GAME THEORY AND INFORMATION
ECO 2023
Principles of Microeconomics
Dr. McCaleb
Game Theory and Information
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TOPIC OUTLINE
I.
Game Theory
II. Economics of Information
Game Theory and Information
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Game Theory
Game Theory and Information
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GAME THEORY
 Basic Elements of Game Theory
Definition
Game theory is the study of strategic behavior—behavior that
recognizes mutual interdependence and takes account of the expected
behavior of others.
Any exchange or interaction among individuals that involves the
possibility of strategic behavior can be analyzed as a game. In a
game, the outcome for each individual depends not only on that
individual’s decisions but also on the decisions of other individuals.
Game Theory and Information
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GAME THEORY
 Basic Elements of Game Theory
Three elements of a game
Players: The individuals involved in the exchange or interaction
Strategies: The possible decisions or choices made by each individual
Payoffs: The gain or loss to each individual
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GAME THEORY
 Single-Play Games
Oligopoly behavior can be modeled as a game
Suppliers in a cartel recognize their interdependence. Each supplier is
aware its price/quantity decisions affect other suppliers’ profits. Each
supplier is aware that its profits are affected by the price/quantity
decisions of other suppliers.
Oligopoly markets are characterized by strategic behavior which is
best analyzed using game theory.
The airframe industry duopoly provides an arena for the application of
game theory.
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GAME THEORY
Payoff Matrix
The table shows data from the
industry demand and revenue
schedule in the previous lecture.
The table is called a payoff matrix.
Each row shows a strategy choice
for Boeing. Each column shows a
strategy choice for Airbus.
Each cell shows the payoffs to
Boeing (gold) and Airbus (red).
The sum of the payoffs to the two
duopolists is the total industry
economic profit.
Boeing’s Strategies
Airbus’s Strategies
Game Theory and Information
4/week
3/week
$32 m.
$30 m.
$32 m.
$40 m.
$40 m.
$36 m.
$30 m.
$36 m.
4/week
3/week
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GAME THEORY
Cooperative Solution
The strategy choice (3 /week, 3
/week) is the cooperative solution
to this game.
Boeing’s Strategies
If the duopolists cooperate and
reach agreement, they restrict total
industry quantity to 6 planes. Total
industry profits (“joint profits”) are
$72 m.
Airbus’s Strategies
Without an effective means of
enforcement, the cooperative
solution is not an equilibrium for
the game. Why not?
Game Theory and Information
4/week
3/week
$32 m.
$30 m.
$32 m.
$40 m.
$40 m.
$36 m.
$30 m.
$36 m.
4/week
3/week
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GAME THEORY
Incentives to Cheat
Suppose they split the market,
each duopolist producing 3 planes
per week. Each duopolist earns
$36 m. in weekly economic profit.
Boeing has an incentive to increase
production from 3 to 4. Its profits
increase to $40 m. Airbus has the
same incentive.
Boeing’s Strategies
Airbus’s Strategies
The result is both produce 4
planes/week, industry profits are
$64 m., and each supplier earns
$32 m. in economic profit.
Game Theory and Information
4/week
3/week
$32 m.
$30 m.
$32 m.
$40 m.
$40 m.
$36 m.
$30 m.
$36 m.
4/week
3/week
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GAME THEORY
Non-cooperative Solution
It results if the duopolists are
unable to form a successful cartel
and end up competing with one
another.
Boeing’s Strategies
Cell I where each supplier
produces 4 planes/week and earns
$32 m. is the non-cooperative
solution to the game.
Airbus’s Strategies
In this game, the non-cooperative
solution minimizes industry
profits.
Game Theory and Information
4/week
3/week
$32 m.
$30 m.
$32 m.
$40 m.
$40 m.
$36 m.
$30 m.
$36 m.
4/week
3/week
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GAME THEORY
Nash Equilibrium
At the non-cooperative solution
(4/week, 4/week), neither Boeing
nor Airbus has any incentive to
change its strategy choice.
As long as Boeing produces 4
planes, Airbus’s best strategy is to
produce 4 planes, and conversely.
The non-cooperative solution is a
Nash equilibrium—an equilibrium
in which each player takes the best
possible action given the action of
the other player.
Boeing’s Strategies
Airbus’s Strategies
Game Theory and Information
4/week
3/week
$32 m.
$30 m.
$32 m.
$40 m.
$40 m.
$36 m.
$30 m.
$36 m.
4/week
3/week
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GAME THEORY
Dominant Strategies
Airbus’s Strategies
Whether Airbus picks 3/week or
4/week, Boeing’s dominant
strategy is 4/week. Whether
Boeing picks 3/week or 4/week,
Airbus’s dominant strategy is
4/week.
Boeing’s Strategies
In this particular game, the Nash
equilibrium is also a dominant
strategy equilibrium.
A dominant strategy is the best
choice no matter what the other
player chooses.
Game Theory and Information
4/week
3/week
$32 m.
$30 m.
$32 m.
$40 m.
$40 m.
$36 m.
$30 m.
$36 m.
4/week
3/week
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GAME THEORY
 Single-Play Games
Comments
A Nash equilibrium is not unique. The same game may have more
than one Nash equilibrium.
A dominant strategy equilibrium is always a Nash equilibrium, but a
Nash equilibrium is not always a dominant strategy equilibrium.
A game in which at least one player does not have a dominant
strategy does not have a dominant strategy equilibrium.
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In a Nash equilibrium, each player takes the best possible
action given the action of the other player. In the video, is the
strategy choice “Empire State Building at noon” a Nash
equilibrium?
1.
Yes
2. No
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In the video, is the strategy choice “Times Square at noon” a
Nash equilibrium?
1.
Yes
2. No
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GAME THEORY
 Repeated Games
Definition
A game played more than once by the same players with the same
strategy choices.
Repeated games may be played indefinitely or a fixed number of
times. This makes a significant difference.
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GAME THEORY
Repeated Oligopoly Game
In Week 2, Boeing increases
production to 4 planes/week. It
gains $4 m. in profit.
Boeing’s Strategies
Suppose in Week 1 Boeing and
Airbus have reached a cartel
agreement to restrict quantity to 6
planes/week and to split the market
(Cell IV).
Airbus’s Strategies
In Week 3, Airbus retaliates by
producing 4 planes/week. Boeing’s
profits decrease to $32 m.
Game Theory and Information
4/week
3/week
$32 m.
$30 m.
$32 m.
$40 m.
$40 m.
$36 m.
$30 m.
$36 m.
4/week
3/week
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GAME THEORY
Repeated Oligopoly Game
If Boeing reduces production to 3
planes, it earns only $30 m., a
reduction of $2 m. But if Airbus
reduces production in Week 5 to 3
planes, we are back to the
cooperative solution where joint
profits are maximized.
Boeing’s Strategies
What is Boeing’s best strategy in
Week 4? If it continues to produce
4 planes, Airbus will continue to
produce 4 planes, and each will
earn profits of $32 m.—the noncooperative solution.
Airbus’s Strategies
Game Theory and Information
4/week
3/week
$32 m.
$30 m.
$32 m.
$40 m.
$40 m.
$36 m.
$30 m.
$36 m.
4/week
3/week
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GAME THEORY
 Repeated Games
Tit-for-tat strategy
This is a tit-for-tat strategy. As long as Boeing chooses the
cooperative strategy in the previous play of the game, Airbus chooses
the cooperative strategy in the current play of the game. If Boeing
deviated from the cooperative strategy in the previous play, Airbus
deviates in the current play.
Boeing follows the same strategy.
It can be shown that over repeated plays of a game, a tit-for-tat
strategy is the best choice for both players. A tit-for-tat strategy
provides a built-in means of enforcement for a cartel agreement.
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GAME THEORY
 Repeated Games
Problems with tit-for-tat
A successful tit-for-tat strategy requires detecting cheating and
identifying cheaters against whom to retaliate. If detection and
punishment of cheaters is costly, the cost may outweigh the gains
from choosing the cooperative strategy.
The larger the number of players in the game, the more costly is
detection and punishment of cheaters likely to be.
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GAME THEORY
 Repeated Games
Endgame problem
Suppose at the beginning of Week 1, Airbus announces its intention
to cease production at the end of Week 5. With no threat of
retaliation, Airbus’s best strategy in Week 5 is to increase production
to 4 planes. If Boeing anticipates this strategy change by Airbus,
Boeing will increase its production in Week 5 to 4 planes.
Anticipating that Boeing will change its strategy in Week 5, Airbus
has an incentive to increase production in Week 4. But if Boeing
anticipates that Airbus will increase production in Week 4, Boeing
has an incentive to increase its production in Week 4.
This is the endgame problem.
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GAME THEORY
 Repeated Games
Finite and indefinite repeated games
Because of the endgame problem, even the tit-for-tat strategy may
not be a sufficient means of enforcement in a finite repeated game.
The non-cooperative solution emerges again as the likely equilibrium
in this kind of game.
Tit-for-tat is more likely to be a sufficient means of enforcement in
an indefinite repeated game. Therefore, the cooperative solution is
most likely to be an equilibrium in this kind of game.
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A tit-for-tat strategy is most likely to be a successful means of
enforcement in
1.
a single-play game.
2. a single-play repeated game.
3.
a finite repeated game.
4.
an indefinite repeated game.
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Economics of Information
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ECONOMICS OF INFORMATION
 Asymmetric Information
Asymmetric information is a source of inefficiency
Asymmetric information exists when one party to a transaction has
more or better relevant information than the other party.
Asymmetric information increases the cost to the less-informed
person of entering into a transaction with the better-informed person.
As a result of asymmetric information, some exchanges that would
make both individuals better off if they had the same information
may not occur.
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ECONOMICS OF INFORMATION
 Asymmetric Information
Two kinds of asymmetric information
• Moral hazard
• Adverse selection
Two approaches to dealing with asymmetric
information
• Signaling
• Screening
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ECONOMICS OF INFORMATION
 Moral hazard
Moral hazard arises in a principal-agent relationship
A principal-agent relationship exists when one person, called the
agent, is performing some task on behalf of the other person, called
the principal.
Moral hazard: If the principal is unable to perfectly monitor the
performance of the agent, the agent has an incentive to pursue
her/his own self-interest rather than the interest of the principal.
Also known as the principal-agent problem.
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ECONOMICS OF INFORMATION
 Moral hazard
Example: Employment relationships
The employer is the principal; the employee is the agent.
If the employer is unable to perfectly monitor employee
performance, the employee has an incentive to put forth less than
maximum effort.
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ECONOMICS OF INFORMATION
 Moral hazard
Example: Automobile repairs
The automobile owner is the principal; the mechanic is the agent.
If the owner is less knowledgeable about automobiles than the
mechanic, the mechanic may sell the owner unneeded repairs or may
bill the owner for work that is not actually performed.
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ECONOMICS OF INFORMATION
 Moral hazard
Example: Property and casualty insurance
The term “moral hazard” was first used to describe a problem with
insurance. In the insurance context, the insurance company is the
principal, and the policyholder is the agent.
An individual who has insurance has less incentive to behave in
ways that minimize the probability of the event against which s/he is
insured.
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ECONOMICS OF INFORMATION
 Moral hazard
Moral hazard in insurance
People with health insurance consume more healthcare and incur
more health expenses than they would if they didn’t have insurance.
People with property insurance are more likely to live in coastal
areas and floodplains than they would if they didn’t have insurance.
People with theft insurance are less likely to purchase home alarm
systems than if they did not have insurance.
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ECONOMICS OF INFORMATION
 Moral hazard
Mitigating moral hazard
Faced with the potential for moral hazard, what can the principal do?
• Improved monitoring—But the marginal benefit of improved
performance from better monitoring must be weighed against the
marginal cost
• Efficiency wages—Paying workers above-market wages, making
it more costly for them to risk losing their jobs because of
underperformance.
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ECONOMICS OF INFORMATION
 Moral hazard
Mitigating moral hazard
• Regulation—Government regulations and requirements by
insurance policies specifying actions to be taken to reduce moral
hazard
• Payment for results—Ties the agent’s reward to the principal’s
reward, making the agent’s self-interest the same as the
principal’s best interests
• Insurance deductibles and co-payments—Provisions in insurance
contracts that impose costs on policyholders for behaving in
ways that increase the risk or cost of the events for which the
insurance is issued
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ECONOMICS OF INFORMATION
 Adverse selection
Definition
Arises when one party to a transaction knows more about the
attributes of the good being exchanged than the other party.
As a result, the selection of goods available in the market may be
“adverse” to the interests of the less-informed party. It includes a
disproportionately large number with less desirable attributes.
Moral hazard concerns behavior of agents that is adverse to the
interests of the principal. Adverse selection concerns attributes of the
agent that are not readily known to the principal.
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ECONOMICS OF INFORMATION
 Adverse selection
Example: Used cars
Sellers of used cars often know more about the true condition of the
car than buyers.
Because buyers have imperfect information about the condition of
the car, the market price is less than the price they’d be willing to
pay for cars in good condition but more than the price they’d be
willing to pay for cars in bad condition. Good cars are underpriced
and bad cars are overpriced.
The result is that bad cars are more likely to be sold into the used car
market and good cars are less likely to be sold as used cars. The used
car market becomes a “market for lemons”.
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ECONOMICS OF INFORMATION
 Adverse selection
Example: Employment relationships
Potential employees differ in their productivities in ways that are not
easily identified by employers.
If employers are unable to distinguish between high and low
productivity employees, the wage paid is likely to be less than the
marginal product of high-productivity employees but more than the
marginal product of low-productivity employees.
As a result, high-productivity employees are more likely to leave
and low-productivity employees are less likely to leave. The
employer ends up with a disproportionate number of lowproductivity workers.
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ECONOMICS OF INFORMATION
 Adverse selection
Example: Insurance
People have better information about their health status than health
insurers do.
Because the insurance company cannot distinguish between people
on the basis of their health status, the premium is less than the
amount required to cover the costs of sicker-than-average people but
more than the amount required to cover the costs of healthier-thanaverage people.
The high price is a disincentive for people in good health to buy
insurance and the insurance company ends up with a pool that
includes a disproportionately high number of sicker-than-average
people.
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If the principal is unable to perfectly monitor the performance of the
agent, the agent has an incentive to pursue her/his own self-interest rather
than the interest of the principal. This is the definition of
1.
moral hazard.
2.
adverse selection
3.
signaling
4.
screening
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__________ arises when one party to a transaction knows more about the
attributes of the good being exchanged than the other party.
1.
moral hazard.
2.
adverse selection
3.
signaling
4.
screening
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ECONOMICS OF INFORMATION
 Signaling
Definition
With asymmetric information, the less-informed party is unwilling to
enter into transactions that would make both parties better off
because the more-informed party has relevant private or hidden
information not available to the less-informed party.
The better-informed party may attempt to induce the less-informed
party to enter into a mutually beneficial transaction by signaling—
actions taken by the better informed party intended to convey the
private or hidden information to the other party.
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ECONOMICS OF INFORMATION
 Signaling
Example: Advertising
Why do advertisers pay large sums of money to have celebrities
promote their products? Do buyers really trust a celebrity to know
anything relevant about the product?
Buyers know that celebrities, unlike unknown commercial actors,
are expensive. Incurring the expense of hiring a celebrity to promote
a product may be a signal to buyers about the quality and reliability
of the product.
It isn’t actually the celebrity that’s conveying information, it’s the
amount of money the supplier is willing to spend on advertising. The
celebrity is just evidence of this willingness.
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ECONOMICS OF INFORMATION
 Signaling
Example: Education
Why do college graduates earn more than high school graduates?
The human capital theory says that education increases productivity.
But many college graduates occupy jobs that do not actually make
use of any skill or knowledge that is learned in college.
An alternative hypothesis is that a college degree is not in fact
evidence of any special skills or knowledge acquired in college, but
a signal that the holder has certain attributes desired by employers—
intelligence, persistence, ambition, a more long-term view, a greater
“work ethic”.
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ECONOMICS OF INFORMATION
 Signaling
When is a signal credible?
For a signal to be credible, it must satisfy two conditions:
• Sending the signal must be costly. Otherwise, everyone would
send a signal and the signal would be meaningless.
• The cost to send the signal must be less or the benefit from sending
the signal must be greater for people with more desirable attributes
so that people with more desirable attributes have a greater
incentive to send the signal.
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ECONOMICS OF INFORMATION
 Screening
Definition
Signaling occurs when the better-informed party takes actions to
convey information to the less-informed party. Screening occurs
when the less-informed party takes actions intended to elicit private
or hidden information from the better-informed party.
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ECONOMICS OF INFORMATION
 Screening
Example: Education
Why do employers require a college degree for jobs that do not
actually make use of any skill or knowledge that is learned in
college?
Much like the signaling hypothesis, requiring a college degree is a
way for employers to identify those individuals who have more
desirable attributes.
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ECONOMICS OF INFORMATION
 Screening
Example: Insurance
Good student discounts—Obviously, not every good student is a
better risk, but if on average good students are a better risk, then
good driver discounts are an effective and low cost way of screening
the more risky young drivers from the less risky.
High deductible policies—The insurer doesn’t know who the highrisk drivers are, but because a high deductible is more costly to a
risky driver than to a safer driver, high-risk drivers are less likely to
buy high-deductible policies. The insurer offers two types of
policies—one with a high premium and a low deductible, the other
with a low premium and a high deductible—as a way of screening
the high-risk drivers from the low-risk drivers.
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For a signal to be credible, it must
i. be costly to send.
ii. be more costly or more beneficial to people with more desirable
attributes.
1.
i only
2.
ii only
3.
Both i and ii
4.
Neither i nor ii
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