Lecture 1 - ComLabGames
Transcript Lecture 1 - ComLabGames
Professor Robert A. Miller
January Special 2013
John Gardner: [email protected]
Being “strategic” means intelligently seeking your own
goals in situations that involve other parties who do not
share your goals, a theme we emphasize in this course.
In business “corporate” typically refers to a publicly
traded company with limited liability, a corporation
owned by shareholders. We will focus more broadly on
business entities, and management goals.
And “management” refers to organizing people, when
you lack the absolute powers of a dictator, but can wield
some incentives and help set the rules.
1. Recognize strategic situations and opportunities
2. Summarize the essential elements in order to
undertake an analysis
3. Predict the outcomes from strategic play
4. Conduct experiments, that is “human simulations”,
to verify and revise your predictions
5. Analyze the experimental data to increase your
knowledge and familiarity using simple statistics
. . . to help you make better strategic decisions.
The course website is:
At the website you can find:
the course syllabus
power point lecture notes
experiments you can download
the on line (draft) textbook
other reading material
Introduction to Strategy:
We begin this course by laying out the four
basic questions of every strategic situation.
Then we define the extensive form, and
explain: what we mean by the empirical
distribution of moves, what is a best
response (to that distribution for example),
and the concept of dominance.
A cola war
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
Management at 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
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
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
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?
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
Illustrating the four critical questions
in an extensive form game
The extensive form
The game we just played was represented by its
The extensive form representation answers the four
critical questions in strategy:
Who are the players?
What are their potential moves?
What is their information?
How do they value the outcomes?
These are the ingredients used to design all games in
Who is involved?
How many major players are there, and whose
decisions we should model explicitly?
Can we consolidate some of the players into a
team because they pool their information and have
Should we model the behavior of the minor players
should be modeled directly as nature, using
probabilities to capture their effects on the game?
Does nature play any other role in resolving
uncertainty, for example through a new technology
that has chance of working?
What can they do?
Each node designates whose turn it is. It could be a
player or nature. The initial node shows how the
game starts, while terminal nodes end the game.
A branch join two nodes to each other. Branches
display the possible choices for the player who
should move, and also the possible random
outcomes of nature’s moves.
Tracing a path from the initial node to a terminal
node is called a history. A history is uniquely
identified by its terminal node.
What are the payoffs?
Payoffs capture the consequences of
playing a game.
They represent the utility or net
benefit to each player from a game
ending at any given terminal node.
Payoffs show how resources are
allocated to all the players contingent
on a terminal node being reached.
What do they know?
Each non-terminal decision node is associated with an
If a decision node is not connected to a dotted line, the
player assigned to the node knows the partial history.
If two nodes are joined by a dotted line, they belong to
the same information set, and the two sets of branches
emanating from them, which define the player’s choice
set, must be identical.
A player cannot distinguish between partial histories
leading to nodes that belong to the same information
Changing the information
available to Coke
Suppose we draw
a dotted line
nodes for Coke.
Then we prevent
Coke from seeing
before it chooses
acquiesce or not.
The empirical distribution
The empirical distribution is the probability
distribution of choices made by all the
players in the game.
It is formed from the relative frequencies of
choices made at each information set
observed in the experiment.
For example, the empirical distribution
characterizing Coke comprise two relative
frequencies, showing how likely Coke is to
cut price if Pepsi advertises in the:
1. Quebec market
2. African American market
Best response to empirical distribution
For any given player (Pepsi), treat the moves by all
other players (Coke) as nature.
Form the choice probabilities for the other players
from the relative frequencies of the choices observed
in the experiment (by experimental subjects playing
This transforms the game into a dynamic
programming problem for the given player (Pepsi).
Use dynamic programming methods, such as
backwards induction, to find the (Pepsi’s )best
response to the empirical distribution.
To compute the best response for Pepsi you need to
know Pepsi’s payoffs but not Coke’s.
The Ware case
10 years ago Ware received a patent for Dentosite that
has since captured 60 percent share in the market.
National had been the largest supplier of material for
dental prosthetics before Dentosite was introduced.
A new material FR 8420 was recently developed by NASA.
If Ware develops a new composite with FR 8420 it will be
a perfect substitute for Dentosite.
If the technique is feasible then Ware would have just as
good a chance as National of proving it first.
If Ware develops it first they could extend the patent
protection to this technique and prevent any competitors.
Ware’s problem is bound to National’s.
Ware does not want to develop a technology that
would not be used if the competitor does not
If National develops the technology Ware cannot
afford to drop out of the race.
It all depends how people at National see this
situation. Are Ware and National equally as well
The Ware Case
$1.9091 Value of $1 in years 1+2
$3.4462 Value of $1 in years 3+4+5+6+7
$0.500 Ware entry cost/yr
$1.000 National entry cost/yr
$15 Range of possible
$20 future annual sales (millions)
50% Probability process feasible
50% Ware chance of winning race
50% Ware market share if Nat'l enters mkt
20% Ware profit margin
Ware case in the extensive form
Using the facts we can present the case
in the following diagram:
Simplifying the extensive form
Folding back the moves of chance that are
related to developing a new technology we
obtain the following simplification.
What should National do?
National is indifferent between the two choices if the
expected profits are equal.
If Ware chooses “in” with probability p, the value to
National from choosing “out” is 0, and the expected
profits to National from choosing “in” are:
-0.401*p + 1.106*(1 – p)
Solving for p we obtain:
-0.401*p + 1.106*(1 – p) = 0
p = 0.734
Thus if Ware enters with a higher probability than
0.734, then National should stay out, but if Ware
enters with a lower probability than 0.734, National
should enter itself.
What should Ware do?
If National chooses “in” with probability q, then the
expected value to Ware from choosing “in” is:
-2.462*q - 0.955*(1 – q)
Also the expected value to Ware from choosing “out” is:
Solving for q we obtain:
2.462*q + 0.955*(1 – q) = 3.015*q
q = .633
Thus if National enters with probability higher than
0.633, then Ware should enter too, but if National
enters with probability lower than 0.633, then Ware
should stay out.
Play a best response to the empirical
distribution as best you understand it.
How much do you need to know
about the other players?
In the cola war, if Coke never acquiesces to Pepsi, then
the best response of Pepsi is to enter Canada, but if Coke
only responds in kind in Canada, then Pepsi should enter
the African American market.
Similarly in the Ware case, the best response of each firm
depended upon the probability that the other firm would
seek to develop the patent.
Under what conditions does your best response depend
on the choices of the other players?
Simultaneous move games
In many situations, you must decide all your
moves without knowing what your rivals are
doing, and their situations are similar to yours.
Even if the moves are not literally taking place
at the same moment, but all the moves must
be made before anybody can react, the moves
are effectively simultaneous.
A game where no player can make a choice
that depends on the moves of the other
players is called a simultaneous move game.
The Ware case is an example of a
simultaneous move game.
Acquiring Federated Department Stores
Robert Campeau and Macy's are competing for control of
Federated Department Stores in 1988.
If both offers fail, then the market price will be
benchmarked at 100. If one succeeds, then any shares
not tendered to the winner will be bought from the
current owner for 90.
The argument here is that losing minority shareholders
will get burned by the new majority shareholders.
Campeau’s offer . . .
Campeau made an unconditional two tier offer. The
price paid per share would depend on what fraction of
the company Campeau was offered.
If Campeau got less than half, it would pay 105 per
share. If it got more than half, it would pay 105 on
the first half of the company, and 90 on any
Each share tendered would receive a blend of these
two prices so that every share received the average
price paid. If a percentage x > 50 of the company is
tendered, then 50/x of them get 105, and (1 - 50/x)
of them get 90 for a blended price of:
105* 50/x + 90(1 - 50/x) = 90 + 15(50/x).
Macy’s offer . . .
Macy's offer was conditional at a price of
102 per share: it offered to pay 102 for each
share tendered, but only if at least 50% of
the shares were tendered to it.
Note that if everyone tenders to Macy's,
they receive 102 per share, while if
everyone tenders to Campeau, they receive
97.50. so, shareholders are collectively
better off tendering to Macy's than to
The game between shareholders
After the offers are made, Federated shareholders
play an acceptance/rejection game.
Each shareholder asks what proportion of their
shares should be:
1. sold to Macy’s
2. sold to Campeau’s
Note the payoffs received by each shareholder
depend on what the other shareholders do.
The payoff matrix to a stockholder
Shareholders are better off as a group tendering to Macy’s,
but each individual shareholder is better off tendering to
Campeau, regardless of what the other players do.
Tender to Campeau
Tender to Macy’s
Do not tender
Strategies that are optimal for a player regardless of
whether the other players play rationally or not are
If a dominant strategy is unique, it is called strictly
Although a player's payoff might depend on the
choices of the other players, when a dominant
strategy exists, the player has no reason to
introspect about the objectives of the other players
in order to make his own decision. He should simply
play the dominant strategy.
A dominant response is always a best response to
the empirical distribution. Therefore if you have a
dominant response, you should play it.
The extensive form summarizes the four dimensions of
every strategic situation (players, actions, information
Playing the best response to the empirical distribution
mimics optimal decision making. It only requires you to
know the other players, and their choice probabilities.
Also in some but not all games the best response is
independent of the empirical distribution.
When this occurs a player has a dominant strategy.