Introducing Game Theory and its Applications
CRC Press, 03.07.2004 - 272 Seiten
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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A₁ A₂ alternately apply assigned assume B₁ B₂ basic point Black C₁ C₂ called canonical lpp choose collection column Consider consists constants constraints contains corresponding determined dominates draw entry equal equation equilibrium pair event Example Exercise expected fact fair Figure Find game matrix Game Theory given graph Heads Hence imputation integer k-tuple least linear look loses Mathematical matrix maximin Maximize maximum mean method Minimize mixed move Nash equilibrium non-losing strategy Note objective function obtain occurs optimal original outcomes P₁ pay-offs perfect pile pivot play player plays strategy position possible probability procedure proof random remove respect result saddle point segment Shapley value side Similarly simplex method solution square standard sticks strategy for player tableau Theorem two-person variables White winning strategy x₁ y₁ yields zero-sum
Seite 247 - AUMANN, A survey of cooperative games without side payments, in "Essays in Mathematical Economics in Honor of Oskar Morgenstern