- 博弈论最新进展--新均衡多矩阵博弈及计算方法(英文版)
- - 作者：(蒙)R.恩科巴图//萨和雅//S.巴特比勒格//G.巴特图尔
  - 出版社：科学
  - ISBN：9787030823007
  - 出版日期：2025/01/01
  - 页数：196
- 售价：39.2

内容大纲
本书的目的是在研究生层面提供博弈论的最新全面、严谨的结果。本书旨在向读者介绍计算游戏均衡的优化方法和算法。作者假设读者熟悉博弈论、数学规划、优化和非凸优化的基本概念。我们打算这本书也用于研究生阶段工程、运筹学、计算机科学和数学系提供的优化、博弈论课程。由于这本书涉及了许多在早期优化教科书中没有描述的计算平衡的新算法和想法，我们希望这本书不仅对博弈论专家有用，而且对优化研究人员也有用。除了纳什均衡、伯杰均衡、非合作博弈等经典主题外，一些重要的最近的发展包括：最大最小和最小最大问题、反纳什、反伯杰均衡、多矩阵博弈、广义纳什均衡、计算方法和算法。
作者介绍
目录
Preface
Chapter1 Introduction
Chapter2 Zero-Sum Game
  2.1  Two-person zero-sumgame
  2.2  Minimax and maxmin
  2.3  Saddle point
  2.4  Matrixgamein pure strategies
  2.5  Matrixgamein mixed strategies
  2.6  Reductionofgame theoryto linear programming
Chapter3 Maxmin and MinimaxProblems
  3.1  Maxmin problem
  3.2  Optimality conditionsfor maxmin problem
  3.3  Optimality conditions for minimax problem
Chapter4 Non-Zero Sum Game
  4.1  Two-person non-zero sumgame
    4.1.1  Bimatrixgame
    4.1.2  Nash equilibrium
    4.1.3  Berge equilibrium
  4.2  Non-zero sum three-persongame
  4.3  Non-zero sum four-persongame
  4.4  Non-zero sum n-persongame
Chapter5 Anti-Nash and Anti-Berge Equilibriumin Bimatrix Game
  5.1  Anti-Nash equilibriumin bimatrixgame
  5.2  Anti-Berge equilibriumin bimatrixgame
Chapter6 Polymatrix Game
  6.1  Three-sidedgame
    6.1.1  Main propertiesof thegame Γ(A， B，C)
    6.1.2  Optimization formulationof three-sidedgame
  6.2  Four-players triplegame
  6.3  Game of N-players
    6.3.1  Nash theorem and the optimization problem
Chapter7 N-Players Non-Cooperative Games
  7.1  Non-cooperativegames
  7.2  Generalized Nash equilibrium problems
  7.3  Someequivalent approachto generalizedNash equilibrium problems
    7.3.1  Variational inequality approach
    7.3.2  Nikaido-Isoda function based approach
    7.3.3  Karush-Kuhn-Tucker conditions approach
  7.4  Global optimization D.Capproach to quadratic nonconvex generalized Nash equilibrium problems
    7.4.1  Generalized Nash equilibrium problem and equivalent optimization formulation
    7.4.2  Quadratic nonconvexgame andgap function
    7.4.3  D.Coptimization approachto non-cooperativegame
  7.5  Generalized Nash equilibrium problem based on Malfatti’s problem
    7.5.1  Malfatti’s problemand convex maximization
    7.5.2  Generalized Nash equilibrium problems
  7.6  Aglobal optimization approach to Berge equilibrium based on a regularized function
    7.6.1  Existence of Berge equilibrium and constrained optimization reformulations 110 Chapter8 Game Theory and Hamiltonian
System
  8.1  Hamiltonian system
  8.2  Evolutionarygames and Hamiltonian systems.

  8.3  Optimal controltheoryandthe Hamiltonian operator
  8.4  Differentialgames and the Hamilton-Jacobi-Bellman (HJB) Principle
    8.4.1  The relationship betweengame theoryandthe Hamiltonian operator
    8.4.2  Two-person zero-sum differentialgames
    8.4.3  Two-person non-zero sum differentialgames
Chapter9 Computational Methods and Algorithmsfor Matrix Game
  9.1  D.Cprogramming approachtoBerge equilibrium
    9.1.1  Local search method
    9.1.2  Global search method
    9.1.3  Numerical results for D.Cprogramming approach to Berge equilibrium
  9.2  Global search method curvilinear algorithm forgame
    9.2.1  The curvilinear global search algorithm
    9.2.2  Numerical results for three-persongame
    9.2.3  Numerical results for four-persongame
    9.2.4  Numerical results N-persongame
  9.3  The numerical approach for anti-Nash equilibrium search
    9.3.1  The modi.ed Rosenbrock algorithm
    9.3.2  Theunivariate global search procedure
    9.3.3  Numerical results for anti-Nash equilibriumby Rosenbrock algorithm
  9.4  Modi.ed parallel tangent algorithm for anti-Berge equilibrium
    9.4.1  The modi.ed parallel tangent algorithm
    9.4.2  Theunivariate global search procedure
    9.4.3  Numerical results for anti-Berge equilibrium by modi.ed tangent algorithm
  9.5  The curvilinear multistart algorithmfor polymatrixgame
    9.5.1  Numericalexperimentof polymatrixgame
  9.6  Numerical resultsfor non-cooperativegame
  9.7  Numerical resultsforMalfati’s problem
Bibliography

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