Description
Taylor & Francis Ltd Introducing Game Theory And Its Applications 2004 Edition by Elliott Mendelson
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. IntroductionCOMBINATORIAL GAMESDefinition of Combinatorial GameThe Fundamental Theorem for Combinatorial GamesNimHex and Other GamesTree GamesGrundy FunctionsBogus Nim-SumsTWO-PERSON ZERO-SUM GAMESGames in Normal FormSaddle Points and Equilibrium PairsMaximin and MinimaxMixed Strategies2 x 2 Matrix Games2 x n, m x 2, and 3 x 3 Matrix GamesLinear Programming. Von Neumann's TheoremTHE SIMPLEX METHOD. THE FUNDAMENTAL THEOREM OF DUALITY. SOLUTION OF TWO-PERSON ZERO-SUM GAMES.Slack Variables. Perfect Canonical Linear Programming ProblemsThe Simplex MethodPivotingThe Perfect Phase of the Simplex MethodThe Big M MethodBland's Rules to Prevent CyclingDuality and the Simplex MethodSolution of Game MatricesProofs of Facts 1-4NON-ZERO-SUM GAMES AND k-PERSON GAMESThe General SettingNash EquilibriaGraphical Method for Finding Nash Equilibria for 2 2 MatricesInadequacies of Nash Equilibria in Non-Zero-Sum Games. Cooperative GamesThe Nash Arbitration ProcedureGames with Two or More PlayersCoalitionsGames in Coalition FormThe Shapley ValueStrategic EquivalenceStable SetsAPPENDICESFinite Probability TheoryUtility TheoryNash's TheoremAnswers to Selected ExercisesBibliographyINDEX