Chance, Strategy, and Choice

An Introduction to the Mathematics of Games and Elections

Samuel Bruce Smith

• Publisher: Cambridge University Press
• Year: 2015
• ISBN:
  9781316028896
• Topic: Mathematics
• Subtopic: Mathematics General
• Index: Mathematics

Games and elections are fundamental activities in society with applications in economics, political science, and sociology. These topics offer familiar, current, and lively subjects for a course in mathematics. This classroom-tested textbook, primarily intended for a general education course in game theory at the freshman or sophomore level, provides an elementary treatment of games and elections. Starting with basics such as gambling, zero-sum and combinatorial games, Nash equilibria, social dilemmas, and fairness and impossibility theorems for elections, the text then goes further into the theory with accessible proofs of advanced topics such as the Sprague–Grundy theorem and Arrow's impossibility theorem. • Uses an integrative approach to probability, game, and social choice theory • Provides a gentle introduction to the logic of mathematical proof, thus equipping readers with the necessary tools for further mathematical studies • Contains numerous exercises and examples of varying levels of difficulty • Requires only a high school mathematical background.

Table of contents

• Cover
• Half-title
• Title page
• Copyright information
• Table of contents
• Preface
• Part I First Notions
• Part II Basic Theory
• Part III Special Topics
• Bibliography
• Index