Lecture 1B
Perfect Information
In games of perfect information players take
turns making their moves, knowing what the
players who have moved before them have
chosen. Every perfect information game has
an extensive form in which all the
information sets are singletons. There are no
dotted lines joining nodes. Thus all the
strategic interactions are sequential.
Pepsi versus Coca Cola
After struggling through the Great Depression
of the 1930s Pepsi finds its soft drink sales are
stalled in the 1940s.
Coke is the industry leader, and its products
command a premium price over Pepsi’s.
The country is at war, but remains segregated
along racial lines, with blacks economically
and socially disadvantaged.
Who are the main players in
this episode?
Pepsi shareholders
Coke shareholders
Management at Pepsi
All-black sales team working in Pepsi
White cola demanders
Black cola demanders
What options or choices
face the main players?
Pepsi could target its product line to African
American consumers, Pepsi could target a new
product line to African American consumers, or
Pepsi could pursue another strategy, such as
expanding its operations in Canada.
Coke could respond aggressively or passively
to any marketing initiative taken by Pepsi.
White consumers might be alienated by a
marketing campaign that targets African
American consumers.
How do the players evaluate the
consequences of their choices?
If Coke responds to an advertising campaign
both firms will sell more cola in return for
lower profits.
If Coke does not respond to Pepsi, how much
value will be added or lost to each company?
If the white community is alienated by both
companies targeting the African American
community, would Coke be hurt more than
Pepsi?
Where are the sources of
uncertainty in this unfolding drama?
Will white cola drinkers be alienated by the
introduction of a marketing campaign that
targets the African American community?
Answering the four critical questions
in an extensive form game
If both companies
target blacks, the
probability of
alienating whites is
higher than if only
Pepsi does.
Moreover as the
company with the
bigger white market
share, Coke has more
to lose in this case.
Day labor
In Los Angeles and other places employer
contractors routinely hire workers directly
off the street for a fixed wage for the day.
Contractors can offer different salary rates
to laborers, but they cannot directly control
the level of effort their laborers work.
Contractors would prefer to extract
strenuous effort from laborers for low
wages, but laborers prefer the opposite,
high wages and low effort.
Employment and effort
In this game a laborer is
willing to give up $8 a day
to provide moderate rather
than strenuous effort, and
a further $6 in return for
low effort.
The employer is willing to
pay $88 to extract
strenuous rather than
moderate effort, and loses
a further $66 if the worker
puts in low versus
moderate effort.
The choice labor faces
Reduced game for the employer
The solution to this
game explains why
most employment
is not contracted in
this fashion.
In 45-976 we
examine strategic
interactions within
the workplace in
greater depth.
Regional markets
A prominent feature of geographically based
markets, such as personal services, retailing,
distribution, and travel is that the regional
markets overlap.
Thus competition in one market can spill over
into the next, creating a cascading effect.
Perhaps nowhere is this more evident than in
the airline industry.
Airline pricing cascades
In this example,
American competes with
Delta, Delta also
competes with United,
United competes with
Delta, and US Airways,
while US Airways only
competes with United.
Thus the payoff to US
Airways is unaffected by
rivalry between American
and Delta.
The first rule of strategy:
Backward induction
Sometimes called a rollback equilibrium the principle
of backwards induction shows how finite games of
complete information can be solved.
Rule 1: Look ahead and reason back.
A follower’s advantage
Through orders bookings and
sales, first entrants typically
learn about potential demand
earlier than later entrants.
If these data cannot be kept
confidential, then followers
can use the data.
Over on the right we see that
Eagle decides whether to
enter or not, only after seeing
what Cheetah has done and
the effects on demand.
Folding back and
simplifying the game tree
If Cheetah begins an air
service then Eagle will
enter only if demand is
high.
If Cheetah does not
create the service, then
Eagle will not get the
information on demand.
In that case we can
exchange the order of
the moves of Eagle and
nature.
A further reduction
Taking expected
values we are left
with a very simple
game tree.
Cheetah should
stay out, and Eagle
should enter.
The value of withholding
data on demand
Now suppose
Cheetah can prevent
Eagle from having
access to data on the
profitability of its new
route.
In this case Eagle
can see whether
Cheetah entered or
not, but not the state
of demand.
Air service -redrawn
The game is
equivalent to the
picture on the
right.
Both firms must
move before the
state of demand
is revealed.
Air service – further reduction
Taking the
expectation over
the payoffs yields a
further
simplification.
Now Cheetah will
enter confident that
Eagle will stay out.
Philips and Sony compete in the
introduction of CD players
In 1982 Philips could commit
immediately to building a CD
processing capacity in the US or
postpone its decision and continue
to import from Europe.
Philips knew its leading competitor,
Sony, might enter if Philips
postponed its decision, but that
Sony would become informed
about demand before Philips.
The numbers are taken from a
study by A. M. McGahan 1994.
An alternative representation
of the Philips Sony CD production
This is a perfect
information game
because we can
exchange the order in
which Sony and popular
buyers move.
Using the first rule one
can prove that Philips
should wait, and then
build (if demand is
high), because Sony
will stay out.
Silicon valley circa 1996
Just after TCPIP
protocol was settled,
a euphoria enveloped
programmers and
investors, who
thought the internet
would turn the world
into a global village.
Notice that in this
game the venture
capitalist has the
same information as
the innovator.
The extensive form redrawn
Redrawing the same game
to reflect the uncertainty of
both parties, we see that
this is a perfect information
game.
If 10p + 2(1-p) > 5, that is
p > 3/8, then the innovator
should request funding, and
the venture capitalist should
fund the project.
Otherwise the innovator
should ignore the
opportunity.
Lecture summary
We discussed how to take a business situation
and put it in a form amenable to strategic
analysis.
We derived our first rule of play. In perfect
information games look ahead and reason back.
We showed that there are many games that
have perfect information, although it may not
appear that way at first.