A Gentle Introduction to Game Theory

by Saul Stahl

The mathematical theory of games was first developed as a model for situations of conflict, whether actual or recreational. It gained widespread recognition when it was applied to the theoretical study of economics by von Neumann and Morgenstern in Theory of Games and Economic Behavior in the 1940s. The later bestowal in 1994 of the Nobel Prize in economics on Nash underscores the important role this theory has played in the intellectual life of the twentieth century. This volume is based on courses given by the author at the University of Kansas. The exposition is "gentle" because it requires only some knowledge of coordinate geometry; linear programming is not used. It is "mathematical" because it is more concerned with the mathematical solution of games than with their applications. Existing textbooks on the topic tend to focus either on the applications or on the mathematics at a level that makes the works inaccessible to most non-mathematicians. This book nicely fits in between these two alternatives. It discusses examples and completely solves them with tools that require no more than high school algebra. In this text, proofs are provided for both von Neumann's Minimax Theorem and the existence of the Nash Equilibrium in the $2 \times 2$ case. Readers will gain both a sense of the range of applications and a better understanding of the theoretical framework of these two deep mathematical concepts.

Genres: Mathematics

176 pages, Paperback

First published January 1, 1999

Reviews

[Deryk Rumbold · Rating 3 out of 5]

The word "gentle" in the title is a bit misleading. Advertised as not needing not much for pre-requisite knowledge to approach this introduction it does start off gentle and get pretty rigorous. Non-math crowds definitely would be intimidated but the exercises provided seemed appropriate for a first step with a decent mathematical background. With my very base level knowledge of game theory I found myself flipping back and forth quite a bit with cross referencing to understand notation and where products/sums came from. Pretty dry read as with many Math texts but there is a curious analysis on the Cuban Missle Crisis from a Game Theory perspective.

[Maurizio Codogno · Rating 3 out of 5]

Molto di base

Questo libro nasce esplicitamente per raccontare la base della teoria dei giochi a chi non arriva da un background di matematica pura. Questo non vuol dire che non ci sia matematica, mi affretto ad aggiungere: i molti esercizi alla fine di ogni capitolo lo stanno a testimoniare. Alla fine, però, è più adatto per avere un'infarinatura di cosa può essere la teoria dei giochi, arrivando al più all'equilibrio di Nash per matrici 2×n, e non per studiarla con un minimo di approfondimento. D'altra parte il lettore è stato avvertito...

[Isaac · Rating 4 out of 5]

A very clear starting point for learning game theory. A touch repetitive in places but that is part of the "gentle" approach.