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

Description

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 undergraduate 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 games, Nash equilibria, zero-sum games, social dilemmas, combinatorial games, 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 theory, game theory, and social choice theory by highlighting the mix of ideas occurring in seminal results on games and elections such as the MiniMax, theorem allowing students to develop intuition in all areas while delving deeper into the theory. -Provides a gentle introduction to the logic of mathematical proof, thus equipping readers with the necessary tools for further mathematical studies, a feature not shared by most game theory texts. -Contains numerous exercises and examples of varying levels of difficulty to help the student learn and retain the material. -Requires only a high school mathematical background, thus making this text accessible to a broad range of students Content: Machine generated contents note: 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.