You are here

Models of Conflict and Cooperation

Rick Gillman and David Housman
American Mathematical Society
Publication Date: 
Number of Pages: 
[Reviewed by
Bonnie Shulman
, on

Early in my career as a professor I realized that the best way to learn something is to teach it. So my own interest in evolutionary game theory, especially as applied to the question of the evolution of cooperation, led me to design a seminar on Mathematical Models of Social Dilemmas. Thus it was that I enthusiastically agreed to review Models of Conflict and Cooperation, whose primary goal, as stated in the Preface, is to help students “learn, practice and use” mathematical models of the decision-making process. While my own course has at least one semester of Calculus as a prerequisite, this book assumes no more than a proficiency in algebra, some basic probability, and a willingness to pick up one’s pencil and think. This is an excellent book for a general education quantitative literacy course.

In fact, there is a movement afoot, spearheaded by the authors, Rick Gillman and David Housman, whose goal is encapsulated by the title of their Minicourse at MathFest 2008: “A Game Theory Path to Quantitative Literacy.” They are not alone in realizing the potential of this topic to intrigue and engage students. In June of 2009, I attended a talk by Rob Root, of Lafayette College, at a conference on incorporating social justice and service learning into the STEM curriculum, where he discussed his course “Social Justice through Quantitative Literacy,” an introduction to evolutionary game theory aimed at a population of first-year students.

The book under review does exactly what every well-crafted presentation should do: tell your audience what you are going to say; say it; summarize what you have said. Each section has a box that states: “By the end of this section you will be able to…” Students are encouraged to play the games, do the exercises, and act out the dialogues that open each chapter. These dialogues are well crafted conversations, reminiscent of Socratic dialogues, that introduce each new topic in a simultaneously entertaining and seriously educational manner.

I thoroughly enjoyed reading this book, and I am confident that students will too. The writing style progresses smoothly from a conversational tone in the early chapters, to a more formal mathematical style in the final chapters. At first students are encouraged to generalize from their particular experiences playing the games and reflecting on their thinking. As their skills mature, they are introduced to general principles and theorems and asked to apply them to specific instances. All along the authors self-consciously reflect on the process of mathematical thinking: “This is fairly typical for mathematicians: to solve a difficult problem, first solve simpler problems” (p. 21).

The material at the back of the book includes answers to selected exercises, a useful index, and a wide-ranging bibliography, helpful for student projects and instructors who want to delve more deeply into the field. In addition, annotated solutions and software for some of the games are available from the authors.

I recommend this book highly, not only as a text for a QL/QR course, but as a source of interesting topics and projects for math majors and minors. Indeed, I intend to put it on reserve and dip into some of the later chapters when I teach my seminar this Winter.

Bonnie Shulman is Chair of the Mathematics Department at Bates College in Lewiston, ME. She loves to combine her teaching and research interests. After a sabbatical spent studying classical game theory, she designed a First Year Seminar and later a senior seminar “Game Theory: The Mathematics of Conflict and Cooperation.” During her most recent sabbatical she studied evolutionary game theory, and wrote eight chapters of a textbook tentatively titled Mathematical Models of Social Dilemmas. In Winter 2010 thirty-three lucky students will attend a seminar using these notes.