# Introduction to Game Theory: a Discovery Approach

Jennifer Firkins Nordstrom, McMinnville, Oregon

Copyright Year:

Last Update: 2020

Publisher: Jennifer Firkins Nordstrom

Language: English

## Formats Available

## Conditions of Use

Attribution-ShareAlike

CC BY-SA

## Reviews

The text is fairly comprehensive across the domain it attempts to cover – it isn’t exhaustive in its coverage of game theory, but it doesn’t try to be. It is short and focused, which is perfect for the goal it sets out to accomplish: an... read more

The text is fairly comprehensive across the domain it attempts to cover – it isn’t exhaustive in its coverage of game theory, but it doesn’t try to be. It is short and focused, which is perfect for the goal it sets out to accomplish: an introduction to quantitative reasoning for non-majors.

The book takes what the author calls a discovery approach, where the reader is asked to think about and attempt to solve problems before being given all the tools to do so. The idea is that students will use some intuition to start to solve the problem, and then they can connect that to the formal solutions. I like this idea a lot, but it might be described as “high-risk/ high-reward”. It could backfire, particularly if students struggle for too long without being given the formal tools and explanations. Section 2.4 is an example, with more than a dozen steps where students step through a problem – if they fail at any one step, the rest is difficult or impossible to continue doing correctly, and students won’t know they’ve taken a wrong turn until they’ve done a lot of work. The value/risk of this approach is related to how the book will be used – the author suggests students tackle this work in class, with opportunities to ask peers or the instructor. I don’t suspect it would work as a traditional text, in very large class settings, or as a set of assignments students read independently. This isn’t a criticism, but a recognition that a lot of the instruction is happening between people in the classroom, and isn’t self-contained in the text.

The basic content and ideas presented are accurate.

Staying close to classical game theory, the content and examples here are unlikely to ever go out of date. However, section 2.7 uses popular culture examples that are 30-50 years old, and it isn’t clear how students are supposed to know the films and characters described in order to answer the questions therein – unless they are shown the films. Showing students Dr. Strangelove and the Princess Bride could possibly be the single best use of class time, ever, though. And while I understand the utility of popular culture to connect with student interests, I’d rather see students engage in meaningful real-world problems.

I found the language and logic to be very clear. However, there are many prompts for student reflection that will likely be met with puzzlement for those not already familiar with formal logic and probability. That is very difficult to avoid, but the “discovery approach” the author uses compounds this problem.

The book is internally consistent.

The sections of the book build from previous ones, so independent sections are unlikely to work out of context. However, the sections and chapters are short, which means they could probably be used in complete chunks in many instructional contexts.

The topics are presented in a progressive fashion, building in complexity (very quickly) as students gain new understanding.

The web interface is excellent, with pop-up questions and exercise and embedded Sage code and results.

I found no grammatical issues.

There is very little cultural reference besides references to popular culture. The preface hints at the application of game theory to real problems in human behavior within social or political spheres, but the examples are fairly abstract.

The author’s declared purpose for this book is to introduce nonmajors to quantitative reasoning and the use of mathematical models to solve problems in an approachable way. Using game theory which often is mathematically rather simple but in turns can be engaging and puzzling and paradoxical, is a fantastic idea. Often the sheer mechanics of algebra and calculus distract new model thinkers away from what they are actually trying to do with a model. There are several minor problems with the implementation of this approach, however. First, most of the problems presented are abstract or uninteresting (i.e. payoff matrices without context, or examples like coin flipping), which don’t capitalize on the engaging nature of game theory applications in real life. I fear students may leave thinking game theory is math meant to solve games, not a powerful tool used across the social and natural sciences. Second, the complexity ramps up very quickly – from examples most people can hold comfortably in their head to a mix of algebra, matrix notation, probability, and graphical solutions that many students (even those with a fair amount of formal math) may struggle with. The steep climb in difficulty, paired with the discovery approach to instruction, may frustrate students.

This book is not as comprehensive as a general Game theory book. However, it covers a large enough portion of Game theory for a Quantitative Reasoning course for non-Math major students. read more

This book is not as comprehensive as a general Game theory book. However, it covers a large enough portion of Game theory for a Quantitative Reasoning course for non-Math major students.

The content is accurate. I didn't find any errors or biased content.

Though the textbook doesn't cover the recent topics of the field, they would be out of scope for the course. Updates would be easy.

The book is well written. it explained all the terminology and concepts pretty well with examples.

The textbook is consistent in terminology and framework. No issue found.

It could be a little hard to divide into smaller sections. There are only four chapters. I don't think there will be a need for modularity in most cases.

The organization is great. This good organization and smooth flow make the textbook hard to be modularity.

No problem with reading in both PDF and Online versions. Free of interface issues.

No grammatical errors found.

This book uses a lot of examples from movies and pop-culture. Even though some movies the book used can be insensitive itself, I don't find any cases that the example is culturally insensitive in the textbook contents.

I was disappointed at first glance because I directly jumped into the contents. However, after reading the preface, I believe it is the right book for its purpose. If you are looking for a Game theory book for Economics, Mathematics, Computer Science, or Operations Research majors, this is not the book you are looking for. If you choose the Game theory as a topic for a quantitative reasoning course, this book will serve perfectly. The book is well written with the non-mathematical major students in mind.

This book does an admirable job of covering the basics of game theory, including classic examples such as tic tac toe, as well as historical pop culture examples. The book also discusses the behavior of individuals as a main focus as opposed to... read more

This book does an admirable job of covering the basics of game theory, including classic examples such as tic tac toe, as well as historical pop culture examples. The book also discusses the behavior of individuals as a main focus as opposed to "winning a game". Including more examples on game theory as applied to business (such as bidding wars between countries) and popular games (such as casino games) could further the material in a fun and useful way!

The author did a nice job of presenting the material without much bias, except for the common accepted bias of the historical pop culture examples.

I believe this book, like the games it covers, are long lived and always relevant. I was delighted to read it.

The book is clear and casual for an easy read. It included lots of illustrative examples that were helpful. The book is also well-structured and organized to be easy on the eyes and clear for the reader.

The book was written well.

The structure of the book is well-organized and split into self-contained sections.

The structure of the book is laid out well, with clear sections and headers, bullet points, and illustrated examples.

The book displays well on both computer and cell phone.

I saw no grammatical mistakes.

It mostly follows classic games of tic tac toe. It does include some references to history and pop culture that may strengthen the interest of some and lose the interest of others.

This was an enjoyable and easy read, specially for non math majors to follow. It is a fun topic and the discussion psychology of individual behaviors vs the math was a great balance.

The text begins with simple examples of game theory such as cake division and tic-tac-toe. Then it moves to two-person zero-sum games discussing areas such as dominated strategies, a brief explanation of probability and equilibrium points. Mixed... read more

The text begins with simple examples of game theory such as cake division and tic-tac-toe. Then it moves to two-person zero-sum games discussing areas such as dominated strategies, a brief explanation of probability and equilibrium points. Mixed strategies are also included in the two-person zero-sum games discussion. The last chapter is about non-zero-sum games. The index provides links from highlighted texts to what you are looking for rather than searching through pages.

The body of the text is accurate. Examples and problems presented in the text contain no bias except when relating to examples of pop culture.

Content is current. It includes examples from current pop culture, which are from classic films like Footloose and The Princess Bride, among others. While the scenarios presented in the book may stand the test of time—for example, the game of chicken or rock-paper-scissors, the references from current popular media may not be easily called to mind by all readers. However, new examples may be included in later editions for future scholars.

Most of the terminology in the book has adequate examples and context for non-math majors to understand. However, it may require a thorough, studied reading of the text. A background in logic would be helpful.

Game theory—and in particular popular mediated examples of such—provides a rich contextual framework for non-mathematics majors to gain understanding and respect for important numerical and statistical theories.

Most sections are fairly short and easily digestible. Each chapter contains multiple subsections along with many examples to illustrate the topics. The book is quite short—only 4 chapters, so in some regards this question is not relevant. The book contains some self-referential material, but that is to be expected in a field of mathematics such as game theory.

The book starts with the basic components of game theory. Everything builds upon previous sections, so the flow works well for readers with foundational knowledge or the lay reader with a basic interest in learning more.

Text is free of interface issues. Multiple devices were used to read the text, and no problems were encountered. All charts were clear and easy to understand. All links worked well. The font was readable.

None found.

Many, if not all, of the pop culture examples used in the book were from movies. The characters in the scenes were mostly white Anglo-Saxon males. Perhaps the author could use examples from media that involve women and minorities, as well.

## Table of Contents

- 1 What is Game Theory?
- 2 Two-Person Zero-Sum Games
- 3 Repeated Two-Person Zero-sum Games
- 4 Non-Zero-Sum Games

## Ancillary Material

## About the Book

Game theory is an excellent topic for a non-majors quantitative course as it develops mathematical models to understand human behavior in social, political, and economic settings. The variety of applications can appeal to a broad range of students. Additionally, students can learn mathematics through playing games, something many choose to do in their spare time! This text also includes an exploration of the ideas of game theory through the rich context of popular culture. It contains sections on applications of the concepts to popular culture. It suggests films, television shows, and novels with themes from game theory. The questions in each of these sections are intended to serve as essay prompts for writing assignments.

Ancillary material are available to verified course instructors by emailing jfirkins@linfield.edu

## About the Contributors

### Author

**Jennifer Firkins Nordstrom**, Department of Mathematics, Linfield College