You are here

Game Theory: A Nontechnical Introduction

Morton D. Davis
Dover Publications
Publication Date: 
Number of Pages: 
BLL Rating: 

The Basic Library List Committee recommends this book for acquisition by undergraduate mathematics libraries.

[Reviewed by
Tom Schulte
, on

When I read that Douglas R. Hofstadter called this work a “lucid and penetrating development of game theory that will appeal to the intuition,” I knew I wanted to read this overview of “the study of mathematical models of conflict and cooperation between intelligent rational decision-makers”, as Roger B. Myerson defined game theory. Published originally in 1970, the reprinted classic looks back to the foundations of game theory laid by John von Neumann. Von Neumann’s basic minimax theorem, proved in 1928, is the core of Chapter 2 on two-person, zero-sum games. Being a nontechnical introduction, proof and a good detail of mathematical mechanics are foregone to get a high-level view of the properties of this technique as an applied art and its many applications to social, economic, and political problems.

While the approach of this book suggests the intended reader might be seeing “The Prisoner Dilemma” for the first time, its value does not end there. For many, a review of the basic ideas in the first few chapters can bolster general comprehension of the more advanced topics, such as utility theory and n-person games. This is because Davis writes clearly and organizes the material logically. Indeed, I feel the reader attracted to this subject that commits to the author’s framework of thoughtful problem consideration, technique exposition, and explained solutions will come away with both acquired knowledge and appreciation for the craft of this modeling approach.

Unlike in a textbook, there are no exercises for the reader at the end or within chapters. Rather, problems are posed at the start of each chapter. Readers are encouraged to deeply consider these problems or to solve them before moving on. At the end of the chapter, the lay reader is presented with the author’s solutions to compare and contrast to their own “common sense” solutions. They will find that the chapter’s techniques have quantified the expected result, or perhaps delineated an unexpected yet superior outcome.

As the book progresses, the author presents more complex classes of problems, such as two person non-zero-sum games and n-person games. As the material become more complex, the author’s patient explanations continue to be well-organized and comprehensible. What other mathematical text finds inspired examples in Fyodor Dostoevsky (The Gambler) and Edgar Allan Poe (The Purloined Letter)? Davis compares Poe to von Neumann as problem solvers, and in Dostoevsky finds an exemplar of human irrationality confounding a pure utility theory.

Davis surveys the important concepts of game theory while requiring of the reader only occasional, basic, high school algebra. He does not even call on anything as arcane as sigma notation, even during an aside on the formula for the Shapley value. For someone new to this fascinating topic, the many real world, illustrative examples and detailed basics make this an enjoyable and enlightening work requiring neither calculus nor really math beyond arithmetic.

Davis illuminates the field with a rich spectrum of examples from the animal world to commerce to politics. Among fauna, fiddler crab territoriality and the delicate bargain a parasite remover makes with its predator are aids to understanding certain games. And politics — especially electioneering, voting rights distribution among unequal populations, and the formation of voting bloc coalitions — connects this theory to the headlines.

Tom Schulte always chooses to cooperate in the dilemmas presented by his students at Oakland Community College.

Foreword to the First Edition by Oskar Morgenstern
Author's Introduction
1. An Overview
2. "The Two-Person, Zero-Sum Game with Equilibrium Points"
3. "The General, Two-Person, Zero-Sum Game"
4. Utility Theory
5. "The Two-Person, Non-Zero-Sum Game"
6. The n-Person Game