{"product_id":"lq-dynamic-optimization-and-differential-games-isbn-9780470015247","title":"LQ Dynamic Optimization and Differential Games","description":"Game theory is the theory of social situations, and the majority of research into the topic focuses on how groups of people interact by developing formulas and algorithms to identify optimal strategies and to predict the outcome of interactions. Only fifty years old, it has already revolutionized economics and finance, and is spreading rapidly to a wide variety of fields.  \u003cp\u003e\u003ci\u003eLQ Dynamic Optimization and Differential Games\u003c\/i\u003e 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.\u003c\/p\u003e \u003cul\u003e \u003cli\u003eCovers cooperative and non-cooperative scenarios, and treats the standard information structures (open-loop and feedback).\u003c\/li\u003e \u003cli\u003eIncludes real-life economic examples to illustrate theoretical concepts and results.\u003c\/li\u003e \u003cli\u003ePresents problem formulations and sound mathematical problem analysis.\u003c\/li\u003e \u003cli\u003eIncludes exercises and solutions, enabling use for self-study or as a course text.\u003c\/li\u003e \u003cli\u003eSupported by a website featuring solutions to exercises, further examples and computer code for numerical examples.\u003c\/li\u003e \u003c\/ul\u003e \u003cp\u003e\u003ci\u003eLQ Dynamic Optimization and Differential Games\u003c\/i\u003e 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.\u003c\/p\u003e  Preface.  \u003cp\u003eNotation and symbols.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 Introduction.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 Historical perspective.\u003c\/p\u003e \u003cp\u003e1.2 How to use this book.\u003c\/p\u003e \u003cp\u003e1.3 Outline of this book.\u003c\/p\u003e \u003cp\u003e1.4 Notes and references.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 Linear algebra.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 Basic concepts in linear algebra.\u003c\/p\u003e \u003cp\u003e2.2 Eigenvalues and eigenvectors.\u003c\/p\u003e \u003cp\u003e2.3 Complex eigenvalues.\u003c\/p\u003e \u003cp\u003e2.4 Cayley–Hamilton theorem.\u003c\/p\u003e \u003cp\u003e2.5 Invariant subspaces and Jordan canonical form.\u003c\/p\u003e \u003cp\u003e2.6 Semi-definite matrices.\u003c\/p\u003e \u003cp\u003e2.7 Algebraic Riccati equations.\u003c\/p\u003e \u003cp\u003e2.8 Notes and references.\u003c\/p\u003e \u003cp\u003e2.9 Exercises.\u003c\/p\u003e \u003cp\u003e2.10 Appendix.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 Dynamical systems.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 Description of linear dynamical systems.\u003c\/p\u003e \u003cp\u003e3.2 Existence–uniqueness results for differential equations.\u003c\/p\u003e \u003cp\u003e3.2.1 General case.\u003c\/p\u003e \u003cp\u003e3.2.2 Control theoretic extensions.\u003c\/p\u003e \u003cp\u003e3.3 Stability theory: general case.\u003c\/p\u003e \u003cp\u003e3.4 Stability theory of planar systems.\u003c\/p\u003e \u003cp\u003e3.5 Geometric concepts.\u003c\/p\u003e \u003cp\u003e3.6 Performance specifications.\u003c\/p\u003e \u003cp\u003e3.7 Examples of differential games.\u003c\/p\u003e \u003cp\u003e3.8 Information, commitment and strategies.\u003c\/p\u003e \u003cp\u003e3.9 Notes and references.\u003c\/p\u003e \u003cp\u003e3.10 Exercises.\u003c\/p\u003e \u003cp\u003e3.11 Appendix.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Optimization techniques.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 Optimization of functions.\u003c\/p\u003e \u003cp\u003e4.2 The Euler–Lagrange equation.\u003c\/p\u003e \u003cp\u003e4.3 Pontryagin’s maximum principle.\u003c\/p\u003e \u003cp\u003e4.4 Dynamic programming principle.\u003c\/p\u003e \u003cp\u003e4.5 Solving optimal control problems.\u003c\/p\u003e \u003cp\u003e4.6 Notes and references.\u003c\/p\u003e \u003cp\u003e4.7 Exercises.\u003c\/p\u003e \u003cp\u003e4.8 Appendix.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 Regular linear quadratic optimal control.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 Problem statement.\u003c\/p\u003e \u003cp\u003e5.2 Finite-planning horizon.\u003c\/p\u003e \u003cp\u003e5.3 Riccati differential equations.\u003c\/p\u003e \u003cp\u003e5.4 Infinite-planning horizon.\u003c\/p\u003e \u003cp\u003e5.5 Convergence results.\u003c\/p\u003e \u003cp\u003e5.6 Notes and references.\u003c\/p\u003e \u003cp\u003e5.7 Exercises.\u003c\/p\u003e \u003cp\u003e5.8 Appendix.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 Cooperative games.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 Pareto solutions.\u003c\/p\u003e \u003cp\u003e6.2 Bargaining concepts.\u003c\/p\u003e \u003cp\u003e6.3 Nash bargaining solution.\u003c\/p\u003e \u003cp\u003e6.4 Numerical solution.\u003c\/p\u003e \u003cp\u003e6.5 Notes and references.\u003c\/p\u003e \u003cp\u003e6.6 Exercises.\u003c\/p\u003e \u003cp\u003e6.7 Appendix.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 Non-cooperative open-loop information games.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 Introduction.\u003c\/p\u003e \u003cp\u003e7.2 Finite-planning horizon.\u003c\/p\u003e \u003cp\u003e7.3 Open-loop Nash algebraic Riccati equations.\u003c\/p\u003e \u003cp\u003e7.4 Infinite-planning horizon.\u003c\/p\u003e \u003cp\u003e7.5 Computational aspects and illustrative examples.\u003c\/p\u003e \u003cp\u003e7.6 Convergence results.\u003c\/p\u003e \u003cp\u003e7.7 Scalar case.\u003c\/p\u003e \u003cp\u003e7.8 Economics examples.\u003c\/p\u003e \u003cp\u003e7.8.1 A simple government debt stabilization game.\u003c\/p\u003e \u003cp\u003e7.8.2 A game on dynamic duopolistic competition.\u003c\/p\u003e \u003cp\u003e7.9 Notes and references.\u003c\/p\u003e \u003cp\u003e7.10 Exercises.\u003c\/p\u003e \u003cp\u003e7.11 Appendix.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 Non-cooperative feedback information games.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1 Introduction.\u003c\/p\u003e \u003cp\u003e8.2 Finite-planning horizon.\u003c\/p\u003e \u003cp\u003e8.3 Infinite-planning horizon.\u003c\/p\u003e \u003cp\u003e8.4 Two-player scalar case.\u003c\/p\u003e \u003cp\u003e8.5 Computational aspects.\u003c\/p\u003e \u003cp\u003e8.5.1 Preliminaries.\u003c\/p\u003e \u003cp\u003e8.5.2 A scalar numerical algorithm: the two-player case.\u003c\/p\u003e \u003cp\u003e8.5.3 The N-player scalar case.\u003c\/p\u003e \u003cp\u003e8.6 Convergence results for the two-player scalar case.\u003c\/p\u003e \u003cp\u003e8.7 Notes and references.\u003c\/p\u003e \u003cp\u003e8.8 Exercises.\u003c\/p\u003e \u003cp\u003e8.9 Appendix.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e9 Uncertain non-cooperative feedback information games.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e9.1 Stochastic approach.\u003c\/p\u003e \u003cp\u003e9.2 Deterministic approach: introduction.\u003c\/p\u003e \u003cp\u003e9.3 The one-player case.\u003c\/p\u003e \u003cp\u003e9.4 The one-player scalar case.\u003c\/p\u003e \u003cp\u003e9.5 The two-player case.\u003c\/p\u003e \u003cp\u003e9.6 A fishery management game.\u003c\/p\u003e \u003cp\u003e9.7 A scalar numerical algorithm.\u003c\/p\u003e \u003cp\u003e9.8 Stochastic interpretation.\u003c\/p\u003e \u003cp\u003e9.9 Notes and references.\u003c\/p\u003e \u003cp\u003e9.10 Exercises.\u003c\/p\u003e \u003cp\u003e9.11 Appendix.\u003c\/p\u003e \u003cp\u003eReferences.\u003c\/p\u003e \u003cp\u003eIndex.\u003c\/p\u003e  \u003cp\u003eJacob Engwerda is the author of LQ Dynamic Optimization and Differential Games, published by Wiley.   Game theory is the theory of social situations, and the majority of research into the topic focuses on how groups of people interact by developing formulas and algorithms to identify optimal strategies and to predict the outcome of interactions. Only fifty years old, it has already revolutionized economics and finance, and is spreading rapidly to a wide variety of fields.  \u003c\/p\u003e\u003cp\u003e\u003ci\u003eLQ Dynamic Optimization and Differential Games\u003c\/i\u003e 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.\u003c\/p\u003e \u003cul\u003e \u003cli\u003eCovers cooperative and non-cooperative scenarios, and treats the standard information structures (open-loop and feedback).\u003c\/li\u003e \u003cli\u003eIncludes real-life economic examples to illustrate theoretical concepts and results.\u003c\/li\u003e \u003cli\u003ePresents problem formulations and sound mathematical problem analysis.\u003c\/li\u003e \u003cli\u003eIncludes exercises and solutions, enabling use for self-study or as a course text.\u003c\/li\u003e \u003cli\u003eSupported by a website featuring solutions to exercises, further examples and computer code for numerical examples.\u003c\/li\u003e \u003c\/ul\u003e \u003cp\u003e\u003ci\u003eLQ Dynamic Optimization and Differential Games\u003c\/i\u003e 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.\u003c\/p\u003e","brand":"Wiley","offers":[{"title":"Default Title","offer_id":47989545271525,"sku":"NP9780470015247","price":150.95,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/1842\/7735\/files\/9780470015247.jpg?v=1761784539","url":"https:\/\/k12savings.com\/products\/lq-dynamic-optimization-and-differential-games-isbn-9780470015247","provider":"K12savings","version":"1.0","type":"link"}