Jacob Engwerda

Lq Dynamic Optimization and Differential Games

• Gebundenes Buch

Produktbeschreibung

A self-contained introduction to an extensively used of economic models.

"Linear Quadratic Differential Games" is an assessment of the state of the art in its field and modern book on linear-quadratic game theory, one of the most commonly used tools for modelling and analysing strategic decision making problems in economics and management. Linear quadratic dynamic models have a long tradition in economics, operations research and control engineering; and the author begins by describing the one-decision maker LQ dynamic optimization problem before introducing LQ differential games.
_ Covers cooperative and non-cooperative scenarios, and treats the standard information structures (open-loop and feedback).
_ Includes real-life economic examples to illustrate theoretical concepts and results.
_ Presents problem formulations and sound mathematical problem analysis.
_ Includes exercises and solutions, enabling use for self-study or as a course text.
_ Supported by a website featuring solutions to exercises, further examples and computer code for numerical examples.

This comprehensive introduction will appeal to applied mathematicians and econometricians as well as researchers and senior undergraduate/ graduate students in economics, mathematics, engineering and management science.

Produktdetails

• Verlag: Wiley & Sons
• 1. Auflage
• Seitenzahl: 512
• Erscheinungstermin: 17. Juni 2005
• Englisch
• Abmessung: 253mm x 174mm x 37mm
• Gewicht: 1116g
• ISBN-13: 9780470015247
• ISBN-10: 0470015241
• Artikelnr.: 14843138

Autorenporträt

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

Inhaltsangabe

Preface. Notation and symbols. 1 Introduction. 1.1 Historical perspective.
1.2 How to use this book. 1.3 Outline of this book. 1.4 Notes and
references. 2 Linear algebra. 2.1 Basic concepts in linear algebra. 2.2
Eigenvalues and eigenvectors. 2.3 Complex eigenvalues. 2.4 Cayley-Hamilton
theorem. 2.5 Invariant subspaces and Jordan canonical form. 2.6
Semi-definite matrices. 2.7 Algebraic Riccati equations. 2.8 Notes and
references. 2.9 Exercises. 2.10 Appendix. 3 Dynamical systems. 3.1
Description of linear dynamical systems. 3.2 Existence-uniqueness results
for differential equations. 3.2.1 General case. 3.2.2 Control theoretic
extensions. 3.3 Stability theory: general case. 3.4 Stability theory of
planar systems. 3.5 Geometric concepts. 3.6 Performance specifications. 3.7
Examples of differential games. 3.8 Information, commitment and strategies.
3.9 Notes and references. 3.10 Exercises. 3.11 Appendix. 4 Optimization
techniques. 4.1 Optimization of functions. 4.2 The Euler-Lagrange equation.
4.3 Pontryagin's maximum principle. 4.4 Dynamic programming principle. 4.5
Solving optimal control problems. 4.6 Notes and references. 4.7 Exercises.
4.8 Appendix. 5 Regular linear quadratic optimal control. 5.1 Problem
statement. 5.2 Finite-planning horizon. 5.3 Riccati differential equations.
5.4 Infinite-planning horizon. 5.5 Convergence results. 5.6 Notes and
references. 5.7 Exercises. 5.8 Appendix. 6 Cooperative games. 6.1 Pareto
solutions. 6.2 Bargaining concepts. 6.3 Nash bargaining solution. 6.4
Numerical solution. 6.5 Notes and references. 6.6 Exercises. 6.7 Appendix.
7 Non-cooperative open-loop information games. 7.1 Introduction. 7.2
Finite-planning horizon. 7.3 Open-loop Nash algebraic Riccati equations.
7.4 Infinite-planning horizon. 7.5 Computational aspects and illustrative
examples. 7.6 Convergence results. 7.7 Scalar case. 7.8 Economics examples.
7.8.1 A simple government debt stabilization game. 7.8.2 A game on dynamic
duopolistic competition. 7.9 Notes and references. 7.10 Exercises. 7.11
Appendix. 8 Non-cooperative feedback information games. 8.1 Introduction.
8.2 Finite-planning horizon. 8.3 Infinite-planning horizon. 8.4 Two-player
scalar case. 8.5 Computational aspects. 8.5.1 Preliminaries. 8.5.2 A scalar
numerical algorithm: the two-player case. 8.5.3 The N-player scalar case.
8.6 Convergence results for the two-player scalar case. 8.7 Notes and
references. 8.8 Exercises. 8.9 Appendix. 9 Uncertain non-cooperative
feedback information games. 9.1 Stochastic approach. 9.2 Deterministic
approach: introduction. 9.3 The one-player case. 9.4 The one-player scalar
case. 9.5 The two-player case. 9.6 A fishery management game. 9.7 A scalar
numerical algorithm. 9.8 Stochastic interpretation. 9.9 Notes and
references. 9.10 Exercises. 9.11 Appendix. References. Index.