Extensive form games

1
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.

2
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.

3
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.

4
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

5
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
• Who are the main players or entities?
• What moves by the players and chance events
  determine the possible outcomes?
• How well informed are the players when making
  their respective decisions?
• How does each player value the consequences of
  any given outcome?

6
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.

7
The experimental approach

• Why use an experimental approach?
• Putting yourself in the shoes of the decision
  maker helps you understand his or her choices.
• Building models for conducting experiments helps
  you answer the four vital questions.
• Predicting the results of your own experiment and
  analyzing the data from it helps you understand
  how your strategic rivals might react.

8
Statistics

• Why bother with a statistical analysis?
• Using statistics helps you evaluate whether your
  predictions were confirmed or not.
• As more data streams become available, managers
  must understand and interpret statistical
  analysis in an increasingly sophisticated
  fashion.
• Strategic consultants must know how to conduct
  statistical analyses that use these data streams.

9
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.

10
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.

11
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.

12
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.

13
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.

14
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.

15
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.

16
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?

17
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?

18
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?

19
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 natures 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.

20
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 players choice set, must be
  identical.
• A player cannot distinguish between partial
  histories leading to nodes that belong to the
  same information set.

21
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.

22
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.