“Loretta’s driving because I’m drinking and I’m drinking

because she’s driving.”- The Lockhorns

Game Theory and Business Strategy

Original content © Mike Shor, 2001-2004.

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Review

Understanding the game Noting if the rules are flexible Anticipating our opponents’ reactions Thinking one step ahead

Where does this lead us? We’ve defined the “game” but not the outcome

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Equilibrium The likely outcome of a game when rational,

strategic agents interact Each player is playing his or her best strategy

given the strategy choices of all other players No player has incentive to change his or her action

unilaterally

Outline: Model interactions as games Identify the equilibria Decide if they are likely to occur

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Equilibrium IllustrationThe Lockhorns

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Cigarette Advertising on TV All US tobacco companies

advertised heavily on TV

Surgeon General issues official warningCigarette smoking may be hazardous

Cigarette companies fear lawsuitsGovernment may recover healthcare costs

Companies strike agreementCarry the warning label and cease

TV advertising in exchange for immunity from federal lawsuits.

1964

1970

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Strategic Interaction Players: Reynolds and Philip Morris Strategies: Advertise or Not Advertise Payoffs: Companies’ Profits

Strategic Landscape: Each firm earns $50 million from its customers Advertising costs a firm $20 million Advertising captures $30 million from competitor

How to represent this game?

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Representing a Game

PLAYERS

STRATEGIESPAYOFFS

Philip Morris

No Ad Ad

Reynolds No Ad 50 , 50 20 , 60

Ad 60 , 20 30 , 30

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What to Do?

If you are advising Reynolds, what strategy do you recommend?

Philip Morris

No Ad Ad

ReynoldsNo Ad 50 , 50 20 , 60

Ad 60 , 20 30 , 30

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Solving the Game

Best reply for Reynolds:If Philip Morris advertises:If Philip Morris does not advertise:

Philip Morris

No Ad Ad

ReynoldsNo Ad 50 , 50 20 , 60

Ad 60 , 20 30 , 30

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Dominance

A strategy is dominant if it outperforms all other choices no matter what opposing players do

Games with dominant strategies are easy to play No need for “what if …” thinking

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DominanceA Technical Point

Strict Dominance:Advertise is strictly dominant for Reynolds if: Profit (Ad , Ad) > Profit (No , Ad) Profit (Ad , No) > Profit (No , No)

Weak Dominance:Advertise is weakly dominant if: Some inequalities are weak (), At least one is strong(>)

By “dominant” we will mean “strictly dominant”

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Dominance

COMMANDMENT

If you have a dominant strategy, use it.

Expect your opponent to use her dominant strategy if she has one.

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Prisoner’s Dilemma

Both players have a dominant strategy The equilibrium results in lower

payoffs for each player

No Ad Ad

No Ad 50 , 50 20 , 60

Ad 60 , 20 30 , 30

Equilibrium

Optimal

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Cigarette Advertising After the 1970 agreement:

Cigarette advertising decreased by $63 million Industry Profits rose by $91 million

Prisoner’s Dilemma An equilibrium is NOT necessarily efficient Players can be forced to accept

mutually bad outcomes Bad to be playing a prisoner’s dilemma,

but good to make others play

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How to Win a Bidding War by Bidding Less?

The battle for Federated (1988)Parent of Bloomingdales

Current share price ≈ $60 Expected post-takeover share price ≈ $60

Macy’s offers $70/share contingent on receiving 50% of the shares

Do you tender your shares to Macy’s?

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How to Win a Bidding War (continued) Robert Campeau bids $74 per share

not contingent on amount acquired

Campeau’s Mixed Scheme: If less than 50% tender their shares,

each receives: $74 per share

If more than 50% tender their shares, (if X% tender), each receives:

60$%

%50% 74$

%

%50

X

X

X

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The Federated Game

To whom do you tender your shares?

Majority of Others

Macy’s Campeau Neither

You

Macy’s $70 $60 $60

Campeau $74 $67 $74

Neither $60 $60 $60

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How to Win a Bidding War

Each player has a dominant strategy: Tender shares to Campeau

Resulting Price:

(½ x 74) + (½ x 60) = $67

BUT: Macy’s offered $70 !

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Dominant Strategies

“ The biggest, looniest deal ever. ” – Fortune Magazine, July 1988 on Campeau’s acquisition of Federated Stores

What if players do not have dominant strategies?

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Pricing without Dominant Strategies

Two bars (bar 1, bar 2) compete Can charge price of $2, $4, or $5

Customer base consists of tourists and natives 6,000 tourists pick a bar randomly 4,000 natives select the lowest price bar

Marginal costs are close to zero

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Tourists & Natives Example scenario:

Bar 1 charges $4, Bar 2 charges $5

Bar 1 gets:3,000 tourists + 4,000 natives = 7,000 customers x $4 = $28K

Bar 2 gets:3,000 tourists + 0 natives= 3,000 customers x $5 = $15K

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Tourists & Natives

$2 $4 $5

Bar 1

$2 10 , 10 14 , 12 14 , 15

$4 12 , 14 20 , 20 28 , 15

$5 15 , 14 15 , 28 25 , 25

Bar 2

in thousands of dollars

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Successive Elimination of Dominated Strategies Does any player have a dominant strategy? Does any player have a dominated strategy?

A strategy is dominated if there is some other strategy which always does better

Eliminate the dominated strategiesReduce the size of the gameIterate the above procedure

What is the equilibrium?

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$2 $4 $5

Bar 1

$2 10 , 10 14 , 12 14 , 15

$4 12 , 14 20 , 20 28 , 15

$5 15 , 14 15 , 28 25 , 25

Successive Elimination of Dominated Strategies

Bar 2

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Dominance

CAVEAT

Expect your opponent to use her dominant strategy if she has one.

BUT

Be sure you understand your opponents’ true payoffs.

(Do you know what really motivates them?)

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No Dominated Strategies Often there are no dominated strategies Some games may have multiple equilibria Equilibrium selection becomes an issue

Method:For each player, find the best response to every strategy of the other player

Games of Coordination Games of Assurance Games of Chicken

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Games of Coordination Joint ventures and supplier choice

Two firms engaged in joint venture Must use the same supplier,

but each firm has a preferred supplier

Firm 2A B

Firm 1A 100 , 50 0 , 0

B 0 , 0 50 , 100

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Games of Coordination Solving:

Firm 2A B

Firm 1A 100 , 50 0 , 0

B 0 , 0 50 , 100

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Games of Assurance Joint research ventures

Each firm may invest $50,000 into an R&D project Project succeeds only if both invest If successful, each nets $75,000

Firm 2$50K $0

Firm 1$50K 75 , 75 -50 , 0

$0 0 , -50 0 , 0

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Games of Chicken Entry into small markets

Firm 2Stay Swerve

Firm 1Stay -50 , -50 100 , 0

Swerve 0 , 100 50 , 50

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The Right Game to Play

Why do we “solve” games?

To know which one to play! How do internal corporate changes impact

the outcome of strategic interaction?

Some games are better than others

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Your Value to a Game Your added value =

the size of the pie when you’re in the game

minus

the size of the pie when you are not Added value limits how much you can get

You cannot receive much more than your added value

Added value provides benchmark You should receive close to your added value

Change the Game! You can increase your payoffs by increasing your added

value OR decreasing the added value of other players.

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Capacity Constraints

Can decreasing others’ added value increase our profits?

Can decreasing total industry value increase our profits?

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Summary Games have predictable outcomes

Notice dominant & dominated strategies Select the right game to play

Seemingly internal corporate changes can impact the outcome of strategic interaction

Looking ahead: Sequential Games:

How do games unfold over time?