Introducing Game Theory and its ApplicationsCRC Press, 2004 M07 3 - 272 páginas 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. |
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Contenido
Introduction | 1 |
4 | 27 |
6 | 38 |
Twoperson zerosum games | 53 |
7 | 72 |
Nonzerosum games and kperson games | 143 |
Finite probability theory | 207 |
Utility theory | 219 |
Answers to selected exercises | 227 |
247 | |
255 | |
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Términos y frases comunes
A₁ A₁ C₁ C₂ arbitration procedure assume B₁ B₁ B₂ B₂ basic point basic variables binary decomposition choose coalition game coefficients combinatorial game Consider the game dominates entry equation equilibrium pair Example Exercise expected pay-off Find a winning following game G-number game matrix Game Theory graph Grundy number Hence hexagons imputation integer ith row k-tuple last person lpp's Mathematical matrix games maximin strategy maximization lpp maximum minimax minimum mixed Nash equilibrium move wins negotiation set non-losing strategy objective function objective row occurs optimal strategy outcomes P₁ pay-offs person to move pile pivot with respect plays strategy probability proof pure Nash equilibrium pure strategy random real numbers remove result S₁ saddle point second player Shapley value simplex method solution sticks strategies B₁ strategy for player strategy X superadditivity tableau Theorem Tic-Tac-Toe v₁ von Neumann's Theorem White winning strategy x₁ x₂ y₁ y₂ yields
Pasajes populares
Página 247 - AUMANN, A survey of cooperative games without side payments, in "Essays in Mathematical Economics in Honor of Oskar Morgenstern
Página 247 - The Bargaining set for Cooperative Games," in Advances in Game Theory, (M.