example of the pressure these firms can exert on one another is the kinked
demand curve, in which competing oligopoly firms commit to match price cuts, but
not price increases. This situation is shown in Figure 1. Say that an oligopoly airline
has agreed with the rest of a cartel to provide a quantity of 10,000 seats on the New
York to Los Angeles route, at a price of $500. This choice defines the kink in the
firm’s perceived demand curve. The reason that the firm faces a kink in its demand
curve is because of how the other oligopolists react to changes in the firm’s price. If
the oligopoly decides to produce more and cut its price, the other members of the
cartel will immediately match any price cuts—and therefore, a lower price brings very
little increase in quantity sold.
If one firm cuts its price to $300, it will be able to sell only 11,000 seats. However, if
the airline seeks to raise prices, the other oligopolists will not raise their prices, and
so the firm that raised prices will lose a considerable share of sales. For example, if
the firm raises its price to $550, its sales drop to 5,000 seats sold. Thus, if
oligopolists always match price cuts by other firms in the cartel, but do not match
price increases, then none of the oligopolists will have a strong incentive to change
prices, since the potential gains are minimal. This strategy can work like a silent form
of cooperation, in which the cartel successfully manages to hold down output,
increase price, and share a monopoly level of profits even without any legally
enforceable agreement.

6. Figure 1. A Kinked Demand Curve. Consider a member firm in an oligopoly cartel that is supposed to
produce a quantity of 10,000 and sell at a price of $500. The other members of the cartel can encourage
this firm to honor its commitments by acting so that the firm faces a kinked demand curve. If the oligopolist
attempts to expand output and reduce price slightly, other firms also cut prices immediately—so if the firm
expands output to 11,000, the price per unit falls dramatically, to $300. On the other side, if the oligopoly
attempts to raise its price, other firms will not do so, so if the firm raises its price to $550, its sales decline
sharply to 5,000. Thus, the members of a cartel can discipline each other to stick to the pre-agreed levels
of quantity and price through a strategy of matching all price cuts but not matching any price increases.
Many real-world oligopolies, prodded by economic changes, legal and political
pressures, and the egos of their top executives, go through episodes of cooperation
and competition. If oligopolies could sustain cooperation with each other on output
and pricing, they could earn profits as if they were a single monopoly. However, each
firm in an oligopoly has an incentive to produce more and grab a bigger share of the
overall market; when firms start behaving in this way, the market outcome in terms of
prices and quantity can be similar to that of a highly competitive market.
The prisoner’s dilemma, one of the most famous game theories, was
conceptualized by Merrill Flood and Melvin Dresher at the Rand
Corporation in 1950. It was later formalized and named by Canadian
mathematician, Albert William Tucker.1
2
The prisoner’s dilemma basically provides a framework for understanding
how to strike a balance between cooperation and competition and is a
useful tool for strategic decision-making.
As a result, it finds application in diverse areas ranging from business,
finance, economics, and political science to philosophy, psychology,
biology, and sociology.

7. KEY TAKEAWAYS
 A prisoner's dilemma describes a situation where, according to game
theory, two players acting selfishly will ultimately result in a
suboptimal choice for both.
 The prisoner’s dilemma also shows us that mere cooperation is not
always in one’s best interests.
 A classic example of the prisoner’s dilemma in the real world is
encountered when two competitors are battling it out in the
marketplace.
 In business, understanding the structure of certain decisions as
prisoner's dilemmas can result in more favorable outcomes.
 This setup allows one to balance both competition and cooperation
for mutual benefit.
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Click Play to Learn the Basics of the Prisoner's Dilemma
Prisoner’s Dilemma Basics
The prisoner’s dilemma scenario works as follows: Two suspects have been
apprehended for a crime and are now in separate rooms in a police
station, with no means of communicating with each other. The prosecutor
has separately told them the following:
 If you confess and agree to testify against the other suspect, who
does not confess, the charges against you will be dropped and you
will go scot-free.
 If you do not confess but the other suspect does, you will be
convicted and the prosecution will seek the maximum sentence of
three years.
 If both of you confess, you will both be sentenced to two years in
prison.
 If neither of you confesses, you will both be charged with
misdemeanors and will be sentenced to one year in prison.2
What should the suspects do? This is the essence of the prisoner’s
dilemma.
Evaluating Best Course of Action

8. Let’s begin by constructing a payoff matrix as shown in the table below.
The “payoff” here is shown in terms of the length of a prison sentence (as
symbolized by the negative sign; the higher the number the better). The
terms “cooperate” and “defect” refer to the suspects cooperating with each
other (as for example, if neither of them confesses) or defecting (i.e., not
cooperating with the other player, which is the case where one suspect
confesses, but the other does not). The first numeral in cells (a) through
(d) shows the payoff for Suspect A, while the second numeral shows it for
Suspect B.
Prisoner’s Dilemma –
Payoff Matrix
Suspect B
CooperateDefect
Suspect A Cooperate(a) -1, -1 (c) -3, 0
Defect (b) 0, -3 (d) -2, -2
The dominant strategy for a player is one that produces the best payoff for
that player regardless of the strategies employed by other players. The
dominant strategy here is for each player to defect (i.e., confess) since
confessing would minimize the average length of time spent in prison.
Here are the possible outcomes:
 If A and B cooperate and stay mum, both get one year in prison—as
shown in the cell (a).
 If A confesses but B does not, A goes free and B gets three years—
represented in the cell (b).
 If A does not confess but B confesses, A gets three years and B
goes free—see cell (c).
 If A and B both confess, both get two years in prison—as the cell (d)
shows.
So if A confesses, they either go free or get two years in prison. But if they
do not confess, they either get one year or three years in prison. B faces
exactly the same dilemma. Clearly, the best strategy is to confess,
regardless of what the other suspect does.
Implications of Prisoner’s Dilemma

9. The prisoner’s dilemma elegantly shows when each individual
pursues their own self-interest, the outcome is worse than if they had both
cooperated. In the above example, cooperation—wherein A and B both
stay silent and do not confess—would get the two suspects a total prison
sentence of two years. All other outcomes would result in a combined
sentence for the two of either three years or four years.
In reality, a rational person who is only interested in getting the maximum
benefit for themselves would generally prefer to defect, rather than
cooperate. If both choose to defect assuming the other won't, instead of
ending up in the cell (b) or (c) option—like each of them hoped for—they
would end up in the cell (d) position and each earn two years in prison.
In the prisoner’s example, cooperating with the other suspect fetches an
unavoidable sentence of one year, whereas confessing would in the best
case result in being set free, or at worst fetch a sentence of two years.
However, not confessing carries the risk of incurring the maximum
sentence of three years, if say A’s confidence that B will also stay mum
proves to be misplaced and B actually confesses (and vice versa).
This dilemma, where the incentive to defect (not cooperate) is so strong
even though cooperation may yield the best results, plays out in numerous
ways in business and the economy
Albert Tucker first presented the Prisoner's Dilemma in 1950 to a group of
graduate psychology students at Stanford University, as an example of
game theory.1
Applications to Business
A classic example of the prisoner’s dilemma in the real world is
encountered when two competitors are battling it out in the marketplace.
Often, many sectors of the economy have two main rivals. In the U.S., for
example, there is a fierce rivalry between Coca-Cola (KO) and PepsiCo
(PEP) in soft drinks and Home Depot (HD) versus Lowe’s (LOW) in building
supplies. This competition has given rise to numerous case studies in
business schools.34 Other fierce rivalries include Starbucks (SBUX) versus
Tim Horton’s (THI) in Canada and Apple (AAPL) versus Samsung in the
global mobile phone sector.
Consider the case of Coca-Cola versus PepsiCo, and assume the former
is thinking of cutting the price of its iconic soda. If it does so, Pepsi may
have no choice but to follow suit for its cola to retain its market share. This
may result in a significant drop in profits for both companies.

10. A price drop by either company may thus be construed as defecting since
it breaks an implicit agreement to keep prices high and maximize profits.
Thus, if Coca-Cola drops its price but Pepsi continues to keep prices high,
the former is defecting, while the latter is cooperating (by sticking to the
spirit of the implicit agreement). In this scenario, Coca-Cola may win
market share and earn incremental profits by selling more colas.
Payoff Matrix
Let’s assume that the incremental profits that accrue to Coca-Cola and
Pepsi are as follows:
 If both keep prices high, profits for each company increase by $500
million (because of normal growth in demand).
 If one drops prices (i.e., defects) but the other does not (cooperates),
profits increase by $750 million for the former because of greater
market share and are unchanged for the latter.
 If both companies reduce prices, the increase in soft drink
consumption offsets the lower price, and profits for each company
increase by $250 million.
The payoff matrix looks like this (the numbers represent incremental dollar
profits in hundreds of millions):
Coca-Cola vs. PepsiCo –
Payoff Matrix
PepsiCo
CooperateDefect
Coca-Cola Cooperate500, 500 0, 750
Defect
750, 0
250, 250
Other oft-cited prisoner’s dilemma examples are in areas such as new
product or technology development or advertising and marketing
expenditures by companies.
For example, if two firms have an implicit agreement to leave advertising
budgets unchanged in a given year, their net income may stay at relatively
high levels. But if one defects and raises its advertising budget, it may earn

11. greater profits at the expense of the other company, as higher sales offset
the increased advertising expenses. However, if both companies boost
their advertising budgets, the increased advertising efforts may offset each
other and prove ineffective, resulting in lower profits—due to the higher
advertising expenses—than would have been the case if the ad budgets
were left unchanged.
Applications to the Economy
The U.S. debt deadlock between the Democrats and Republicans that
springs up from time to time is a classic example of a prisoner’s dilemma.
Let’s say the utility or benefit of resolving the U.S. debt issue would be
electoral gains for the parties in the next election. Cooperation in this
instance refers to the willingness of both parties to work to maintain the
status quo with regard to the spiraling U.S. budget deficit. Defecting implies
backing away from this implicit agreement and taking the steps required to
bring the deficit under control.
If both parties cooperate and keep the economy running smoothly, some
electoral gains are assured. But if Party A tries to resolve the debt issue in
a proactive manner, while Party B does not cooperate, this recalcitrance
may cost B votes in the next election, which may go to A.
However, if both parties back away from cooperation and play hardball in
an attempt to resolve the debt issue, the consequent economic turmoil
(sliding markets, a possible credit downgrade, and government shutdown)
may result in lower electoral gains for both parties.
How Can You Use It?
The prisoner’s dilemma can be used to aid decision-making in a number of
areas in one’s personal life, such as buying a car, salary negotiations and
so on.
For example, assume you are in the market for a new car and you walk into a
car dealership. The utility or payoff, in this case, is a non-numerical
attribute (i.e., satisfaction with the deal). You want to get the best possible
deal in terms of price, car features, etc., while the car salesman wants to
get the highest possible price to maximize his commission.
Cooperation in this context means no haggling; you walk in, pay the sticker
price (much to the salesman’s delight), and leave with a new car. On the
other hand, defecting means bargaining. You want a lower price, while the
salesman wants a higher price. Assigning numerical values to the levels of

12. satisfaction, where 10 means fully satisfied with the deal and 0 implies no
satisfaction, the payoff matrix is as shown below:
Car Buyer vs. Salesman –
Payoff Matrix
Salesman
CooperateDefect
Buyer Cooperate(a) 7, 7 (c) 0,10
Defect (b) 10, 0 (d) 3, 3
What does this matrix tell us? If you drive a hard bargain and get a
substantial reduction in the car price, you are likely to be fully satisfied with
the deal, but the salesman is likely to be unsatisfied because of the loss of
commission (as can be seen in cell b).
Conversely, if the salesman sticks to his guns and does not budge on
price, you are likely to be unsatisfied with the deal while the salesman
would be fully satisfied (cell c).
Your satisfaction level may be less if you simply walked in and paid the full
sticker price (cell a). The salesman in this situation is also likely to be less
than fully satisfied, since your willingness to pay full price may leave him
wondering if he could have “steered” you to a more expensive model, or
added some more bells and whistles to gain more commission.
Cell (d) shows a much lower degree of satisfaction for both buyer and
seller, since prolonged haggling may have eventually led to a reluctant
compromise on the price paid for the car.
Likewise, with salary negotiations, you may be ill-advised to take the first
offer that a potential employer makes to you (assuming you know that
you’re worth more).
Cooperating by taking the first offer may seem like an easy solution in a
difficult job market, but it may result in you leaving some money on the
table. Defecting (i.e., negotiating) for a higher salary may indeed fetch you
a fatter pay package. Conversely, if the employer is not willing to pay
more, you may be dissatisfied with the final offer.

13. Hopefully, the salary negotiations do not turn acrimonious, since that may
result in a lower level of satisfaction for you and the employer. The buyer-
salesman payoff matrix shown earlier can be easily extended to show the
satisfaction level for the job seeker versus the employer.
What Is an Example of the Prisoner's Dilemma?
This “exchange game” has the same structure as the prisoner's dilemma,
and indicates the benefits of cooperation. Greg has a green cap and would
prefer a blue one, while Brenda has a blue cap and would prefer a green
one. Both would rather have two caps to just one and either of the caps to
no cap at all. They are each given a choice between keeping the cap they
have or giving it to the other. Whether Rose keeps her cap or gives it to
Bill, Bill is better off keeping his, and she is better off if he gives it to her.
Whether Bill keeps his cap or gives it to Rose, Rose is better off keeping
hers and he is better off if she gives it to him. The ideal is to have two
caps, but that's only possible if one person behaves selfishly—and it
means one person goes capless. However, both are better off if they
exchange caps than if they just keep the one they have—because it'll be
the color they prefer.
What Is the Dominant Strategy in the Prisoner's
Dilemma?
In the prisoner's dilemma, neither suspect—let's call them Herb and Lee—
knows the decision chosen by the other suspect. Herb is afraid of
remaining silent because in such a case, he can receive more years in
prison if Lee blames him. If Herb chooses to blame Lee, he can be set free
if Lee remains silent. However, that is not likely, because Lee is using the
same rationale and she is also going to blame Herb.
So, the decision of remaining silent by both suspects (the ultimate in trust
and cooperation) provides the more optimal payoff (less jail time for each).
But it's not a really rational option because both parties are bound to act in
their own self-interest and blame the other person, in a shot at doing no
time at all. So, the second-best strategy is for both suspects to confess.
Each will get more jail time than if both had stayed silent—but less than if
one stayed silent and one confessed.
How Do You Beat the Prisoner's Dilemma?
Over time, people have worked out a variety of solutions to prisoner’s
dilemmas in order to overcome individual incentives in favor of the

14. common good. In the real world, most economic and other human
interactions are repeated more than once. A true prisoner's dilemma is
typically played only once; with repetition, people can begin to predict
others' behavior and learn from mistakes and adverse outcomes.
People have developed formal institutional strategies to alter the incentives
that individual decision-makers face. Collective action to enforce
cooperative behavior through reputation, rules, laws, democratic or
another collective decision making, and explicit social punishment for
defections transforms many prisoner’s dilemmas toward the more
collectively beneficial cooperative outcomes.
Also, some people and groups of people have developed psychological
and behavioral biases over time such as higher trust in one another, long-
term future orientation in repeated interactions, and inclinations toward
positive reciprocity of cooperative behavior or negative reciprocity of
defecting behaviors. These tendencies may evolve through a kind
of natural selection within a society over time or group selection across
different competing societies. In effect, they lead groups of individuals to
“irrationally” choose outcomes that are actually the most beneficial to all of
them together.
The tragedy of the commons is a prime example of the prisoner's dilemma
operating in an economy. It may be in everyone’s collective advantage to
conserve and reinvest in the propagation of a common pool natural
resource in order to be able to continue consuming it, but each individual
always has an incentive to instead consume as much as possible as
quickly as possible, which then depletes the resource.
The Bottom Line
The prisoner’s dilemma shows us that mere cooperation is not always in
one’s best interests. In fact, when shopping for a big-ticket item such as a
car, bargaining is the preferred course of action from the consumers' point
of view. Otherwise, the car dealership may adopt a policy of inflexibility in
price negotiations, maximizing its profits but resulting in consumers
overpaying for their vehicles.
Understanding the relative payoffs of cooperating versus defecting may
stimulate you to engage in significant price negotiations before you make a
big purchase.