- 208 pages
- English
- ePUB (mobile friendly)
- Available on iOS & Android
eBook - ePub
The Mathematics of Games of Strategy
About this book
Melvin Dresher, noted research mathematician for the Rand Corporation, puts forth an exceptionally clear presentation of the mathematical theory of games of strategy and its applications to many fields including: economics, military, business, and operations research. The mathematical presentation is elementary in the sense that no advanced algebra or non-elementary calculus occurs in most of the mathematical proofs.
The author presents game theory as a branch of applied mathematics. In addition to developing a mathematical theory for solving games, he shows how to formulate a game model associated with a given competitive or conflicting situation. Furthermore, he shows how some decision problems, such as timing of decisions, which do not resemble game situations, can be analyzed as a game, yielding rich insights into the decision problems.
Beginning with an exposition of games of strategy, with examples from parlor games as well as military games, Dr. Dresher proceeds to treat the basic topics in the theory of finite games, i.e., the existence of optimal strategies and their properties. An elementary proof of the minimax theorem is given that provides an efficient method for computing optimal strategies.
Since many games involve an infinite number of strategies, succeeding chapters deal with such games by first developing the necessary mathematics (e.g., probability distribution functions and Stieltjes integrals) for analyzing infinite games. The results of infinite games are then applied to two general classes of games — timing games and tactical games. A final chapter provides an application of moment space theory to the solution of infinite games.
This is a book about decision making in the absence of perfect information. In particular, it analyzes decision problems in a competitive environment where conflicting interests exist, and uncertainties and risk are involved. For the reader who is interested in the applications of the theory of games of strategy to military, economic, or political problems, or to decision making in business, operations research, or the behavior sciences, it will prove a most rewarding study.
The author presents game theory as a branch of applied mathematics. In addition to developing a mathematical theory for solving games, he shows how to formulate a game model associated with a given competitive or conflicting situation. Furthermore, he shows how some decision problems, such as timing of decisions, which do not resemble game situations, can be analyzed as a game, yielding rich insights into the decision problems.
Beginning with an exposition of games of strategy, with examples from parlor games as well as military games, Dr. Dresher proceeds to treat the basic topics in the theory of finite games, i.e., the existence of optimal strategies and their properties. An elementary proof of the minimax theorem is given that provides an efficient method for computing optimal strategies.
Since many games involve an infinite number of strategies, succeeding chapters deal with such games by first developing the necessary mathematics (e.g., probability distribution functions and Stieltjes integrals) for analyzing infinite games. The results of infinite games are then applied to two general classes of games — timing games and tactical games. A final chapter provides an application of moment space theory to the solution of infinite games.
This is a book about decision making in the absence of perfect information. In particular, it analyzes decision problems in a competitive environment where conflicting interests exist, and uncertainties and risk are involved. For the reader who is interested in the applications of the theory of games of strategy to military, economic, or political problems, or to decision making in business, operations research, or the behavior sciences, it will prove a most rewarding study.
Frequently asked questions
Yes, you can cancel anytime from the Subscription tab in your account settings on the Perlego website. Your subscription will stay active until the end of your current billing period. Learn how to cancel your subscription.
At the moment all of our mobile-responsive ePub books are available to download via the app. Most of our PDFs are also available to download and we're working on making the final remaining ones downloadable now. Learn more here.
Perlego offers two plans: Essential and Complete
- Essential is ideal for learners and professionals who enjoy exploring a wide range of subjects. Access the Essential Library with 800,000+ trusted titles and best-sellers across business, personal growth, and the humanities. Includes unlimited reading time and Standard Read Aloud voice.
- Complete: Perfect for advanced learners and researchers needing full, unrestricted access. Unlock 1.4M+ books across hundreds of subjects, including academic and specialized titles. The Complete Plan also includes advanced features like Premium Read Aloud and Research Assistant.
We are an online textbook subscription service, where you can get access to an entire online library for less than the price of a single book per month. With over 1 million books across 1000+ topics, we’ve got you covered! Learn more here.
Look out for the read-aloud symbol on your next book to see if you can listen to it. The read-aloud tool reads text aloud for you, highlighting the text as it is being read. You can pause it, speed it up and slow it down. Learn more here.
Yes! You can use the Perlego app on both iOS or Android devices to read anytime, anywhere — even offline. Perfect for commutes or when you’re on the go.
Please note we cannot support devices running on iOS 13 and Android 7 or earlier. Learn more about using the app.
Please note we cannot support devices running on iOS 13 and Android 7 or earlier. Learn more about using the app.
Yes, you can access The Mathematics of Games of Strategy by Melvin Dresher in PDF and/or ePUB format, as well as other popular books in Mathematics & Game Theory. We have over one million books available in our catalogue for you to explore.
Information
Table of contents
- Cover
- Title Page
- Dedication
- Preface
- Contents
- 1 Game, Strategy, And Saddle-Point
- 2 The Fundamental Theorem
- 3 Properties of Optimal Strategies
- 4 Games in Extensive Form
- 5 Methods of Solving Games
- 6 Games with Infinite Number of Strategies
- 7 Solution of Infinite Games
- 8 Games with Convex Payoff Functions
- 9 Games of Timing—Duels
- 10 Tactical Air-War Game
- 11 Infinite Games with Separable Payoff Functions
- Bibliography
- Index