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The Game’s Afoot! Game Theory in Myth and Paradox

Опубликовано на портале: 07-07-2005
Providence: American Mathematical Society, 2000, 159 с.
It all started with von Neumann and Morgenstern half a century ago. Their Theory of Games and Economic Behavior gave birth to a whole new area of mathematics concerned with the formal problems of rational decision as experienced by multiple agents. Now, game theory is all around us, making its way even into regular conversations. In the present book, Mehlmann presents mathematical foundations and concepts illustrated via social quandaries, mock political battles, evolutionary confrontations, economic struggles, and literary conflict. Most of the standard models--the prisoners' dilemma, the arms race, evolution, duels, the game of chicken, etc.--are here. Many non-standard examples are also here: the Legend of Faust, shootouts in the movies, the Madness of Odysseus, to name a few. The author uses familiar formulas, fables, and paradoxes to guide readers through what he calls the "hall of mirrors of strategic decision-making". His light-hearted excursion into the world of strategic calculation shows that even deep insights into the nature of strategic thought can be elucidated by games, puzzles, and diversions. Originally written in German and published by Vieweg-Verlag, this AMS edition is a translation tailored for the English-speaking reader. It offers an intriguing look at myths and paradoxes through the lens of game theory, bringing the mathematics into sharper focus at the same time. This book is a must for those who wish to consider game theory from a different perspective: one that embraces science, literature, and real-life conflict. The Game's Afoot! would make an excellent book for an undergraduate course in game theory. It can also be used for independent study or as supplementary course reading. The connections to literature, films and everyday life also make it highly suitable as a text for a challenging course for non-majors. Its refreshing style and amusing combination of game theoretic analysis and cultural issues even make it appealing as recreational reading.

List of Figures

Part I. The Glass Bead Game
Introduction to Part I

Chapter 1. Games, Form(ula)s, and Scholars
1.1. Scissors-Stone-Paper
1.2. A Game of Hackenbush
1.3. The Paladins of Game Theory

Chapter 2. Equilibrium and Game as Metaphor
2.1. The Arms Race Dilemma
2.2. Rebel Without a Cause
2.3. The Parable of the Deer Hunt
2.4. The Revenge of the Mutants

Chapter 3. In the Forest of Game Trees
3.1. The Strange Case of Lord Strange
3.2. A Game-Theoretic Bestiary

Chapter 4. Games Against Time
4.1. Duels and Other AÆairs of Honor
4.2. The Curse of Irreversibility
4.3. Mephisto's Joust with Doctor Faust

Part II. The Myths of Game Theory
Introduction to Part II

Chapter 5. The Prisoner's Dilemma
5.1. Variants That We Knew
5.2. The Tournament of the Automata
5.3. Foresighted Equilibria
5.4. Gridlock on the Internet

Chapter 6. Paradoxes of Backward Induction
6.1. The Market-Entry Game
6.2. The Chain-Store Paradox
6.3. The Centipede Game
6.4. The Bottle Imp Paradox
6.5. Rituals of Division

Chapter 7. Strategic Accents of Game-Theoretic Scholasticism
7.1. Seeing Through the Opponent
7.2. Common Knowledge
7.3. Going Against the Course of Events

Chapter 8. Odysseus Goes to War
8.1. The Madness of Odysseus
8.2. The Game-Theoretic Model
8.3. Behavioral{Strategic Analysis

A Postlude in Rhyme

Appendix: Games in the Network of Networks



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