Week 4
The Strategic Value of Information
This lecture analyze the value of information in
strategic contexts. The intuition from decision
theory, that more information cannot hurt, does not
easily extend to strategic situations, because the
anticipation and reactions of the other players must
be accounted for.
The strategic value of information
In decision theory, new information is never harmful and
has positive value if it leads you to change your behavior.
The rules we have developed for solving games can be
used to value information in strategic contexts. We ask:
1. Is there value form withholding information for the
competition, or should we release it?
2. Does providing (the same) new information to
everyone increase value?
3. What can we learn from the choices of others when
they are more informed than us?
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.
Product development race
Often companies do not know precisely how much
competition they will face before launching a new product:
Strategic form of
product development race
Both firms have a dominant strategy to advertise the product,
which determines the unique solution to this game.
An industry newsletter
Now suppose a newsletter is produced to keep firms
abreast of the latest developments. The extensive
form becomes:
Subgames
There are three proper sub-games beginning at nodes 2,
3, and 4.
If Thompson is the only firm to develop the product, it
should advertise rather than choose a low price, and
similarly for Smith.
The sub-game starting node 4,
when both firms develop the
product, illustrates the
prisoners’ dilemma. The unique
solution is for both firms to
charge the low price.
The strategic cost of better information
and the value of information silos
This example shows that more information about an
industry could sometimes hurt it.
Additional information helps firms to identify
situations where their positions are opposed to each
other, and induce competition that might lead to the
detriment of all firms.
Finally suppose Smith and Thompson were two plants
owned by the one firm! This example shows the value
of having information silos when different profit
centers are competing with each other.
Bottling wine
Corks are traditionally used in bottling wine,
but recent research shows that screwtops
give a better seal, and hence the reduce the
risk of oxidation and tainting. They are also
less expensive.
However consumers associate screwtops
with cheaper varieties of wine, so wineries
risk losing brand reputation from moving too
quickly ahead of the consumer tastes.
To illustrate this problem consider two Napa
valley wineries who face the choice of
immediately introducing screwtops or
delaying their introduction.
Extensive form game
Mondavi has
resources to
conduct market
research into
this issue, but
Jarvis does not.
However Jarvis
can retool more
quickly than its
larger rival, so it
can copy what
Mondavi does.
Eliminating the
dominated strategies of Mondavi
We can simplify the
problem that Jarvis
has by drawing its
decision problem
when Mondavi
follows its dominant
strategy.
Solving for Jarvis
Since 4 > 0, Jarvis bottles with cork if Mondavi does.
The expected value of using screwtops when
Mondavi does is:
(0.3*4 + 0.2*4 )/(0.2 +0.3) = 4.0
while the expected value of retaining corking when
Mondavi switches is:
(0.3 + 0.2*6)/(0.2 +0.3) = 3.0
Therefore Jarvis always follows the lead of Mondavi.
Rivals as a source of information
The solution to this game shows that rivals can be a
valuable source of information.
Although Jarvis could undertake its own research into
bottling, it eliminates these costs by piggybacking off
Mondavi’s extensive marketing research.
Nevertheless Jarvis receives a noisy signal from
Mondavi. Jarvis cannot tell whether consumers prefer
screwtops or are indifferent.
How much would Jarvis be prepared to pay to conduct
its own research, and receive a clear signal?
The value of independent research
When consumers are
indifferent Jarvis could
capture a niche market by
corking, increasing its
profits by 6 – 4 = 2.
Hence access to Mondavi’s
superior market research
increases Jarvis’s expected
net profits by:
0.2*2 = 0.4.
This sets the upper bound
Jarvis is willing to pay for
independent research.
Summary
We developed the strategic form of a game, and
demonstrated that some games are easier to analyze in
their strategic form than in their extensive form.
We analyzed a third principle for strategic play, iterative
dominance, and showed that it encompasses backwards
induction as an application.
Then in the latter parts of this lecture we showed that the
effects of new information are much more complicated to
analyze in strategic situations than in decision theory.
For example, we showed that when new information is
provided to every player, they can all lose, while another
example highlighted the benefits of withholding
information.