博弈论：有趣的介绍[True PDF]

这本书温和地介绍了博弈论的两个方面：组合数学和经典数学。这两种结合使我们能够通过一个共同的主题——战略推理——对主题进行动态而丰富的探索。前四章发展了组合博弈论，首先介绍了博弈树和数学归纳法，然后研究了尼姆和哈肯布什的博弈。对这些博弈的分析以Sprague-Grundy定理和简单性原则为基础。这本书的最后八章通过经典博弈论的数学精髓提供了一个风景优美的旅程。这包括对零和博弈和冯·诺依曼极小极大定理的彻底处理，以及对学生友好的纳什均衡定理的发展和证明。民俗定理、阿罗的投票悖论、进化生物学、蛋糕切割和其他引人入胜的辅助主题也出现了。这本书是为本科生数学课设计的教科书。本书内容丰富，各章之间的依赖性有限，适用于各种情况和各种受众。教师、学生和独立读者都将欣赏内容选择的灵活性，以及各种级别的大量练习。
Game Theory: A Playful Introduction [True PDF]
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.

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