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

CasesUsing 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.

AssessmentThere 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 treeThe 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.