Game Theory: A Playful Introduction
- Length: 343 pages
- Edition: 1
- Language: English
- Publisher: American Mathematical Society
- Publication Date: 2016-12-27
- ISBN-10: 1470422107
- ISBN-13: 9781470422103
- Sales Rank: #372119 (See Top 100 Books)
This book offers a gentle introduction to the mathematics of both sides of game theory: combinatorial and classical. The combination allows for a dynamic and rich tour of the subject united by a common theme of strategic reasoning. The first four chapters develop combinatorial game theory, beginning with an introduction to game trees and mathematical induction, then investigating the games of Nim and Hackenbush. The analysis of these games concludes with the cornerstones of the Sprague-Grundy Theorem and the Simplicity Principle. The last eight chapters of the book offer a scenic journey through the mathematical highlights of classical game theory. This contains a thorough treatment of zero-sum games and the von Neumann Minimax Theorem, as well as a student-friendly development and proof of the Nash Equilibrium Theorem. The Folk Theorem, Arrow’s voting paradox, evolutionary biology, cake cutting, and other engaging auxiliary topics also appear. The book is designed as a textbook for an undergraduate mathematics class. With ample material and limited dependencies between the chapters, the book is adaptable to a variety of situations and a range of audiences. Instructors, students, and independent readers alike will appreciate the flexibility in content choices as well as the generous sets of exercises at various levels.
Contents Preface Combinatorial Games Game Trees Zermelo Theorem Strategy Normal-Play Games Positions & their Types Sums of Positions Equivalence Impartial Games Nim Sprague-Grundy Theorem Applying the MEX Principle Hackenbush & Partizan Games Hackenbush Dyadic Numbers & Positions Simplicity Principle Zero-Sum Matrix Games Dominance Mixed Strategies Von Neumann Solutions Von Neumann Minimax Theorem Equating Opponent's Results 2D Games Proof of the Minimax Theorem General Games Utility Matrix Games Game Trees Trees vs Matrices Nash Equilibrium & Applications Nash Equilibrium Evolutionary Biology Cournot Duopoly Nash Equilibrium Theorem Sperner Lemma Brouwer Fixed Point Theorem Strategy Spaces Nash Flow & the Proof Cooperation The Negotiation Set Nash Arbitration Repeated Games & Folk Theorem n-Player Games Matrix Games Coalitions Shapley Value Preferences & Society Fair Division Stable Marriages Arrow’s Impossibility Theorem Games & Numbers Linear Programming Basic Theory Connection to Game Theory LP Duality Nash Equilibrium in High Dimensions Game Boards Biblio Index of Games Index
Donate to keep this site alive
1. Disable the AdBlock plugin. Otherwise, you may not get any links.
2. Solve the CAPTCHA.
3. Click download link.
4. Lead to download server to download.