Theory and Practice of Games in Economics and Evolution

 
 

ISCI 344 "Game Theory"

Course Description

Game theory involves the study of cooperation and competition. It provides a theoretical framework for reasoning about a wide variety of phenomena including, for instance, the price of gasoline, nuclear proliferation, who pays for dinner when friends dine out, or the biological conditions necessary for the evolution of cooperation. This course presents the basic ideas of game theory, starting with how to represent and classify different kinds of interactions in terms of games where players choose among alternative strategies in order to maximize their own benefit. Game theory is useful across a broad range of scientific disciplines because situations involving conflicts of interest are ubiquitous, and because the meaning of “players” in game theory is very general. For example, players could be individual genes competing for representation in subsequent generations or whole countries negotiating trade agreements with each other. Of particular interest are social dilemmas where rational behaviour by individual players paradoxically does not necessarily lead to a collectively rational outcome. Such situations are sometimes referred to as a tragedy of the commons, a prisoner’s dilemma, or a public goods game and they characterize many social, economic, evolutionary biology, and political problems.

Emphasis in the course is on understanding the findings of game theory and its usefulness in analyzing a variety of interesting phenomena, rather than on the purely technical aspects of the theory. This course should be of particular interest to biologists and social scientists, but also to any student wishing to gain formal tools for reasoning about cooperation and competition in social interactions. The course emphasizes student participation, featuring seminar-style discussion as well as some traditional lectures. The course will culminate in a small research project in which students survey existing literature and possibly explore open research questions.

Learning Objectives

By the end of the course, and for many years after, you should be able to:

Grasp, or recognize, real situations where game theory can be enlightening,
Abstract a real situation into game theoretic formalism,
Manipulate the formalism via game theory to reveal insights, and
Explain your insights in terms of the real situation.

Topics

Here are some topics you can expect to cover in this course (in no particular order):

  • What is a game?
  • Foundations of game theory
  • Evolutionary game theory
  • Payoff matrices
  • Zero-sum games
  • Extensive form
  • Solution concepts
  • Nash equilibria
  • Pareto optima
  • Mixed Nash equilibria
  • Replicator equation
  • Evolutionarily stable strategy
  • Comparison of evolutionary and classical game theory
  • Repeated games
  • Many-player games
  • Reward and punishment

Grading Scheme

The exact percentage breakdowns shown here may change. The following grading scheme should be approximately accurate and indicates the components upon which grades will be based.

Component Weight
Assignments 20
Midterm 20
Project 30
Final Exam 30
Total 100

Students must pass the final exam to pass the course.

Assignments

The course will include assignments (sometimes with class presentations). Assignments will probably not be weighted equally. In particular, later assignments may be weighted more heavily since they will cover material not reviewed on the midterm exam. There may also be short in-class assignments, and presentations.

Assignments are to be handed in at the location, time, and date specified in the assignment handout. Late assignments will be penalized 10% per calendar day (or part of day) the assignment is late. Please allow ample buffer in your schedule when completing your assignments to account for unexpected circumstances. These include things such as moderate illness, conflicts with other courses, extracurricular obligations, job interviews, etc. All students will be granted one free late day (or part of day) without penalty. Additional late days (without penalty) will NOT be granted except under truly exceptional circumstances. Delivery of late assignments should be arranged with instructors via email and may include either scanning and emailing or faxing of your assignment.

Project

ISCI 344 will culminate with a project that allows students to explore material that was not covered in class and to share that material with other students and instructors. The project may involve students writing a paper on a topic of interest within Game Theory or conducting and writing up some original research and/or analysis. More details on projects will be available as the course proceeds. Collaborative projects will be encouraged.

Some sample project areas include:

  • Game Theory and Canadian Politics
  • Game Theory and Fisheries Management
  • Game Theory and the Evolution of Cooperation
  • Game Theory and Climate Change
  • Many other possibilities – what interests you?

Please note that because of the peer review process your final project must be submitted by the due date.

Flex points and flex weight

Student participation in sample games is an essential part of learning about game theory. To encourage students to make an effort to “win” the games (so that the axioms of game theory apply) the rewards need to be meaningful. Flex points will be rewarded in class as incentives to participate and excel in games. Flex points may also be awarded for optional “ad hoc” assignments.

Students can earn an unlimited number of flex points over the term; at the end of the course they will be used to modify the weights of the components of the course. At the end of the course the accumulated flex points will be translated into flex weight according to the following formula:

The weight of each student's worst component will be reduced by their accumulated flex weight and the weight of the best component increased accordingly. By earning flex points you can tailor the grading scheme to favour your learning style! We assume this creates sufficient incentive to turn the in-class games into proper game theoretic learning environments.

 

Example

Rikky does well on projects and assignments but lousy on tests. He scores 90% on the assignments, 80% on the project, 70% on the midterm, and 60% on the exam. With the default grading scheme Rikky would earn an overall grade of 74%.

But throughout the course Rikky earned 10 flex weight (from 14 flex points), so the weights of his best and worst component are adjusted as shown:

Component Rikky's Score Weight before flex Weight after flex
Assignments 90 (best) 20 30 = 20 + 10
Midterm 70 20 20
Project 80 30 30
Final Exam 60 (worst) 30 20 = 30 - 10
Rikky's overall grade   74 77

So, Rikky is able to increase his overall grade from 74% to 77% just by “winning” some in-class games.

Text

There are no required textbooks for the course but the following books are useful resources:

Game theory: a nontechnical introduction by Morton D. Davis.
Call Number: QA269 .D38 1983
Location: I.K. BARBER LEARNING CENTRE

Evolutionary dynamics by Martin A. Nowak.
Call Number: QH371.3.M37 N69 2006
Location: WOODWARD LIBRARY

Essentials of Game Theory: A Concise Multidisciplinary Introduction by Kevin Leyton-Brown‌ & Yoav Shoham‌
Available from Morgan & Claypool (free through UBC EZproxy).

Additional readings may be recommended during the course of the term.

In addition you may check out the VirtualLabs and EvoLudo, a collection of interactive tutorials on evolutionary games.

Canvas

The following additional course content is available to registered students via Canvas:

  • Announcements
  • Video lectures
  • Discussion forums
  • Project work
  • Grades

To log in, please click on the CWL Login button below:

Registration Details

 
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