Extensive form games
This
lecture
provides
a
general
introduction to the course, explains the
extensive form representation of games
and introduces you to Comlabgames,
software for designing, playing and
analyzing experimental games.
Preamble
Being “strategic” means intelligently seeking your
own goals in situations that involve other parties who
do not share your goals.
In this school “corporate” typically refers to a
business entity, for example a corporation owned by
shareholders whose interests in the firm are
exclusively financial.
And “management” refers to the kind of job you will
enter upon graduating from here.
Course objectives
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
6. Exploit such situations for your own benefit.
Methodology and tools
We will draw upon
Cases
Game theory
Experimental methods
Statistics
The main tool we use is Comlabgames, free
software you can download from:
www.comlabgames.com
Cases
Using a case to describe a business situation is a
starting point for many of the concepts we discuss.
In distilling the essential features of a case our goal will
be to answer four critical questions:
1. Who are the main players or entities?
2. What moves by the players and chance events
determine the possible outcomes?
3. How well informed are the players when making
their respective decisions?
4. How does each player value the consequences
of any given outcome?
Game theory
A strategic situation exists when the
actions of one person directly affects
the payoff of someone else.
Game theory is the study of such
interactions among players.
A premise of game theory is that each
player pursues his or her respective
objectives taking that
interdependence into account.
The experimental approach
Why use an experimental approach?
1. Putting yourself in the shoes of the decision maker
helps you understand his or her choices.
2. Building models for conducting experiments helps you
answer the four vital questions.
3. Predicting the results of your own experiment and
analyzing the data from it helps you understand how
your strategic rivals might react.
Statistics
Why bother with a statistical analysis?
1. Using statistics helps you evaluate whether your
predictions were confirmed or not.
2. As more data streams become available, managers
must understand and interpret statistical analysis in
an increasingly sophisticated fashion.
3. Strategic consultants must know how to conduct
statistical analyses that use these data streams.
Assessment
There are 2 projects : the first project is worth 35 percent
and the second project is worth 65 percent.
See due dates in the syllabus. Each project consists of

Modeling an issue in business.

Explaining its predictions.

Conducting your own experiment in class.

Participating in the other class projects as a subject.

Analyzing of the data from your own experiment.
Projects may undertaken individually, or in groups of two to
four. Each member of a group will receive the same mark.
Introductory examples
To introduce you to experimental methods, let us
conduct some experiments designed using the
extensive form game module on the comlabgames
web site.
Next lecture we will show how translate a case into
an extensive form game.
Food fight on Lake Erie
There is a Wild Oats supermarket and a Coop organic
grocery in Cleveland OH selling organic food, but only
a Coop in Buffalo NY.
There is greater demand for organic food in Cleveland
than in Buffalo, mainly attributable to differences in
population.
Whole Foods is contemplating entry into one of those
markets as it expands across the Midwest into the
Northeast.
If Whole Foods builds a new store in either location,
one or both rivals might respond by cutting prices and
offering the similar product lines, or they might
passively accommodate Whole Foods’ high end entry.
Whole Foods versus Wild Oats
If Whole Foods
enters Cleveland,
then the Buffalo
Coop retains its
monopoly in
organic food.
In this case the
profits of the
existing stores in
Cleveland depend
on their response
to entry.
Soaking the rich
The goal of the Internal Revenue Service is to maximize
tax revenue given the resources at its disposal.
The IRS audits those reporting incomes over $200,000
far more than those reporting $50,000. Similarly full
time wage earners are audited much less than self
employed businessmen.
If the IRS audited everyone, then nobody would cheat,
but the costs of a universal audit are prohibitive.
We ask how much auditing the IRS will conduct, and
how much tax fraud will occur.
Tax Audit
It is more costly to undertake an
audit than to only check for
irregularities, and if no fraud was
committed the extra tax revenue
and penalties garnered is the same.
Undetected fraud is more lucrative
to the taxpayer then committing
some accounting irregularities.
Truthful reporting and passing over
use up no resources, merely
redistributing wealth from the
taxpayer to the IRS.
Developing a
factory dump or an archeological site
As the economy shifts from the manufacturing to the
service sector, former factory sites and waste dumps
are rapidly becoming prime real estate.
Real estate developers are more savvy about parceling
up land tracts and marketing them than industrial
enterprises.
However the original factory owners know more about
the sources of contaminants and pollutants on their
former factory sites.
The law holds the current owner of a site responsible
for problems caused by hazardous waste on it.
Temporal integration
In this game the factory
owner can develop the site
by itself, but then retains full
liability for all the
contaminants on it.
Selling the site divests the
factory of its liabilities for
any hazardous waste on the
site.
Should the factory owners
move into real estate
development?
Game tree
The games we just played were represented by their
extensive forms.
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?
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
common goals?
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 do they know?
Each non-terminal decision node is associated with an
information set.
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
set.
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.
Lecture summary
We defined the four critical questions for
analyzing any strategic situation.
We introduced the extensive form
representation of a game to depict the
answers to those critical questions.
We conducted several experiments in
class to explore how players might
resolve some strategic interactions.