Chapter 13
Game Theory
and Competitive
Strategy
Topics to be Discussed

Gaming and Strategic Decisions

Dominant Strategies

The Nash Equilibrium Revisited

Repeated Games
Chapter 13
Slide 2
Topics to be Discussed

Sequential Games

Threats, Commitments, and Credibility

Entry Deterrence

Bargaining Strategy
Chapter 13
Slide 3
Gaming and Strategic Decisions

“If I believe that my competitors are
rational and act to maximize their own
profits, how should I take their behavior
into account when making my own
profit-maximizing decisions?”

Definition of a game
Chapter 13
Slide 4
Gaming and Strategic Decisions

Noncooperative versus Cooperative
Games

Cooperative Game

Players negotiate binding contracts that
allow them to plan joint strategies
 Example:
Buyer and seller negotiating the
price of a good or service or a joint venture
by two firms (i.e. Microsoft and Apple)
 Binding contracts are possible
Chapter 13
Slide 5
Gaming and Strategic Decisions

Noncooperative versus Cooperative
Games

Noncooperative Game

Negotiation and enforcement of a
binding contract are not possible
 Example:
Two competing firms assuming
the others behavior determine,
independently, pricing and advertising
strategy to gain market share
 Binding contracts are not possible
Chapter 13
Slide 6
Gaming and Strategic Decisions

Noncooperative versus Cooperative
Games

Chapter 13
“The strategy design is based on
understanding your opponent’s point of
view, and (assuming you opponent is
rational) deducing how he or she is likely to
respond to your actions”
Slide 7
Dominant Strategies

Dominant Strategy
 One
that is optimal no matter what an
opponent does.
 An
Chapter 13
Example

A & B sell competing products

They are deciding whether to undertake
advertising campaigns
Slide 8
Payoff Matrix for Advertising Game
Firm B
Advertise
Advertise
Don’t
Advertise
10, 5
15, 0
6, 8
10, 2
Firm A
Don’t
Advertise
Chapter 13
Slide 9
Payoff Matrix for Advertising Game

Observations


Chapter 13
A: regardless of
B, advertising is
the best
B: regardless of
A, advertising is
best
Firm B Don’t
Advertise
Advertise
Advertise
10, 5
15, 0
6, 8
10, 2
Firm A
Don’t
Advertise
Slide 10
Payoff Matrix for Advertising Game

Observations



Chapter 13
Dominant
strategy for A &
B is to advertise
Do not worry
about the other
player
Firm B Don’t
Advertise
Advertise
Advertise
10, 5
15, 0
6, 8
10, 2
Firm A
Don’t
Advertise
Equilibrium in
dominant
strategy
Slide 11
Dominant Strategies

Game Without Dominant Strategy
 The
optimal decision of a player without a
dominant strategy will depend on what the
other player does.
Chapter 13
Slide 12
Modified Advertising Game
Firm B
Advertise
Advertise
Don’t
Advertise
10, 5
15, 0
6, 8
20, 2
Firm A
Don’t
Advertise
Chapter 13
Slide 13
Modified Advertising Game

Observations



A: No dominant
strategy;
depends on B’s
actions
B: Advertise
Question

Firm B Don’t
Advertise
Advertise
Advertise
10, 5
15, 0
6, 8
20, 2
Firm A
Don’t
Advertise
What should A
do? (Hint:
consider B’s
decision
Chapter 13
Slide 14
The Nash Equilibrium Revisited

Dominant Strategies

“I’m doing the best I can no matter what
you do.”

“You’re doing the best you can no matter
what I do.”
Chapter 13
Slide 15
The Nash Equilibrium Revisited

Nash Equilibrium

“I’m doing the best I can given what you
are doing”

“You’re doing the best you can given what I
am doing.”
Chapter 13
Slide 16
The Nash Equilibrium Revisited
Product Choice Problem

Examples With A Nash Equilibrium

Two cereal companies

Market for one producer of crispy cereal

Market for one producer of sweet cereal

Each firm only has the resources to
introduce one cereal

Noncooperative
Chapter 13
Slide 17
Product Choice Problem
Firm 2
Crispy
Crispy
Sweet
-5, -5
10, 10
10, 10
-5, -5
Firm 1
Sweet
Chapter 13
Slide 18
Product Choice Problem

Question

Is there a Nash
equilibrium?

If not, why?

If so, how can
it be reached
Firm 2
Crispy
Crispy
-5, -5
10, 10
10, 10
-5, -5
Firm 1
Sweet
Chapter 13
Sweet
Slide 19
The Nash Equilibrium Revisited

Maximin Strategies
 Scenario
Chapter 13

Two firms compete selling file-encryption
software

They both use the same encryption
standard (files encrypted by one
software can be read by the other advantage to consumers)
Slide 20
The Nash Equilibrium Revisited

Maximin Strategies
 Scenario
Chapter 13

Firm 1 has a much larger market share
than Firm 2

Both are considering investing in a new
encryption standard
Slide 21
Maximin Strategy
Firm 2
Don’t invest
Don’t invest
Invest
0, 0
-10, 10
-100, 0
20, 10
Firm 1
Invest
Chapter 13
Slide 22
Maximin Strategy

Observations


Dominant
strategy Firm 2:
Invest
Nash equilibrium
 Firm 1: invest
 Firm 2: Invest
Chapter 13
Firm 2
Don’t invest
Don’t invest
Invest
0, 0
-10, 10
-100, 0
20, 10
Firm 1
Invest
Slide 23
Maximin Strategy

Observations


If Firm 2 does
not invest, Firm
1 incurs
significant
losses
Firm 1 might
play don’t invest
 Minimize
losses to 10
--maximin
strategy
Chapter 13
Firm 2
Don’t invest
Don’t invest
Invest
0, 0
-10, 10
-100, 0
20, 10
Firm 1
Invest
Slide 24
The Nash Equilibrium Revisited
Maximin Strategy

If both are rational and informed

Both firms invest

Nash equilibrium
Chapter 13
Slide 25
The Nash Equilibrium Revisited
Maximin Strategy

Consider

If Player 2 is not rational or completely
informed



Chapter 13
Firm 1’s maximin strategy is to not
invest
Firm 2’s maximin strategy is to invest.
If 1 knows 2 is using a maximin
strategy, 1 would invest
Slide 26
Prisoners’ Dilemma
Prisoner B
Confess
Confess
Don’t Confess
-5, -5
-1, -10
-10, -1
-2, -2
Prisoner A
Don’t
Confess
Chapter 13
Slide 27
Prisoners’ Dilemma

What is the:



Dominant
strategy
Prisoner B
Confess
Don’t Confess
Nash equilibrium
Maximin solution
Confess
-5, -5
-1, -10
-10, -1
-2, -2
Prisoner A
Don’t
Confess
Chapter 13
Slide 28
Repeated Games

Oligopolistic firms play a repeated
game.

With each repetition of the Prisoners’
Dilemma, firms can develop reputations
about their behavior and study the
behavior of their competitors.
Chapter 13
Slide 29
Pricing Problem
Firm 2
Low Price
Low Price
High Price
10, 10
100, -50
-50, 100
50, 50
Firm 1
High Price
Chapter 13
Slide 30
Pricing Problem

Non-repeated
game

Firm 2
Low Price
Strategy is Low1,
Low2
Low Price

Repeated game

Tit-for-tat
strategy is the
most profitable
Chapter 13
High Price
10, 10
100, -50
-50, 100
50, 50
Firm 1
High Price
Slide 31
Repeated Games

Conclusion:

With repeated game

Chapter 13
The Prisoners’ Dilemma can have a
cooperative outcome with tit-for-tat
strategy
Slide 32
Repeated Games

Conclusion

Chapter 13
Cooperation is difficult at best since these
factors may change in the long-run.
Slide 33
Sequential Games

Players move in turn

Players must think through the possible
actions and rational reactions of each
player
Chapter 13
Slide 34
Sequential Games

Examples

Responding to a competitor’s ad campaign

Entry decisions

Responding to regulatory policy
Chapter 13
Slide 35
Sequential Games
The Extensive Form of a Game

Scenario

Two new (sweet, crispy) cereals

Successful only if each firm produces one
cereal

Sweet will sell better

Both still profitable with only one producer
Chapter 13
Slide 36
Modified Product Choice Problem
Firm 2
Crispy
Crispy
Sweet
-5, -5
10, 20
20, 10
-5, -5
Firm 1
Sweet
Chapter 13
Slide 37
Modified Product Choice Problem

Question

What is the
likely outcome if
both make their
decisions
independently,
simultaneously,
and without
knowledge of
the other’s
intentions?
Chapter 13
Firm 2
Crispy
Crispy
Sweet
-5, -5
10, 20
20, 10
-5, -5
Firm 1
Sweet
Slide 38
Modified Product Choice Problem
The Extensive Form of a Game

Assume that Firm 1 will introduce its
new cereal first (a sequential game).

Question

Chapter 13
What will be the outcome of this game?
Slide 39
Sequential Games
The Extensive Form of a Game

The Extensive Form of a Game

Using a decision tree

Chapter 13
Work backward from the best outcome
for Firm 1
Slide 40
Product Choice Game in Extensive Form
Crispy
Chapter 13
-5, -5
Sweet
10, 20
Crispy
20, 10
Sweet
-5, -5
Firm 2
Firm 1
Sweet
Crispy
Firm 2
Slide 41
Sequential Games

The Advantage of Moving First

Chapter 13
In this product-choice game, there is a
clear advantage to moving first.
Slide 42
Threats, Commitments, and Credibility

Strategic Moves

Chapter 13
What actions can a firm take to gain
advantage in the marketplace?

Deter entry

Induce competitors to reduce output,
leave, raise price

Implicit agreements that benefit one firm
Slide 43
Threats, Commitments, and Credibility

How To Make the First Move

Demonstrate Commitment

Firm 1 must constrain his behavior to the
extent Firm 2 is convinced that he is
committed
Chapter 13
Slide 44
Threats, Commitments, and Credibility

Empty Threats

Chapter 13
If a firm will be worse off if it charges a low
price, the threat of a low price is not
credible in the eyes of the competitors.
Slide 45
Pricing of Computers
and Word Processors
Firm 2
High Price
High Price
Low Price
100, 80
80, 100
Firm 1
Low Price
Chapter 13
20, 0
10, 20
Slide 46
Pricing of Computers
and Word Processors

Question

Can Firm 1 force
Firm 2 to charge
a high price by
threatening to
lower its price?
Firm 2
High Price
Low Price
100, 80
80, 100
Firm 1
Low Price
Chapter 13
High Price
20, 0
10, 20
Slide 47
Threats, Commitments, and Credibility

Scenario

Race Car Motors, Inc. (RCM) produces
cars

Far Out Engines (FOE) produces specialty
car engines and sells most of them to RCM

Sequential game with RCM as the leader

FOE has no power to threaten to build big
since RCM controls output.
Chapter 13
Slide 48
Production Choice Problem
Race Car Motors
Small engines
Small cars
Big cars
3, 6
3, 0
1, 1
8, 3
Far Out Engines
Big engines
Chapter 13
Slide 49
Threats, Commitments, and Credibility

Question

Chapter 13
How could FOE force RCM to shift to big
cars?
Slide 50
Modified Production Choice Problem
Race Car Motors
Small engines
Small cars
Big cars
0, 6
0, 0
1, 1
8, 3
Far Out Engines
Big engines
Chapter 13
Slide 51
Modified Production Choice Problem

Questions
1) What is the risk of this strategy?
2) How could irrational behavior give
FOE some power to control output?
Chapter 13
Slide 52
Wal-Mart Stores’
Preemptive Investment Strategy

Question

How did Wal-Mart become the largest
retailer in the U.S. when many established
retail chains were closing their doors?
Hint
 How
did Wal-Mart gain monopoly power?
 Preemptive game with Nash equilibrium
Chapter 13
Slide 53
The Discount Store Preemption Game
Company X
Enter
Enter
Don’t enter
-10, -10
20, 0
0, 20
0, 0
Wal-Mart
Don’t enter
Chapter 13
Slide 54
The Discount Store Preemption Game

Two Nash
equilibrium
Company X


Low left

Upper right
Must be
preemptive to
win
Chapter 13
Enter
Enter
Don’t enter
-10, -10
20, 0
Wal-Mart
Don’t enter
0, 20
0, 0
Slide 55
Entry Deterrence

To deter entry, the incumbent firm must
convince any potential competitor that
entry will be unprofitable.
Chapter 13
Slide 56
Entry Possibilities
Potential Entrant
High price
(accommodation)
Enter
Stay out
100, 20
200, 0
70, -10
130, 0
Incumbent
Low Price
(warfare)
Chapter 13
Slide 57
Entry Deterrence

Question
 How

Chapter 13
could I keep X out?
Is the threat credible?
Slide 58
Entry Deterrence

How could I keep X out?
1) Make an investment before entry
(irrevocable commitment)
2) Irrational behavior
Chapter 13
Slide 59
Entry Deterrence
After $50 million Early Investment
Potential Entrant
High price
(accommodation)
Enter
Stay out
50, 20
150, 0
70, -10
130, 0
Incumbent
Low Price
(warfare)
Chapter 13
Slide 60
Entry Deterrence
After $50 million Early Investment

Warfare likely
Potential Entrant

X will stay out
High price
(accommodation)
Enter
Stay out
50, 20
150, 0
70, -10
130, 0
Incumbent
Low Price
(warfare)
Chapter 13
Slide 61
Entry Deterrence

Airbus vs. Boeing

Chapter 13
Without Airbus being subsidized, the payoff
matrix for the two firms would differ
significantly from one showing
subsidization.
Slide 62
Development of a New Aircraft
Airbus
Produce
Don’t produce
Produce
-10, -10
100, 0
Don’t produce
0, 100
0, 0
Boeing
Chapter 13
Slide 63
Development of a New Aircraft


Boeing will
produce
Airbus will not
produce
Airbus
Produce
Produce
Don’t produce
-10, -10
100, 0
0, 100
0, 0
Boeing
Don’t produce
Chapter 13
Slide 64
Development of a Aircraft
After European Subsidy
Airbus
Produce
Don’t produce
Produce
-10, 10
100, 0
Don’t produce
0, 120
0, 0
Boeing
Chapter 13
Slide 65
Development of a Aircraft
After European Subsidy


Airbus will
produce
Boeing will not
produce
Airbus
Produce
Produce
Don’t produce
-10, 10
100, 0
0, 120
0, 0
Boeing
Don’t produce
Chapter 13
Slide 66
Bargaining Strategy

Alternative outcomes are possible if
firms or individuals can make promises
that can be enforced.
Chapter 13
Slide 67
Bargaining Strategy

Consider:

Chapter 13
Two firms introducing one of two
complementary goods.
Slide 68
Bargaining Strategy
Firm 2
Produce A
Produce A
Produce B
40, 5
50, 50
60, 40
5, 45
Firm 1
Produce B
Chapter 13
Slide 69
Bargaining Strategy

With collusion:


Produce A1B2
Without
collusion:


Produce A1B2
Nash equilibrium
Chapter 13
Firm 2
Produce A
Produce A
Produce B
40, 5
50, 50
60, 40
5, 45
Firm 1
Produce B
Slide 70
Bargaining Strategy

Suppose

Chapter 13
Each firm is also bargaining on the
decision to join in a research consortium
with a third firm.
Slide 71
Bargaining Strategy
Firm 2
Work alone
Work alone
Enter consortium
10, 10
10, 20
20, 10
40, 40
Firm 1
Enter
consortium
Chapter 13
Slide 72
Bargaining Strategy

Dominant
strategy

Firm 2
Both enter
Work alone
Work alone
Enter consortium
10, 10
10, 20
20, 10
40, 40
Firm 1
Enter
consortium
Chapter 13
Slide 73
Bargaining Strategy

Linking the Bargain Problem
 Firm
1 announces it will join the consortium
only if Firm 2 agrees to produce A and
Firm 1 will produce B.

Chapter 13
Firm 1’s profit increases from 50 to 60
Slide 74
Bargaining Strategy

Strengthening Bargaining Power

Credibility

Reducing flexibility
Chapter 13
Slide 75
Summary

A game is cooperative if the players can
communicate and arrange binding
contracts; otherwise it is
noncooperative.

A Nash equilibrium is a set of strategies
such that all players are doing their
best, given the strategies of the other
players.
Chapter 13
Slide 76
Summary

Some games have no Nash equilibrium
in pure strategies, but have one or more
equilibria in mixed strategies.

Strategies that are not optimal for a
one-shot game may be optimal for a
repeated game.

In a sequential game, the players move
in turn.
Chapter 13
Slide 77
Summary

An empty threat is a threat that one
would have no incentive to carry out.

To deter entry, an incumbent firm must
convince any potential competitor that
entry will be unprofitable.

Bargaining situations are examples of
cooperative games.
Chapter 13
Slide 78
End of Chapter 13
Game Theory
and Competitive
Strategy