Chance, Strategy, and Choice: An Introduction to the Mathematics of Games and Elections (Cambridge Mathematical Textbooks)

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 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-- 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. Samuel Bruce Smith, Saint Joseph's University, Philadelphia, Pa, Usa. Includes Bibliographical References (pages 373-375) And Index. This classroom-tested undergraduate textbook is intended for a general education course in game theory at the freshman or sophomore level. While it starts off with the basics and introduces the reader to mathematical proofs, this text also presents several advanced topics, including accessible proofs of the Sprague–Grundy theorem and Arrow's impossibility theorem.