chapter 9: games and strategic behavior
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Chapter 9: Games and Strategic Behavior. Learning Objectives. Describe the basic elements of a game Define and find an equilibrium for a game Recognize and show the effects of dominant strategies. Define and explain the Prisoner's Dilemma and how it applies to real-world situations - PowerPoint PPT PresentationTRANSCRIPT
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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
Philip Morris: $35 M
RJR: $20 M
Philip Morris: $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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Sometimes Timing Matters
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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Sometimes Timing Matters
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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Sometimes Timing Matters
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