Managerial Economics in a Global Economy, 5th Edition by Dominick Salvatore Chapter 10 Game Theory...

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Managerial Economics in a Global Economy, 5th Edition

byDominick Salvatore

Chapter 10Game Theory andStrategic Behavior

Strategic Behavior

Decisions that take into account the predicted reactions of rival firms Interdependence of outcomes

Game Theory Players Strategies Payoff matrix

Strategic Behavior

Types of Games Zero-sum games Nonzero-sum games

Nash Equilibrium Each player chooses a strategy that is

optimal given the strategy of the other player

A strategy is dominant if it is optimal regardless of what the other player does

Advertising Example 1

Advertise Don't AdvertiseAdvertise (4, 3) (5, 1)

Don't Advertise (2, 5) (3, 2)

Firm B

Firm A

Firm B

Firm A

What is the optimal strategy for Firm A if Firm B chooses to advertise?

Firm B

Firm A

If Firm A chooses to advertise, the payoff is 4. Otherwise, the payoff is 2. The optimal strategy is to advertise.

Firm B

Firm A

What is the optimal strategy for Firm A if Firm B chooses not to advertise?

Firm B

Firm A

If Firm A chooses to advertise, the payoff is 5. Otherwise, the payoff is 3. Again, the optimal strategy is to advertise.

Firm B

Firm A

Regardless of what Firm B decides to do, the optimal strategy for Firm A is to advertise. The dominant strategy for Firm A is to advertise.

Firm B

Firm A

What is the optimal strategy for Firm B if Firm A chooses to advertise?

Firm B

Firm A

If Firm B chooses to advertise, the payoff is 3. Otherwise, the payoff is 1. The optimal strategy is to advertise.

Firm B

Firm A

What is the optimal strategy for Firm B if Firm A chooses not to advertise?

Firm B

Firm A

If Firm B chooses to advertise, the payoff is 5. Otherwise, the payoff is 2. Again, the optimal strategy is to advertise.

Firm B

Firm A

Regardless of what Firm A decides to do, the optimal strategy for Firm B is to advertise. The dominant strategy for Firm B is to advertise.

Firm B

Firm A

The dominant strategy for Firm A is to advertise and the dominant strategy for Firm B is to advertise. The Nash equilibrium is for both firms to advertise.

Firm B

Firm A

Firm B

Firm A

If Firm A chooses to advertise, the payoff is 4. Otherwise, the payoff is 2. The optimal strategy is to advertise.

Firm B

Firm A

Firm B

Firm A

If Firm A chooses to advertise, the payoff is 5. Otherwise, the payoff is 6. In this case, the optimal strategy is not to advertise.

Firm B

Firm A

Firm B

Firm A

The optimal strategy for Firm A depends on which strategy is chosen by Firms B. Firm A does not have a dominant strategy.

Firm B

Firm A

If Firm B chooses to advertise, the payoff is 3. Otherwise, the payoff is 1. The optimal strategy is to advertise.

Firm B

Firm A

Firm B

Firm A

If Firm B chooses to advertise, the payoff is 5. Otherwise, the payoff is 2. Again, the optimal strategy is to advertise.

Firm B

Firm A

Regardless of what Firm A decides to do, the optimal strategy for Firm B is to advertise. The dominant strategy for Firm B is to advertise.

Firm B

Firm A

Firm B

Firm A

The dominant strategy for Firm B is to advertise. If Firm B chooses to advertise, then the optimal strategy for Firm A is to advertise. The Nash equilibrium is for both firms to advertise.

A Normal Form Game

Strategy A B Cabc

Player 2

1 12,11 11,12 14,13

11,10 10,11 12,12

10,15 10,13 13,14

Putting Yourself in your Rival’s Shoes

What should player 2 do? 2 has no dominant strategy! But 2 should reason that 1 will play “a”. Therefore 2 should choose “C”.

Strategy A B Cabc

Player 2

1 12,11 11,12 14,13

11,10 10,11 12,12

10,15 10,13 13,14

The Outcome

This outcome is called a Nash equilibrium: “a” is player 1’s best response to “C”. “C” is player 2’s best response to “a”.

Strategy A B Cabc

Player 2

1 12,11 11,12 14,13

11,10 10,11 12,12

10,15 10,13 13,14

The Market-Share Game in Normal Form

Strategy P=$10 P=$5 P = $1P=$10 .5, .5 .2, .8 .1, .9P=$5 .8, .2 .5, .5 .2, .8P=$1 .9, .1 .8, .2 .5, .5

Manager 2

No Equilibrium - Child’s play

Strategy Scissors Rock PaperScissors 0, 0 -1, 1 1, -1

Rock 1, -1 0, 0 -1, 1Paper -1, 1 1, -1 0, 0

Player 2

Player 1

Multiple Equilibria - Battle of the Sexes

Strategy Ballet BoxingBallet 4, 5 0 , 0Boxing 1, 1 5, 4

Prisoners’ Dilemma

Two suspects are arrested for armed robbery. They are immediately separated. If convicted, they will get a term of 10 years in prison. However, the evidence is not sufficient to convict them of more than the crime of possessing stolen goods, which carries a sentence of only 1 year.

The suspects are told the following: If you confess and your accomplice does not, you will go free. If you do not confess and your accomplice does, you will get 10 years in prison. If you both confess, you will both get 5 years in prison.

Confess Don't ConfessConfess (5, 5) (0, 10)

Don't Confess (10, 0) (1, 1)

Individual B

Individual A

Payoff Matrix (negative values)

Confess Don't ConfessConfess (5, 5) (0, 10)

Don't Confess (10, 0) (1, 1)

Individual B

Individual A

Dominant StrategyBoth Individuals Confess

(Nash Equilibrium)

Normal Form Game(Simultaneous Movers - Prisoner’s Dilemma)

Environment - Police station after a crime wave. Police have evidence on a minor crime. Police have insufficient evidence on major crime

Players - Bonnie and Clyde

Rules - no escape is possible

Strategies - Rat or not rat

Payoffs - No one rats: both get 3 years One rats and the other stays quiet: rat gets 1 year, Silent partner

gets 23 years Both rat: both get 16 years

The Normal Form of Prisoner’s Dilemma

Strategy Rat Don't RatRat

Don't Rat

Bonnie

Clyde16,16 1, 23

23,1 3,3

Resolving Bonnie & Clyde

If Bonnie Rats and Clyde doesn’t rat, then Bonnie gets 1 year Clyde rats, then Bonnie gets 16 years

If Bonnie doesn’t Rat and Clyde doesn’t rat, then Bonnie gets 3 years Clyde rats, then Bonnie gets 23 years

If Clyde Rats and Bonnie doesn’t rat, then Clyde gets 1 year Bonnie rats, then Clyde gets 16 years

If Clyde doesn’t Rat and Bonnie doesn’t rat, then Clyde gets 3 years Bonnie rats, then Clyde gets 23 years

Resolving Bonnie & Clyde

Bonnie has a dominant strategy - RatClyde has a dominant strategy - RatNash Equilibrium - set of strategies that

are “best responses” to each otherNash here is: {Rat; Rat}Payoffs here are: {16 years; 16 years}Best outcome is {Don’t Rat; Don’t Rat}

with payoffs of {3 yrs; 3 years}How do we get cooperation?Suppose each promised the other not to

Low Price High PriceLow Price (2, 2) (5, 1)High Price (1, 5) (3, 3)

Firm B

Firm A

Application: Price Competition

Low Price High PriceLow Price (2, 2) (5, 1)High Price (1, 5) (3, 3)

Firm B

Firm A

Application: Price Competition

Dominant Strategy: Low Price

Firm B

Firm A

Application: Nonprice Competition

Dominant Strategy: Advertise

Firm B

Firm A

Cheat Don't CheatCheat (2, 2) (5, 1)

Don't Cheat (1, 5) (3, 3)

Firm B

Firm A

Application: Cartel Cheating

Cheat Don't CheatCheat (2, 2) (5, 1)

Don't Cheat (1, 5) (3, 3)

Firm B

Firm A

Application: Cartel Cheating

Dominant Strategy: Cheat

Extensions of Game Theory

Repeated Games Many consecutive moves and

countermoves by each playerTit-For-Tat Strategy

Do to your opponent what your opponent has just done to you

Tit-For-Tat Strategy Stable set of players Small number of players Easy detection of cheating Stable demand and cost conditions Game repeated a large and

uncertain number of times

Threat Strategies Credibility Reputation Commitment Example: Entry deterrence

Entry Deterrence

Enter Do Not EnterLow Price (4, -2) (6, 0)High Price (7, 2) (10, 0)

Firm B

Firm A

Firm B

Firm A

Credible Entry Deterrence

No Credible Entry Deterrence

Entry Deterrence

Firm B

Firm A

Firm B

Firm A

Credible Entry Deterrence

No Credible Entry Deterrence

International Competition

Produce Don't ProductProduce (-10, -10) (100, 0)

Don't Produce (0, 100) (0, 0)

Airbus

Boeing

Boeing Versus Airbus Industrie

Sequential Games

Sequence of moves by rivalsPayoffs depend on entire sequenceDecision trees

Decision nodes Branches (alternatives)

Solution by reverse induction From final decision to first decision

High-price, Low-priceStrategy Game

High Price

Low Price

$100 $100

$130 $50

$180 $80

$150 $120

Firm A Firm B

High Price

Low Price

$100 $100

$130 $50

$180 $80

$150 $120

Firm A Firm B

High Price

Low Price

$100 $100

$130 $50

$180 $80

$150 $120

Firm A Firm B

XXSolution:Both firmschoose lowprice.

Airbus and Boeing

Jumbo Jet

Sonic Cruiser

$50 $50

$120 $100

$0 $150

$0 $200

Airbus Boeing

Airbus and Boeing

Jumbo Jet

Sonic Cruiser

$50 $50

$120 $100

$0 $150

$0 $200

Airbus Boeing

Airbus and Boeing

Jumbo Jet

Sonic Cruiser

$50 $50

$120 $100

$0 $150

$0 $200

Airbus Boeing

Solution:Airbus buildsA380 andBoeing buildsSonic Cruiser.

Integrating Case Study

100 50

Firm A Firm B

Managerial Economics in a Global Economy, 5th Edition by Dominick Salvatore Chapter 10 Game Theory...

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