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Game Theory
It is true that life must beunderstood backward, but
it must be lived forward.
- Sren Kierkegaard
Mike ShorLecture 4
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Review
Understanding the outcomes of games
Sometimes easy
Dominant strategies
Sometimes more challenging
I know that you know
What if a game is sequential?
Market entry
Mike Shor
Game Theory & Business Strategy2
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Very Large Airplanes:Airbus vs. Boeing
Airbus lacked a jumbo jet: The problem is the monopoly of the 747
They have a product. We have none. - Airbus Executive
Initiated plans to build a super-jumbo jet
Industry feasibility studies: Room for at most one megaseater
Boeing preemption: Boeing, the worlds top aircraft maker, announced
it was building a plane with 600 to 800 seats, thebiggest and most expensive airliner ever.
- BusinessWeek, 1993
Mike Shor
Game Theory & Business Strategy3
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Sequential Games
Mike Shor
Game Theory & Business Strategy4
The Game
Airbus
Boeing $4 billion,
$4billion
$0.3 billion,$3 billion
$1 billion,$1billion
$0,$0
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Looking Forward
Airbus makes the first move:Must consider how Boeing will respond
If stay out:
Boeing stays outMike Shor
Game Theory & Business Strategy5
Boeing
$0billion
$1 billion
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Looking Forward
Airbus makes the first move:Must consider how Boeing will respond
If enter:
Boeing accommodates, stays outMike Shor
Game Theory & Business Strategy6
Boeing
$3billion
$4 billion
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And Reasoning Back
Now consider the first move:
Only ( In, Out ) is sequentially rational
In is not credible (for Boeing)
Mike Shor
Game Theory & Business Strategy7
Airbus
Boeing
$0,$0
out $0.3 billion,$3 billion
out
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Boeing, the worlds top aircraft maker,announced it was building a plane with 600 to800 seats, the biggest and most expensiveairliner ever.
- BusinessWeek, 1993
Airbus vs. BoeingWhat a Difference Seven Years Make
Mike Shor
Game Theory & Business Strategy8
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Solving Sequential Games
Thinking backwards is easy in game trees
Start at the end and trim the tree to the present
Thinking backwards is challenging in practice
Outline:
Strategic moves in early rounds
The rule of three (again)
Seeing the end of the game
Mike Shor
Game Theory & Business Strategy9
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Voting Revisited
Gore v. Bush
before the U.S. Supreme Court
Recall member preferences:
4 (B>G>R) 3 (G>R>B) 2 (R>B>G)
Majority rule results:
Bbeats G ; Gbeats R ; Rbeats B
Voting results (example):
Rbeats G then winner versus B BMike Shor
Game Theory & Business Strategy10
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Voting as a Sequential Game
Mike Shor
Game Theory & Business Strategy11
R vs. G
B vs. R
B vs. G
B
R
G
B
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Looking Forward
Mike Shor
Game Theory & Business Strategy12
A majority prefers R to B
A majority prefers B to G
B vs. R
B vs. G
B
R
G
B
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And Reasoning Back
Three judges prefer G to R to B.
How should they vote in the first round?
Mike Shor
Game Theory & Business Strategy13
R vs. G
B vs. R
B vs. G
R
B
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What Happened?
Gore supporters have preferences
Gore > Remand > Bush
First round vote between Remand and Gore
Gore supporters prefer Gore
But a vote for Gore is in effecta vote for Bush!
So Gore supporters vote for remand.
Guarantee themselves second best choice
Thinking forwardmisses chance for strategic voting
Thinking forwardleads us to pick the wrong game
Mike Shor
Game Theory & Business Strategy14
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Sequential Rationality
Mike Shor
Game Theory & Business Strategy15
COMMANDMENT
Look forward and reason back.
Anticipate what your rivals will dotomorrow
in response to your actionstoday
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Examples of Strategic Voting
Not necessarily good to vote your true preferences
Amendments to make bad bills worse
Crossing over in open primaries
Centrist voting in primaries
Outcome is still predetermined: Bbeats G then winner versus R
Bbeats R then winner versus G
Gbeats R then winner versus B
Mike Shor
Game Theory & Business Strategy16
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Accommodating aPotential Entrant
Do you enter?
Do you accommodate entry?
What if there are fifty potential entrants?
Mike Shor
Game Theory & Business Strategy17
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SurvivorImmunity Challenge
There are 21 flags
Players alternate removing 1, 2, or 3 flags
The player to take the last flag wins
Mike Shor
Game Theory & Business Strategy18
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Sequential Games
You have a monopoly market in every state
There is one potential entrant in each state
They make their entry decisions sequentially Florida may enter today
New York may enter tomorrow
etc.
Each time, you can accommodate or fight
What do you do the first year?
Mike Shor
Game Theory & Business Strategy19
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The Game
Mike Shor
Game Theory & Business Strategy20
E1
M
E2
M
E3
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Looking Forward
In the last period:
No reason to fight final entrant, thus
( In,Accommodate )
Mike Shor
Game Theory & Business Strategy21
E
M
$0, $100 + previous
50, 50 + previous
50, 50 + previous
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And Reasoning Back
The Incumbent will not fight the last entrant But then, no reason to fight the previous entrant
But then, no reason to fight the first entrant
Only one sequential equilibriumAll entrants play In
Incumbent playsAccommodate
But for long games, this is mostly theoretical
People see the end two to three periods out!
Mike Shor
Game Theory & Business Strategy22
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Game Theory
Example
Sequential Entry
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Market Opportunity Analysis
Assesses the potential of a geographic
market for a specific set of products,providing a prioritization of market
coverage voids and recommending
market entry strategies.
Mike Shor
Game Theory & Business Strategy24
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Prioritizationof Market Coverage
Mike Shor
Game Theory & Business Strategy25
400SBCs
700
SBCs
Break even point: 300 SBCs
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Extended Market Analysis
If enter 400 SBC market: Next entrant, to break even,
must expect market share of 300/400
Must expect market share of 75%
If enter 700 SBC market: Next entrant, to break even,
must expect market share of 300/700
Must expect market share of 43%
Real decision:All of 400 or half of 700
Mike Shor
Game Theory & Business Strategy26
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Breakfast Cereals
A small sampling of the Kelloggs portfolio
Mike Shor
Game Theory & Business Strategy27
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Breakfast Cereals
Mike Shor
Game Theory & Business Strategy28
product development costs:$1.2M per product
600
500
400
300
200
100
000
less
sweet
more
sweet
1 2 3 4 5 6 7 8 9 10 11
sales
(in
thousa
nds)
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First Product Entry
Mike Shor
Game Theory & Business Strategy29
Profit = 5(600) 1200 = 300600
500
400
300
200
100
000
lesssweet
moresweet
1 2 3 4 5 6 7 8 9 10 11
SCENARIO 1
sales
(in
thousa
nds)
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Second Product Entry
Mike Shor
Game Theory & Business Strategy30
600
500
400
300
200
100
000
lesssweet
moresweet
1 2 3 4 5 6 7 8 9 10 11
Profit = 2 x 300 = 600SCENARIO 2
sales
(in
thousa
nds)
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Third Product Entry
Mike Shor
Game Theory & Business Strategy31
600
500
400
300
200
100
000
lesssweet
moresweet
1 2 3 4 5 6 7 8 9 10 11
Profit = 300 x 3 240 x 2 = 420SCENARIO 3
sales
(in
thousa
nds)
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Competitor Enters
Mike Shor
Game Theory & Business Strategy32
600
500
400
300
200
100
000
lesssweet
moresweet
1 2 3 4 5 6 7 8 9 10 11
Profit = 300 x 2 - 240 = 360SCENARIO 4
sales
(in
thousa
nds)
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Summary
Thinking forwardmisses chancesto make money
Make sure to see the gamethrough to the logical end
Dont expect others to seethe end until it is close
The rule of three stepsMike Shor
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