Introducing Game Theory and its Applications
Introducing Game Theory and its Applications
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DOI：
10.1201/b21050
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发表时间：
2004-06
期刊：
影响因子：
3.7
通讯作者：
E. Mendelson
中科院分区：
文献类型：
--
作者：
E. Mendelson
介绍组合对策的定义组合对策的基本定理Nim Hex和其他对策树对策Grundy函数伪尼姆和二人零和对策正规形式鞍点和均衡对极大极小和极小极大混合策略2×2矩阵对策2×2矩阵对策2×n，m×2和3×3矩阵对策线性规划。冯·诺依曼的单纯形法定理。对偶性的基本定理。二人零和对策的解。松弛的变量。完美正则线性规划问题单纯形法中旋转完美相的单纯形法、大M法、防止循环对偶的Bland法则和对策矩阵的单纯形法1-4非零和对策和k人对策的证明求2‘2矩阵纳什均衡的一般图解法非零和对策中纳什均衡的不足。合作博弈有两个或多个参与者的纳什仲裁程序博弈联盟博弈Shapley值战略等价稳定集附录有限概率理论效用理论纳什定理选定习题的答案书目索引
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