LQ Dynamic Optimization and Differential Games

Jacob Engwerda is the author of LQ Dynamic Optimization and Differential Games, published by Wiley.

• Preface ixNotation and symbols xi1 Introduction 11.1 Historical perspective 11.2 How to use this book 101.3 Outline of this book 101.4 Notes and references 142 Linear algebra 152.1 Basic concepts in linear algebra 152.2 Eigenvalues and eigenvectors 212.3 Complex eigenvalues 232.4 Cayley–Hamilton theorem 312.5 Invariant subspaces and Jordan canonical form 342.6 Semi-definite matrices 422.7 Algebraic Riccati equations 432.8 Notes and references 542.9 Exercises 552.10 Appendix 593 Dynamical systems 633.1 Description of linear dynamical systems 643.2 Existence–uniqueness results for differential equations 703.2.1 General case 703.2.2 Control theoretic extensions 743.3 Stability theory: general case 783.4 Stability theory of planar systems 833.5 Geometric concepts 913.6 Performance specifications 963.7 Examples of differential games 1053.8 Information, commitment and strategies 1143.9 Notes and references 1143.10 Exercises 1153.11 Appendix 1184 Optimization techniques 1214.1 Optimization of functions 1214.2 The Euler–Lagrange equation 1254.3 Pontryagin’s maximum principle 1334.4 Dynamic programming principle 1544.5 Solving optimal control problems 1624.6 Notes and references 1624.7 Exercises 1634.8 Appendix 1705 Regular linear quadratic optimal control 1755.1 Problem statement 1755.2 Finite-planning horizon 1775.3 Riccati differential equations 1925.4 Infinite-planning horizon 1965.5 Convergence results 2095.6 Notes and references 2185.7 Exercises 2195.8 Appendix 2246 Cooperative games 2296.1 Pareto solutions 2306.2 Bargaining concepts 2406.3 Nash bargaining solution 2466.4 Numerical solution 2516.5 Notes and references 2536.6 Exercises 2546.7 Appendix 2597 Non-cooperative open-loop information games 2617.1 Introduction 2647.2 Finite-planning horizon 2657.3 Open-loop Nash algebraic Riccati equations 2787.4 Infinite-planning horizon 2837.5 Computational aspects and illustrative examples 2997.6 Convergence results 3057.7 Scalar case 3127.8 Economics examples 3197.8.1 A simple government debt stabilization game 3207.8.2 A game on dynamic duopolistic competition 3227.9 Notes and references 3267.10 Exercises 3277.11 Appendix 3408 Non-cooperative feedback information games 3598.1 Introduction 3598.2 Finite-planning horizon 3628.3 Infinite-planning horizon 3718.4 Two-player scalar case 3838.5 Computational aspects 3898.5.1 Preliminaries 3908.5.2 A scalar numerical algorithm: the two-player case 3938.5.3 The N-player scalar case 3998.6 Convergence results for the two-player scalar case 4038.7 Notes and references 4128.8 Exercises 4138.9 Appendix 4219 Uncertain non-cooperative feedback information games 4279.1 Stochastic approach 4289.2 Deterministic approach: introduction 4339.3 The one-player case 4359.4 The one-player scalar case 4449.5 The two-player case 4509.6 A fishery management game 4559.7 A scalar numerical algorithm 4619.8 Stochastic interpretation 4729.9 Notes and references 4749.10 Exercises 4759.11 Appendix 481References 485Index 495