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Game Theory and Python: An educational tutorial to game theory and repeated games using Python |
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5 December 2019 |
paper.bib |
These materials are an open-source educational tutorial aimed at introducing
participants to game theory and more specifically to repeated games. The
tutorial uses the open-source library called
Axelrod-Python and Jupyter
Notebooks making this an open-source, reproducible and
interactive tutorial.
We are mathematicians and Python programmers with interests in game theory and pedagogy. This tutorial was created as a resource for computer workshops and for introducing mathematicians to programming. As a result, this tutorial is aimed at two groups of individuals:
- those familiar with Python (programmers) who want to start to learn game theory,
- mathematicians with little or no programming knowledge as a pathway to programming through the interesting subject that is game theory
Game theory is a field of applied mathematics interested in strategic interactions. Game theory itself has a number of subfields and the one considered in this tutorial is the area of repeated games. Repeated games have been the subject of research [@Axelrod1981; @Nowak2006; @Glynatsi2021] but have also been used extensively as an entry to the subject for students at undergraduate level courses [@Brokaw2004; @Knight2015]. This tutorial focuses on the Iterated Prisoner's Dilemma. The advantage of studying the Iterated Prisoner's Dilemma is that it models situations in which self-interest clashes with collective interest, thus it provides a framework for illustrating the usage of mathematics in real-life decision making.
These materials consist of four tutorials that focus on the Iterated Prisoner's
Dilemma, the notion of strategies and computer tournaments whilst using
Axelrod-Python [@axelrodproject].
In 1980, a political scientist called Robert Axelrod ran a computer
tournament of the Iterated Prisoner’s Dilemma where strategies written in
computer code would repeatedly choose between self and collective interest. The
strategies would decide on their next action using the history of previous
interactions and the winner was decided based on the average score. The open-source
package Axelrod-Python was created in order to reproduce Axelrod's original work
but to also serve as an educational and research tool.
Following the tutorial, participants will be able to reproduce Axelrod's tournament but also create their own unique tournaments from a selection of more than 200 strategies. Furthermore, participants will be able to progress their comprehension of the topic by producing strategies and implement them in Python. The new strategies can then be placed in different tournaments in order to access their success and weakness. This progression of the tutorial fits within a constructive framework of learning [@Jordan2008] and, by the nature of participants actively writing the required software, an active learning setting [@Freeman2014]. Participants with knowledge of Python will benefit from an understanding of game theory and participants with no knowledge of Python will also be introduced to basic programming concepts through the tangible ideas of the Prisoner's Dilemma.
The tutorial Game Theory and Python can be used in a workshop environment or
through independent learning.
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Workshop: The material has been designed for a 2 hour workshop. A suggested timetable is:
- 0:00 - 0:15 Installation (guidelines are given in the README)
- 0:15 - 0:30 An introduction to game theory and the Iterated Prisoner's Dilemma
- 0:30 - 0:55 Creating matches and tournaments using Axelrod-Python
- 0:55 - 1:20 Writing strategies and contributing to Axelrod-Python
- 1:20 - 1:50 Playing against strategies of the Iterated Prisoner's Dilemma
- 1:50 - 2:00 Closing remarks and wrapping up
In a workshop environment we suggest that the instructor has familiarized themselves with the written parts of the tutorial beforehand. The written parts of each notebook include an introduction to the topic being covered. It is advised that the instructor discusses the introduction to the topic followed by them typing out/running the material while the participants follow using their own machines. The instructor should encourage the participants to try the exercises of each notebook alone or with other participants. Before moving to the next notebook the instructor should encourage a discussion amongst everyone regarding the results of the exercises each had and their interpretation.
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Independent Learning: An independent learner should aim to spend the same amount of time on the material, approximately 2 hours. A suggested timetable is:
- 0:00 - 0:15 Installation (guidelines are given in the README)
- 0:15 - 0:30 An introduction to game theory and the Iterated Prisoner's Dilemma
- 0:30 - 1:00 Creating matches and tournaments using Axelrod-Python
- 1:00 - 1:30 Writing strategies and contributing to Axelrod-Python
- 1:30 - 2:00 Playing against strategies of the Iterated Prisoner's Dilemma
If the tutorial is being followed by an individual learner, we suggest that the learner reads the written parts of each notebook followed by running the tutorial and completing the exercises. The individual should take some time to reflect on the results of each notebook and their interpretation.
These instructions can also be found in the README. Though we recommend that the material can be covered in 2 hours, in both a workshop environment and through independent learning, some audience/learners might need more time to complete all the exercises. We recommend any facilitator/learner to adjust as necessary.
This tutorial was originally formulated to run a game theory workshop at PyCon Namibia 2017. It has attracted the attention of the community ever since and has been used in other events.
The tutorial has been made possible due to the existence of the open-source package Axelrod-Python. We would like to express our appreciation to the maintainers of the package as well as anyone that has ever contributed to it.