Introducing game theory and its applications


Introducing game theory and its applications

Elliott Mendelson

(Discrete mathematics and its applications / Kenneth H. Rosen, series editor)

Chapman & Hall/CRC, c2004

大学図書館所蔵 件 / 38



Includes bibliographical references (p. 247-254) and index



The mathematical study of games is an intriguing endeavor with implications and applications that reach far beyond tic-tac-toe, chess, and poker to economics, business, and even biology and politics. Most texts on the subject, however, are written at the graduate level for those with strong mathematics, economics, or business backgrounds. In a clear and refreshing departure from this trend, Introducing Game Theory and its Applications presents an easy-to-read introduction to the basic ideas and techniques of game theory. After a brief introduction, the author begins with a chapter devoted to combinatorial games--a topic neglected or treated minimally in most other texts. The focus then shifts to two-person zero-sum games and their solution. Here the author presents the simplex method, based on linear programming, for solving these games and develops within his presentation the required background in linear programming. The final chapter presents some of the fundamental ideas and tools of non-zero-sum games and games with more than two players, including an introduction to cooperative game theory. This book will not only satisfy the curiosity of those whose interest in the subject was piqued by the 1994 Nobel Prize awarded to Harsanyi, Nash, and Selten. It also prepares its readers for more advanced study of game theory's applications in economics, business, and the physical, biological, and social sciences.


Introduction COMBINATORIAL GAMES Definition of Combinatorial Game The Fundamental Theorem for Combinatorial Games Nim Hex and Other Games Tree Games Grundy Functions Bogus Nim-Sums TWO-PERSON ZERO-SUM GAMES Games in Normal Form Saddle Points and Equilibrium Pairs Maximin and Minimax Mixed Strategies 2 x 2 Matrix Games 2 x n, m x 2, and 3 x 3 Matrix Games Linear Programming. Von Neumann's Theorem THE SIMPLEX METHOD. THE FUNDAMENTAL THEOREM OF DUALITY. SOLUTION OF TWO-PERSON ZERO-SUM GAMES. Slack Variables. Perfect Canonical Linear Programming Problems The Simplex Method Pivoting The Perfect Phase of the Simplex Method The Big M Method Bland's Rules to Prevent Cycling Duality and the Simplex Method Solution of Game Matrices Proofs of Facts 1-4 NON-ZERO-SUM GAMES AND k-PERSON GAMES The General Setting Nash Equilibria Graphical Method for Finding Nash Equilibria for 2 ' 2 Matrices Inadequacies of Nash Equilibria in Non-Zero-Sum Games. Cooperative Games The Nash Arbitration Procedure Games with Two or More Players Coalitions Games in Coalition Form The Shapley Value Strategic Equivalence Stable Sets APPENDICES Finite Probability Theory Utility Theory Nash's Theorem Answers to Selected Exercises Bibliography INDEX

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  • ISBN
    • 1584883006
  • LCCN
  • 出版国コード
  • タイトル言語コード
  • 本文言語コード
  • 出版地
    Boca Raton, Fla.
  • ページ数/冊数
    259 p.
  • 大きさ
    25 cm
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