A History of Game Theory - Vol. 1

By Mary Ann Dimand; Robert W. Dimand | Go to book overview

1

INTRODUCTION

Defining game theory and its history

This book is about the history of game theory up to and including von Neumann and Morgenstern (1944)—i.e. it discusses the history of an economic concentration for over 200 years before the concentration was named, and ends with its demarcation as a separate field. The continued study of the economics of Aristotle and, indeed, Adam Smith shows that there is no novelty in this: we can learn from our predecessors.

To discuss a literature we call game theory before the term was invented, we must define what problems and approaches we include under this rubric: authors did not label their work with a term which did not yet exist. The first section includes a discussion of the structure of the book within this context.

Moreover, since there are many possible approaches to examining the history of a discipline or concentration, we would like to define the task we attempt in this book—and also what tasks we are not attempting. This is the subject of the second section.

We would also like to make a distinction between game theory and conceptual tools (of which probability theory and treatment of preferences under uncertainty are particularly prominent for this period). Some of this literature, as well as intellectual connections between its proponents and game theorists in our sense, are discussed in the third section.

In the fourth section, we discuss some literature of interest to historians of game theory which we have nonetheless chosen not to examine in the body of the book. This literature, including Pascal’s Wager, focuses on works which can receive, or have received, more game-theoretic interpretation.

A brief conclusion sums up the matter of this introductory chapter.


DEFINING GAME THEORY

When non-cooperative game theory is introduced as a classroom topic, many instructors introduce a game as an event tree with certain properties (e.g. a structure representing perfect memory). Cooperative games are typically defined as sets of players and of imputations for different subsets of players. In the classroom, game theory is implicitly demarcated as the study of the

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A History of Game Theory - Vol. 1
Table of contents

Table of contents

  • Title Page iii
  • Contents vii
  • Preface ix
  • 1 - Introduction 1
  • 2 - Strategic Interdependence 18
  • 3 - Strategic Interdependence 35
  • 4 - Strategic Interdependence 54
  • 5 - Lewis Carroll and the Game of Politics 84
  • 6 - Early Mathematical Models of Conflict 104
  • 7 - The Minimax Approach to Non-Cooperative Strategic Games from Waldegrave to Borel 120
  • 8 - From Games of Pure Chance to Strategic Games 131
  • 9 142
  • Notes 158
  • Bibliography 170
  • Index 184
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