Chapter 9: Games and Strategic Behavior

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Chapter 9: Games and Strategic Behavior


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Learning Objectives

1. Describe the basic elements of a game2. Define and find an equilibrium for a game3. Recognize and show the effects of

dominant strategies.4. Define and explain the Prisoner's

Dilemma and how it applies to real-world situations

5. Show how games in which timing matters differ from games in which it does not.

6. Discuss commitment problems and explain how altering preferences can solve commitment problems


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Story

At a dinner party in 1997, Hollywood actor Robert DeNiro pulled singer Tony Bennett aside: “Hey, Tony - there’s a film I want you in,” DeNiro said

Bennett heard nothing further about the project for almost a year. Then his son and financial manager, got a phone call from Warner Brothers, in which the studio offered Tony $15,000 to sing in the movie’s final scene As Danny described the conversation, “. . . they

made a fatal mistake. They told me they had already shot the film

Warner Brothers wound up paying $200,000 for Bennett’s performance


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Strategies and Payoffs

Actions have payoffs that depend on The actions When they are taken The actions of others

Some markets are characterized by interdependence Apply to monopolistic competition and

oligopoly An imperfectly competitive firm weigh the likely

responses of rivals when deciding whether to cut prices or to increase its advertising budget

• Interdependencies of this sort are the rule rather than the exception in economic and social life


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Using Game Theory to Analyze Strategic Decisions

A game has three basic elements 1. The players2. Their available strategies, actions, or

decisions3. The payoff to each player for each

possible action


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Etihad Airways and Emirates – Scenario 1

Players: Etihad and Emirates are the only carriers supplying non-stop service to Casablanca, Morocco

Assumption Each earns an economic profit of

$6,000 per flight All payoffs are known to all parties

Strategies: Increase advertising by $1,000 or not


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Payoff Matrix

Payoff is symmetricDominant strategy is raise advertising

spending Both companies are worse off

Emirates Airlines Options

Etihad Airways Options

Raise Spending No Raise

Raise Spending

Etihad: $5,500

Emirates: $5,500

Etihad: $8,000

Emirates: $2,000

No RaiseEtihad: $2,000

Emirates: $8,000

Etihad: $6,000

Emirates: $6,000


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Etihad Airways and Emirates – Scenario 1

In this particular game, no matter which strategy Emirates chooses, Etihad will earn a higher economic profit by increasing its spending on advertising Since this game is perfectly symmetric, a

similar conclusion holds for Emirates

A dominant strategy is one that yields a higher payoff no matter what the other player does A Dominated strategy is any other

strategy available to a player who has a dominant strategy


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Equilibrium in a Game

Nash equilibrium is any combination of strategies in which each player’s strategy is her or his best choice, given the other player’s strategies Equilibrium occurs when each player

follows his dominant strategy, if it exists Following Scenario 1: (raise spending; raise

spending) is a Nash equilibrium However, a Nash equilibrium can also

occur in games with no dominant strategy Scenario 2


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Etihad and Emirates– Scenario 2

Same situation Different payoffs; non-symmetric

Emirates raises spending Etihad anticipates Emirates action; does not raise

Emirates Airlines Options

Etihad Options Raise Spending No Raise

Raise Spending

Etihad: $3,000

Emirates: $4,000

Etihad $8,000

Emirates $3,000

No Raise

Etihad: $4,000

Emirates: $5,000

Etihad: $5,000

Emirates: $2,000


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Prisoner’s Dilemma

The advertising example belongs to an important class of games referred to as prisoner’s dilemma prisoner’s dilemma: a game in

which each player has a dominant strategy, and when each plays it, the resulting payoffs are smaller than if each had played a dominated strategy


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Prisoner's Dilemma

The prisoner's dilemma has a dominant strategy

The resulting payoffs are smaller than if each had stayed silent

Murtashi’s Options

Rashi's Options

Confess Don't Confess

ConfessRashi: 5 years

Murtashi: 5 years

Rashi: 0 years

Murtashi:20 years

Don't Confess

Rashi: 20 years

Murtashi: 0 years

Rashi: 1 year

Murtashi: 1 year

Dominant strategy

Optimal strateg

y


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The Economics of Cartels

A cartel is a coalition of firms that agree to restrict output to increase economic profit Restrict total output

Allocate quotas to each player

The problem confronting oligopolists who are trying to form a cartel is a classic illustration of the prisoner’s dilemma


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Cartel in Action

Two suppliers (Aquapure and Mountain Spring) of bottled water agree to split the market equally Each firm draws water free of charge

from a mineral spring located on its own land. Customers supply their own bottles Marginal cost is zero

Agreement is not legally enforceable Price is set at monopoly level

If one party charges less, he gets all of the market


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Bottled Water Cartel

Each party has an incentive to lower the price a little to increase its economic profits

Successive reductions result in price equal to marginal cost

Monopoly price: $1 Each firm profit

= $500 Decrease price to

0.9 and receive profit of $990


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Bottled Water Cartel

Mountain Spring's Options

Aquapure's Options

Charge $1 Charge $0.90

Charge $1Aquapure: $500

Mtn Spring: $500

Aquapure: $0

Mtn Spring: $990

Charge $0.90

Aquapure: $990

Mtn Spring: $0

Aquapure: $495

Mtn Spring: $495


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Repeated Prisoner's Dilemma

Two players with repeated interactionsTit-for-tat strategy says my move in

this round is whatever your move was in the last round

If you defected, I defect Tit-for-tat strategy limits defections

Tit-for-tat is rarely observed in the market This strategy breaks down with more than

two players or potential players Each player has to have significant stake in

future outcomes


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Ban on TV Ads for Cigarettes

Advertising shifts demand rightward for two reasons

First, people who have never used that type of product learn about it, and some buy it

Second, people who consume a different brand of the product may switch brands The first effect boosts sales industry-wide;

the second only redistributes existing sales among brands

Although advertising produces both effects in the cigarette industry, its primary effect is brand switching


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Ban on TV Ads for Cigarettes

U.S. Congressional ban started 1/1/1971 Advertising spending decreased by

$60 million Legislation moved players to optimal

outcome!!Philip Morris's Options

RJR's Options TV Ads No TV Ads

TV adsRJR: $10 M

Philip Morris: $10 M

RJR: $35 M

Philip Morris: $5 M

No TV adsRJR: $5 M


RJR: $20 M



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Why do People Shout at Parties?

If everyone spoke at a normal volume at parties, the overall noise level would be lower, and people would hear just as well So why do people shout?

Party begins with everyone speaking at normal volume More people arrive conversation partners have

difficulty hearing one another (its getting crowded) The natural solution, from the point of the

individual, is to simply raise one’s voice a bit But that is also the natural solution for everyone else No matter what others do, the individual will do better by

speaking more loudly Shouting is the dominant strategy


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Sometimes Timing Matters

In the games discussed so far, players were assumed to choose their strategies simultaneously, and which player moved first didn’t matter

For example, in the prisoner’s dilemma, self-interested players would follow their dominant strategies even if they knew in advance what strategies their opponents had chosen

But in other situations, such as the negotiations between Warner Brothers and Tony Bennett described at the beginning of this chapter, timing is of the essence


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Simultaneous Decisions

Dodge Viper's Options

Chevy Corvette's

OptionsHybrid No Hybrid

Hybrid

Chevy:

$60 MDodge:

$60 M

Chevy:

$80 MDodge:

$70 M

No hybrid

Chevy:

$70 MDodge:

$80 M

Chevy:

$50 MDodge:

$50 M


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From the previous slide, we can see that neither company has a dominant strategy, but we can see that In the upper-right cell, Chevrolet wouldn’t want to

change (that cell is, after all, the best possible outcome for Chevrolet) and neither would Dodge (since switching to a hybrid would reduce its profit from $70 million to $60 million)

Same applies to the lower-left cell Both these cells represent Nash equilibria

However, without being told more, we simply cannot predict where the two companies will end up


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For games in which timing matters, a decision tree, or game tree, is a more useful way of representing the payoffs than a traditional payoff matrix Decision tree: a diagram that describes

the possible moves in a game in sequence and lists the payoffs that correspond to each possible combination of moves

One party moves first The second can adjust his strategy accordingly


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$80 million for Chevy$70 million for Dodge

$70 million for Chevy$80 million for DodgeE

F

$50 million for Chevy$50 million for DodgeG

$60 million for Chevy$60 million for Dodge

D

FinalOutcome

Suppose Dodge Moves First

Dodgedecides

A

Offer hybrid

Don’t offer

hybrid

B

C

Offerhybrid

Don’toffer

hybrid

Offerhybrid

Don’toffer

hybrid

Chevroletdecides


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In thinking strategically about this game, the key for Dodge is to put itself in Chevrolet’s shoes and imagine how Chevrolet would react to the various choices it might confront

In general, it will make sense for Dodge to assume that Chevrolet will respond in a self-interested way So when Dodge has the first move in this

game, its best strategy is to offer a hybrid Chevrolet then follows by choosing not to offer one


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Threats and Promises

Could Chevrolet have deterred Dodge from offering a hybrid by threatening to offer a hybrid of its own, no matter what Dodge did? The problem with this strategy is such

a threat would not have been credibleCredible threat is a threat to take

an action that is in the threatener's best interest to carry out Analyze This and Tony Bennett's

compensation


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Threats and Promises

Just as in some games credible threats are impossible to make, in others credible promises are impossible A credible promise is a promise to take an action

that is in the promiser's interest to carry out The owner of a thriving business wants to

start up an office in a distant city If she hires someone to manage the new

office, she can afford to pay a weekly salary of $1,000 The manager could earn $500 working elsewhere The owner earns a weekly economic profit of

$1,000 for herself


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The Remote Office

The owner’s concern is that she will not be able to monitor the manager’s behavior

The owner knows that by managing the remote office dishonestly, the manager can boost his take-home pay to $1,500 while causing the owner an economic loss of $500 per week. Will she open the new office?

Players: Business owner and remote office manager

Options: Business owner can open the office or not Manager can be honest or not


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Remote Office Pay-Off

A

No remote office

Managerial candidatepromises honesty

B

Open remote office

Honest managerOwner: $1,000Manager: $1,000

C

Dishonest ManagerOwner: -$500Manager: $1,500

Owner: $0Manager: $500working elsewhere


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Monopolistic Competition and Location

First mover advantage With Viper and Corvette, firms did

better if products were different Tic-tac-toe

If the differentiator is time or location, the last mover may have the advantage Suppose that customers go to the

nearest convenience store Store A is located 1 mile from Freeway Where will Store B be located?


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Store B's Location

A chooses its locationNew business plans to enter the market

Location C minimizes customer's travel distance

Location B maximizes customers

Freeway

1 mile1,200 people

A B

C⅓ mile800 people

⅓ mile800 people

⅓ mile800 people

1 mile1,200 people


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Commitment Problems

A commitment problem arises from an inability to make credible threats or promises Example: prisoner’s dilemma Commitment problems could be

solved with a device A commitment device changes

incentives to make threats or promises credible

• Tips for waiters


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Restaurant Service

Restaurant wants to provide superior service Increases pay of wait-staff; monitoring

problem If wait-staff are not diligent, restaurant

wasted money Restaurant cannot insure good service

by paying higher wagesRepeat customers can ensure good

service by tipping A one-time, self-interested diner will not

tip


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The Strategic Role of Preferences

Game theory assumes that the goal of the players is to maximize their outcome Get the highest monetary payoff, the

shortest jail sentence, the best chance to be heard, etc…

Ironically, in most games, players do not attain the best outcomes

Altering psychological incentives may improve the outcome of a game


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Honest Manager for Remote Office

A

Honest ManagerOwner: $1,000

Manager: $1,000

Managerial candidatepromises honesty

B

C

Owner: $0Manager: works

elsewhere for $500

No remote office

Openremote office Dishonest Manager

Owner: $500Manager: – $8,500

An honest manager earns

more than a dishonest manager


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Self-Interest Evaluated

There are exceptions to outcomes based on self-interest Tips at out-of-town restaurants Revenge Passing on "unfair" opportunities


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The Strategic Role of Preferences

Preferences are given; however: Preferences affect choices through

Sympathy for an adversary Generosity Honesty

Commitment problem is reduced if preferences can be known to the other party and affect the other party Example: Trustworthy employee


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Character Judgments

If character were known perfectly, businesses could avoid the costs of dishonesty, shirking, etc. Since people are victimized, make

hiring mistakes, and so on, either Character cannot be judged perfectly OR Character information is expensive.


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Caveat Emptor

The payoff of deceit Advantage to seeming honest while

being dishonest Greater opportunities Greater exploitation of opportunities

Documents

Chapter 9: Games and Strategic Behavior