Chance, Strategy, and Choice
An Introduction to the Mathematics of Games and Elections

This classroom-tested undergraduate textbook is primarily intended for a general education course in game theory at the freshman or sophomore level.

Samuel Bruce Smith (Author)

9781107084520, Cambridge University Press

Hardback, published 29 June 2015

352 pages, 60 b/w illus. 243 tables 300 exercises
26.1 x 18.4 x 2.9 cm, 1.01 kg

'Chance, Strategy, and Choice fits an important niche for general audience textbooks about games, elections, and other introductory material related to social choice theory … One of my favorite features of the book is that it does an excellent job of integrating the topics of games and elections to illustrate the interconnections between the different areas of social choice theory, often through illustrative examples.' Adam Graham-Squire, MAA Reviews

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.

1. Introduction
2. Games and elections
3. Chance
4. Strategy
5. Choice
6. Strategy and choice
7. Choice and chance
8. Chance and strategy
9. Nash equilibria
10. Proofs and counterexamples
11. Laws of probability
12. Fairness in elections
13. Weighted voting
14. Gambling games
15. Zero-sum games
16. Partial conflict games
17. Take-away games
18. Fairness and impossibility
19. Paradoxes and puzzles in probability
20. Combinatorial games
21. Borda versus Condorcet
22. The Sprague–Grundy theorem
23. Arrow's impossibility theorem.

Subject Areas: Game theory [PBUD], Optimization [PBU], Mathematics [PB], Microeconomics [KCC], Political science & theory [JPA]