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“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?