Game Theory
The Art of War, Sun Tzu

“Thus, it is said that one who knows the
enemy and knows himself will not be
endangered in a hundred engagements.
One who does not know the enemy but
knows himself will sometimes be
victorious, sometimes meet with defeat.
One who knows neither the enemy nor
himself will invariably be defeated in every
engagement.”
Strategy Game







Each team starts with 10 armed tanks
The game consists of two 5 move rounds
During each move, a team may choose to arm
or disarm 0, 1, or 2 tanks
The teams must negotiate after moves 1 and 3
Teams may request a negotiation after any other
move, but the other team must agree
Either team may attack the other team on any
move except move 5
The round is over when a team attacks
Strategy Game (cont)


Objective – Score the most points possible
Points


If you attack you get 10 points for every
armed tank you have in excess of the other
team
At the end of round 5, if no one attacks, both
teams get 5 points for each tank they have
disarmed
Structured Games


The game has a more formal structure:
there are rules and a reasonably small set
of possible outcomes
The basic rule for structured games is “to
look forward to determine the outcomes
and then reason backward to determine
the best action”
Game Theory: payoff matrix




There are two (or more) players, each of
whom has a finite number of options
List the choices for each player on one of the
axes
Each cell in the matrix represents the payoff
(reward to a player) resulting from choosing
an option assuming that the other player will
choose a particular option
Usually the payoffs for both players are given
in the same cell, separated by a diagonal
slash or as an ordered pair (row, column)
The Prisoner’s Dilemma
Two vagrants, Al and Joe, have been arrested for vagrancy. The DA
suspects them of complicity in a robbery, but she doesn’t have
enough evidence to convict them. (Al and Joe don’t know this for
sure.) The DA interrogates each of them separately and offers the
following deal:
“If you confess and your friend does not, you will be released and I
will throw the book at your friend. I have made the same offer to
your friend.” Assume the relevant prison times (in months) are as
follows:
Al
Joe
Confess
Don’t Confess
Confess
(-8, -8)
(0, -15)
Don’t Confess
(-15, 0)
(-1, -1)
How will the game turn out?
The Rational Pigs
Two pigs, one dominant and one subordinate, are in a pen. There is a
lever at one end of the pen which, when pressed, dispenses 6 units of food
into a trough at the other end of the pen. Thus, a pig that presses the
lever must run to the other end of the pen before it can eat. By the time
it gets there, the other pig may have eaten some or most of the food.
The dominant pig is able to prevent the subordinate pig from getting any
of the food when both are at the trough. Assume it requires energy
equivalent to ½ unit of food to run from one end of the pen to the other.
Suppose that if both of the pigs press the lever, the subordinate pig is
faster than the dominant pig and can eat two units of food before the
dominant pig gets to the food. Which pig will press the lever?
Dominant Pig:
Subordinate Pig:
Press
Don’t Press
Press
(1.5, 3.5)
(-0.5, 6)
Don’t Press
(5, 0.5)
(0, 0)
Strategic Principles




Use Strategic Foresight
Know Yourself as Well as Others
Differentiate Between One-Time and
Repeated Interactions
Managers Must Unify Minds to Promote
Cooperation
Co-opetition Combines
Cooperation and Competition
Cooperation
affects the
size of the
pie
Competition
affects the
market
share --size
of the slice
Profit is the product of the size
of the pie and the market share
The Value Net
Customers
Substitutors
Company
Complementors
Suppliers
Source: Adam Brandenburger and Barry Nalebuff, Co-opetition
(New York: Currency Doubleday, 1996), p. 17
The Value Net
A player is your
substitutor with respect
to customers if
customers value your
product less when they
have the other player’s
product as well
Substitutors
A player is your
substitutor with respect
to suppliers if it is less
attractive for a supplier
to provide resources to
you when it is also
supplying the other
player
Customers
Firm
Suppliers
A player is your
complementor with
respect to customers if
customers value your
product more when they
have the other player’s
product as well
Complementors
A player is your
complementor with
respect to suppliers if it
is more attractive for a
supplier to provide
resources to you when it
is also supplying the
other player
Source: Adam Brandenburger and Barry Nalebuff,
Co-opetition (New York: Currency Doubleday, 1996)
Expanded Industry Analysis
Threat of New
Entry
Bargaining Power
of Suppliers
Rivalry Among
Existing
Competitors
Bargaining Power
of Customers
Threat of
Substitutes
Availability of
Complements
Changing the game


First: Identify the players and draw the
value net
Second: identify the elements of the
game (PARTS)



Players, Added values, Rules, Tactics, Scope
Change one or more of these elements
No elements of the game should be
considered fixed and unchangeable
Boeing, Airbus and the
super-jumbo airframe (1991)
Boeing
(A/B)
Airbus
Develop
Develop
(6-8+5=3 /
9-8=1)
Doesn’t
Develop
(-2/15-8=7)
Doesn’t Develop
(15-3=12/ -6)
(-1/12)
Market =$15b, Development Cost=$8b, Airbus subsidy=$5b
How Will the Game Turn Out?



It is the rational pig situation: Airbus has a
dominant strategy: introduce the super jumbo.
Boeing’s strategy depends on what Airbus does.
Since Airbus will introduce, Boeing will introduce
also
But Boeing’s strongly preferred solution is for
neither to introduce the super jumbo so it can
continue its 747 monopoly!
Therefore, Boeing must find ways to change the
game!!
How Boeing Has Changed the Game





Change players: Jan 1993, Boeing invites Deutsche
Aerospace to be its partner in super jumbo
development (Nearly splits up Airbus) (Great fun in
the newspapers!!!)
Change tactics (perceptions) and added values:
June 1995, Boeing announces that the market
wants a supersonic—not a super jumbo (it builds
neither!)
Change rules: (constantly) Petition the WTO and EU
to ban subsidies to Airbus
December 1999 Airbus announces it will develop a
super jumbo (None has been built, yet!)
Boeing has delayed super jumbo introduction by 9
years (so far). Value of playing the game =
$117billion (9 years @ $ [12b-(-1b)]
Conclusion


Use of Game Theory Helps Managers
Predict Actions of Competitors
Common Framework and Language for
Analysis of Competitive Decisions and
Interactions
Traps of Strategy








Not understanding the present game
Believing you must accept the present game
Thinking that change must come at the expense
of another player (win-lose)
Believing you must do something unique
Failing to see the whole game
Failing to think methodically
Failing to think dynamically
Not expecting another player will change the
game