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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