LQ Dynamic Optimization and Differential Games
LQ Dynamic Optimization and Differential Games is an assessment of the state of the art in its field and the first 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.
LQ Dynamic Optimization and Differential Games offers a comprehensive introduction to the theory and practice of this extensively used class of economic models, and will appeal to applied mathematicians and econometricians as well as researchers and senior undergraduate/graduate students in economics, mathematics, engineering and management science.
Notation and symbols.
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.
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.
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.
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.
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.
7 Non-cooperative open-loop information games.
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.
8 Non-cooperative feedback information games.
8.2 Finite-planning horizon.
8.3 Infinite-planning horizon.
8.4 Two-player scalar case.
8.5 Computational aspects.
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.
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.
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-and- Problems Book to accompany Mathematics for Economists (US $47.95)
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