Post on 17-Dec-2015
Chapter 13
Game Theory and Competitive
Strategy
Game Theory and Competitive
Strategy
Chapter 13 Slide 2
Topics to be Discussed
Gaming and Strategic Decisions
Dominant Strategies
The Nash Equilibrium Revisited
Repeated Games
Chapter 13 Slide 3
Topics to be Discussed
Sequential Games
Threats, Commitments, and Credibility
Entry Deterrence
Bargaining Strategy
Chapter 13 Slide 4
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 5
Gaming and Strategic Decisions
Noncooperative versus Cooperative GamesCooperative 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 6
Gaming and Strategic Decisions
Noncooperative versus Cooperative GamesNoncooperative 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 7
Gaming and Strategic Decisions
Noncooperative versus Cooperative Games“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”
Chapter 13 Slide 8
Dominant Strategies
Dominant Strategy
One that is optimal no matter what an opponent does.
An Example
A & B sell competing products
They are deciding whether to undertake advertising campaigns
Chapter 13 Slide 9
Payoff Matrix for Advertising Game
Firm A
Advertise
Don’tAdvertise
Advertise
Don’tAdvertise
Firm B
10, 5 15, 0
10, 26, 8
Chapter 13 Slide 10
Payoff Matrix for Advertising Game
Firm A
AdvertiseDon’t
Advertise
Advertise
Don’tAdvertise
Firm B
10, 5 15, 0
10, 26, 8
ObservationsA: regardless of
B, advertising is the best
B: regardless of A, advertising is best
Chapter 13 Slide 11
Payoff Matrix for Advertising Game
Firm A
AdvertiseDon’t
Advertise
Advertise
Don’tAdvertise
Firm B
10, 5 15, 0
10, 26, 8
ObservationsDominant
strategy for A & B is to advertise
Do not worry about the other player
Equilibrium in dominant strategy
Chapter 13 Slide 12
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 13
10, 5 15, 0
20, 26, 8
Firm A
Advertise
Don’tAdvertise
Advertise
Don’tAdvertise
Firm B
Modified Advertising Game
Chapter 13 Slide 14
10, 5 15, 0
20, 26, 8
Firm A
AdvertiseDon’t
Advertise
Advertise
Don’tAdvertise
Firm B
Modified Advertising Game
Observations A: No dominant
strategy; depends on B’s actions
B: Advertise
Question What should A
do? (Hint: consider B’s decision
Chapter 13 Slide 15
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 16
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 17
Examples With A Nash EquilibriumTwo 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
The Nash Equilibrium Revisited
Product Choice ProblemProduct Choice Problem
Chapter 13 Slide 18
Product Choice Problem
Firm 1
Crispy Sweet
Crispy
Sweet
Firm 2
-5, -5 10, 10
-5, -510, 10
Chapter 13 Slide 19
Product Choice Problem
Firm 1
Crispy Sweet
Crispy
Sweet
Firm 2
-5, -5 10, 10
-5, -510, 10
Question Is there a Nash
equilibrium? If not, why? If so, how can
it be reached
Chapter 13 Slide 20
The Nash Equilibrium Revisited
Maximin Strategies
Scenario
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)
Chapter 13 Slide 21
The Nash Equilibrium Revisited
Maximin Strategies
Scenario
Firm 1 has a much larger market share than Firm 2
Both are considering investing in a new encryption standard
Chapter 13 Slide 22
Maximin Strategy
Firm 1
Don’t invest InvestFirm 2
0, 0 -10, 10
20, 10-100, 0
Don’t invest
Invest
Chapter 13 Slide 23
Maximin Strategy
Firm 1
Don’t invest InvestFirm 2
0, 0 -10, 10
20, 10-100, 0
Don’t invest
Invest
ObservationsDominant
strategy Firm 2: Invest
Nash equilibrium Firm 1: invest Firm 2: Invest
Chapter 13 Slide 24
Maximin Strategy
Firm 1
Don’t invest InvestFirm 2
0, 0 -10, 10
20, 10-100, 0
Don’t invest
Invest
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 Slide 25
If both are rational and informedBoth firms invest
Nash equilibrium
The Nash Equilibrium Revisited
Maximin StrategyMaximin Strategy
Chapter 13 Slide 26
ConsiderIf Player 2 is not rational or completely
informedFirm 1’s maximin strategy is to not
investFirm 2’s maximin strategy is to invest. If 1 knows 2 is using a maximin
strategy, 1 would invest
The Nash Equilibrium Revisited
Maximin StrategyMaximin Strategy
Chapter 13 Slide 27
Prisoners’ Dilemma
Prisoner A
Confess Don’t Confess
Confess
Don’tConfess
Prisoner B
-5, -5 -1, -10
-2, -2-10, -1
Chapter 13 Slide 28
Prisoners’ Dilemma
Prisoner A
Confess Don’t Confess
Confess
Don’tConfess
Prisoner B
-5, -5 -1, -10
-2, -2-10, -1
What is the:Dominant
strategyNash equilibriumMaximin solution
Chapter 13 Slide 29
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 30
Pricing Problem
Firm 1
Low Price High Price
Low Price
High Price
Firm 2
10, 10 100, -50
50, 50-50, 100
Chapter 13 Slide 31
Pricing Problem
Firm 1
Low Price High Price
Low Price
High Price
Firm 2
10, 10 100, -50
50, 50-50, 100
Non-repeated game
Strategy is Low1, Low2
Repeated game
Tit-for-tat strategy is the most profitable
Chapter 13 Slide 32
Repeated Games
Conclusion:With repeated game
The Prisoners’ Dilemma can have a cooperative outcome with tit-for-tat strategy
Chapter 13 Slide 33
Repeated Games
ConclusionCooperation is difficult at best since these
factors may change in the long-run.
Chapter 13 Slide 34
Sequential Games
Players move in turn
Players must think through the possible actions and rational reactions of each player
Chapter 13 Slide 35
Sequential Games
ExamplesResponding to a competitor’s ad campaign
Entry decisions
Responding to regulatory policy
Chapter 13 Slide 36
ScenarioTwo new (sweet, crispy) cereals
Successful only if each firm produces one cereal
Sweet will sell better
Both still profitable with only one producer
Sequential Games
The Extensive Form of a GameThe Extensive Form of a Game
Chapter 13 Slide 37
Modified Product Choice Problem
Firm 1
Crispy Sweet
Crispy
Sweet
Firm 2
-5, -5 10, 20
-5, -520, 10
Chapter 13 Slide 38
Modified Product Choice Problem
Firm 1
Crispy Sweet
Crispy
Sweet
Firm 2
-5, -5 10, 20
-5, -520, 10
QuestionWhat is the
likely outcome if both make their decisions independently, simultaneously, and without knowledge of the other’s intentions?
Chapter 13 Slide 39
Assume that Firm 1 will introduce its new cereal first (a sequential game).
QuestionWhat will be the outcome of this game?
Modified Product Choice Problem
The Extensive Form of a GameThe Extensive Form of a Game
Chapter 13 Slide 40
Sequential Games
The Extensive Form of a GameUsing a decision tree
Work backward from the best outcome for Firm 1
The Extensive Form of a GameThe Extensive Form of a Game
Chapter 13 Slide 41
Product Choice Game in Extensive Form
Crispy
Sweet
Crispy
Sweet
-5, -5
10, 20
20, 10
-5, -5
Firm 1
Crispy
Sweet
Firm 2
Firm 2
Chapter 13 Slide 42
Sequential Games
The Advantage of Moving FirstIn this product-choice game, there is a
clear advantage to moving first.
Chapter 13 Slide 43
Threats, Commitments, and Credibility
Strategic MovesWhat 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
Chapter 13 Slide 44
How To Make the First MoveDemonstrate Commitment
Firm 1 must constrain his behavior to the extent Firm 2 is convinced that he is committed
Threats, Commitments, and Credibility
Chapter 13 Slide 45
Empty ThreatsIf 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.
Threats, Commitments, and Credibility
Chapter 13 Slide 46
Pricing of Computers and Word Processors
Firm 1
High Price Low Price
High Price
Low Price
Firm 2
100, 80 80, 100
10, 2020, 0
Chapter 13 Slide 47
Pricing of Computers and Word Processors
Firm 1
High Price Low Price
High Price
Low Price
Firm 2
100, 80 80, 100
10, 2020, 0
QuestionCan Firm 1 force
Firm 2 to charge a high price by threatening to lower its price?
Chapter 13 Slide 48
ScenarioRace 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.
Threats, Commitments, and Credibility
Chapter 13 Slide 49
Production Choice Problem
Far Out Engines
Small cars Big cars
Small engines
Big engines
Race Car Motors
3, 6 3, 0
8, 31, 1
Chapter 13 Slide 50
QuestionHow could FOE force RCM to shift to big
cars?
Threats, Commitments, and Credibility
Chapter 13 Slide 51
Modified Production Choice Problem
0, 6 0, 0
8, 31, 1
Far Out Engines
Small cars Big cars
Small engines
Big engines
Race Car Motors
Chapter 13 Slide 52
Questions
1) What is the risk of this strategy?
2) How could irrational behavior give FOE some power to control
output?
Modified Production Choice Problem
Chapter 13 Slide 53
Wal-Mart Stores’Preemptive Investment Strategy
QuestionHow 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 54
The Discount Store Preemption Game
Wal-Mart
Enter Don’t enter
Enter
Don’t enter
Company X
-10, -10 20, 0
0, 00, 20
Chapter 13 Slide 55
The Discount Store Preemption Game
Wal-Mart
Enter Don’t enter
Enter
Don’t enter
Company X
-10, -10 20, 0
0, 00, 20
Two Nash equilibrium
Low left
Upper right
Must be preemptive to win
Chapter 13 Slide 56
Entry Deterrence
To deter entry, the incumbent firm must convince any potential competitor that entry will be unprofitable.
Chapter 13 Slide 57
Entry Possibilities
Incumbent
Enter Stay out
High price(accommodation)
Low Price(warfare)
Potential Entrant
100, 20 200, 0
130, 070, -10
Chapter 13 Slide 58
Entry Deterrence
Question
How could I keep X out?
Is the threat credible?
Chapter 13 Slide 59
Entry Deterrence
How could I keep X out?
1) Make an investment before entry (irrevocable commitment)
2) Irrational behavior
Chapter 13 Slide 60
Entry Deterrence
Incumbent
Enter Stay out
High price(accommodation)
Low Price(warfare)
Potential Entrant
50, 20 150, 0
130, 070, -10
After $50 million Early InvestmentAfter $50 million Early Investment
Chapter 13 Slide 61
Entry Deterrence
Incumbent
Enter Stay out
High price(accommodation)
Low Price(warfare)
Potential Entrant
50, 20 150, 0
130, 070, -10
After $50 million Early InvestmentAfter $50 million Early Investment
Warfare likely
X will stay out
Chapter 13 Slide 62
Airbus vs. BoeingWithout Airbus being subsidized, the payoff
matrix for the two firms would differ significantly from one showing subsidization.
Entry Deterrence
Chapter 13 Slide 63
Development of a New Aircraft
Boeing
Produce Don’t produce
Airbus
-10, -10 100, 0
0, 00, 100
Produce
Don’t produce
Chapter 13 Slide 64
Development of a New Aircraft
Boeing
Produce Don’t produce
Airbus
-10, -10 100, 0
0, 00, 100
Produce
Don’t produce
Boeing will produce
Airbus will not produce
Chapter 13 Slide 65
Development of a AircraftAfter European Subsidy
Boeing
Produce Don’t produce
Airbus
-10, 10 100, 0
0, 00, 120
Produce
Don’t produce
Chapter 13 Slide 66
Boeing
Produce Don’t produce
Airbus
-10, 10 100, 0
0, 00, 120
Produce
Don’t produce
Airbus will produce
Boeing will not produce
Development of a AircraftAfter European Subsidy
Chapter 13 Slide 67
Bargaining Strategy
Alternative outcomes are possible if firms or individuals can make promises that can be enforced.
Chapter 13 Slide 68
Bargaining Strategy
Consider:Two firms introducing one of two
complementary goods.
Chapter 13 Slide 69
Bargaining Strategy
Firm 1
Produce A Produce B
Produce A
Produce B
Firm 2
40, 5 50, 50
5, 4560, 40
Chapter 13 Slide 70
Bargaining Strategy
Firm 1
Produce A Produce B
Produce A
Produce B
Firm 2
40, 5 50, 50
5, 4560, 40
With collusion:
Produce A1B2
Without collusion:
Produce A1B2
Nash equilibrium
Chapter 13 Slide 71
Bargaining Strategy
SupposeEach firm is also bargaining on the
decision to join in a research consortium with a third firm.
Chapter 13 Slide 72
Bargaining Strategy
Firm 1
Work alone Enter consortium
Work alone
Enterconsortium
Firm 2
10, 10 10, 20
40, 4020, 10
Chapter 13 Slide 73
Bargaining Strategy
Firm 1
Work alone Enter consortium
Work alone
Enterconsortium
Firm 2
10, 10 10, 20
40, 4020, 10
Dominant strategy
Both enter
Chapter 13 Slide 74
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.
Firm 1’s profit increases from 50 to 60
Chapter 13 Slide 75
Bargaining Strategy
Strengthening Bargaining PowerCredibility
Reducing flexibility
Chapter 13 Slide 76
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 77
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 78
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.
End of Chapter 13Game Theory
and Competitive Strategy
Game Theory and Competitive
Strategy