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Game Theory

Decisions, Interaction and Evolution

  • Authors
  • James N. Webb

Part of the Springer Undergraduate Mathematics Series book series (SUMS)

Table of contents

  1. Front Matter
    Pages i-ix
  2. Decisions

    1. Front Matter
      Pages 1-1
  3. Interaction

    1. Front Matter
      Pages 59-59
    2. Pages 61-87
    3. Pages 89-105
    4. Pages 119-135
  4. Evolution

    1. Front Matter
      Pages 137-137
    2. Pages 139-163
    3. Pages 165-185
  5. Back Matter
    Pages 187-241

About this book

Introduction

This introduction to game theory is written from a mathematical perspective. Its primary purpose is to be a first course for undergraduate students of mathematics, but it also contains material which will be of interest to advanced students or researchers in biology and economics.

The outstanding feature of the book is that it provides a unified account of three types of decision problem:

  • Situations involving a single decision-maker: in which a sequence of choices is to be made in "a game against nature". This introduces the basic ideas of optimality and decision processes.
  • Classical game theory: in which the interactions of two or more decision-makers are considered. This leads to the concept of the Nash equilibrium.
  • Evolutionary game theory: in which the changing structure of a population of interacting decision makers is considered. This leads to the ideas of evolutionarily stable strategies and replicator dynamics.

An understanding of basic calculus and probability is assumed but no prior knowledge of game theory is required. Detailed solutions are provided for the numerous exercises.

Keywords

Nash equilibrium biology calculus decision theory dynamics economics equilibrium game theory mathematics optimization population

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-84628-636-0
  • Copyright Information Springer-Verlag London Limited 2007
  • Publisher Name Springer, London
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-1-84628-423-6
  • Online ISBN 978-1-84628-636-0
  • Series Print ISSN 1615-2085
  • Buy this book on publisher's site