game theory and information1 game theory and information eco 2023 principles of microeconomics dr....

Game Theory and Information 1

GAME THEORY AND INFORMATION

ECO 2023Principles of Microeconomics

Dr. McCaleb


TOPIC OUTLINE

I. Game Theory

II. Economics of Information


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


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

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.

GAME THEORY


4/week 3/week

4/week

$32 m. $30 m.

$32 m. $40 m.

3/week

$40 m. $36 m.

$30 m. $36 m.

Airbus’s Strategies

Boe

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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.

Payoff Matrix

GAME THEORY


4/week 3/week

4/week

$32 m. $30 m.

$32 m. $40 m.

3/week

$40 m. $36 m.

$30 m. $36 m.


Boe

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If the duopolists cooperate and reach agreement, they restrict total industry quantity to 6 planes. Total industry profits (“joint profits”) are $72 m.

The strategy choice (3 /week, 3 /week) is the cooperative solution to this game.

Without an effective means of enforcement, the cooperative solution is not an equilibrium for the game. Why not?

Cooperative Solution

GAME THEORY


4/week 3/week

4/week

$32 m. $30 m.

$32 m. $40 m.

3/week

$40 m. $36 m.

$30 m. $36 m.


Boe

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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.

The result is both produce 4 planes/week, industry profits are $64 m., and each supplier earns $32 m. in economic profit.

Incentives to Cheat

GAME THEORY


4/week 3/week

4/week

$32 m. $30 m.

$32 m. $40 m.

3/week

$40 m. $36 m.

$30 m. $36 m.


Boe

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Cell I where each supplier produces 4 planes/week and earns $32 m. is the non-cooperative solution to the game.

It results if the duopolists are unable to form a successful cartel and end up competing with one another.

In this game, the non-cooperative solution minimizes industry profits.

Non-cooperative Solution

GAME THEORY


4/week 3/week

4/week

$32 m. $30 m.

$32 m. $40 m.

3/week

$40 m. $36 m.

$30 m. $36 m.


Boe

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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.

Nash Equilibrium

GAME THEORY


4/week 3/week

4/week

$32 m. $30 m.

$32 m. $40 m.

3/week

$40 m. $36 m.

$30 m. $36 m.


Boe

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In this particular game, the Nash equilibrium is also a dominant strategy equilibrium.

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.

A dominant strategy is the best choice no matter what the other player chooses.

Dominant Strategies

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.

GAME THEORY


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


In the video, is the strategy choice “Times Square at noon” a Nash equilibrium?

1. Yes

2. No


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.

GAME THEORY


4/week 3/week

4/week

$32 m. $30 m.

$32 m. $40 m.

3/week

$40 m. $36 m.

$30 m. $36 m.


Boe

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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).

In Week 2, Boeing increases production to 4 planes/week. It gains $4 m. in profit.

In Week 3, Airbus retaliates by producing 4 planes/week. Boeing’s profits decrease to $32 m.

Repeated Oligopoly Game

GAME THEORY


4/week 3/week

4/week

$32 m. $30 m.

$32 m. $40 m.

3/week

$40 m. $36 m.

$30 m. $36 m.


Boe

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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 non-cooperative solution.

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.

Repeated Oligopoly Game

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.

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.

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.

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.

GAME THEORY


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.


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.

ECONOMICS OF INFORMATION


Asymmetric Information

Two kinds of asymmetric information

• Moral hazard

• Adverse selection

Two approaches to dealing with asymmetric information

• Signaling

• Screening



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.



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.



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.



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.



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.



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.



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



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.



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”.



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 low-productivity workers.



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-than-average 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.



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


__________ 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


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.



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.



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”.



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.



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.



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.



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 high-risk 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.



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

game theory and information1 game theory and information eco 2023 principles of microeconomics dr....

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