Differential Games and Applications

Differential Games and Applications
Author: Tamer S. Basar
Publisher: Springer
Total Pages: 205
Release: 2014-03-12
Genre: Technology & Engineering
ISBN: 9783662168660

This volume contains fifteen articles on the topic of differential and dynamic games, focusing on both theory and applications. It covers a variety of areas and presents recent developments on topics of current interest. It should be useful to researchers in differential and dynamic games, systems and control, operations research and mathematical economics.

Differential Games

Differential Games
Author: Avner Friedman
Publisher: Courier Corporation
Total Pages: 372
Release: 2013-06-06
Genre: Mathematics
ISBN: 0486153274

Graduate-level text surveys games of fixed duration, games of pursuit and evasion, the computation of saddle points, games of survival, games with restricted phase coordinates, and N-person games. 1971 edition.

Differential Games

Differential Games
Author: Rufus Isaacs
Publisher: Courier Corporation
Total Pages: 420
Release: 2012-04-26
Genre: Mathematics
ISBN: 0486135985

Definitive work draws on game theory, calculus of variations, and control theory to solve an array of problems: military, pursuit and evasion, athletic contests, many more. Detailed examples, formal calculations. 1965 edition.

Differential Games in Economics and Management Science

Differential Games in Economics and Management Science
Author: Engelbert Dockner
Publisher: Cambridge University Press
Total Pages: 398
Release: 2000-11-16
Genre: Business & Economics
ISBN: 9780521637329

A comprehensive, self-contained survey of the theory and applications of differential games, one of the most commonly used tools for modelling and analysing economics and management problems which are characterised by both multiperiod and strategic decision making. Although no prior knowledge of game theory is required, a basic knowledge of linear algebra, ordinary differential equations, mathematical programming and probability theory is necessary. Part One presents the theory of differential games, starting with the basic concepts of game theory and going on to cover control theoretic models, Markovian equilibria with simultaneous play, differential games with hierarchical play, trigger strategy equilibria, differential games with special structures, and stochastic differential games. Part Two offers applications to capital accumulation games, industrial organization and oligopoly games, marketing, resources and environmental economics.

Differential Games in Industrial Economics

Differential Games in Industrial Economics
Author: Luca Lambertini
Publisher: Cambridge University Press
Total Pages: 275
Release: 2018-04-26
Genre: Business & Economics
ISBN: 1316732630

Game theory has revolutionised our understanding of industrial organisation and the traditional theory of the firm. Despite these advances, industrial economists have tended to rely on a restricted set of tools from game theory, focusing on static and repeated games to analyse firm structure and behaviour. Luca Lambertini, a leading expert on the application of differential game theory to economics, argues that many dynamic phenomena in industrial organisation (such as monopoly, oligopoly, advertising, R&D races) can be better understood and analysed through the use of differential games. After illustrating the basic elements of the theory, Lambertini guides the reader through the main models, spanning from optimal control problems describing the behaviour of a monopolist through to oligopoly games in which firms' strategies include prices, quantities and investments. This approach will be of great value to students and researchers in economics and those interested in advanced applications of game theory.

Dynamic Games: Theory and Applications

Dynamic Games: Theory and Applications
Author: Alain Haurie
Publisher: Springer Science & Business Media
Total Pages: 296
Release: 2005-05-06
Genre: Business & Economics
ISBN: 9780387246017

Dynamic games continue to attract strong interest from researchers interested in modelling competitive as well as conflict situations exhibiting an intertemporel aspect. Applications of dynamic games have proven to be a suitable methodology to study the behaviour of players (decision-makers) and to predict the outcome of such situations in many areas including engineering, economics, management science, military, biology and political science. Dynamic Games: Theory and Applications collects thirteen articles written by established researchers. It is an excellent reference for researchers and graduate students covering a wide range of emerging and revisited problems in both cooperative and non-cooperative games in different areas of applications, especially in economics and management science.

Lyapunov Functions in Differential Games

Lyapunov Functions in Differential Games
Author: Vladislav I Zhukovskiy
Publisher: CRC Press
Total Pages: 308
Release: 2003-01-16
Genre: Mathematics
ISBN: 9780415273411

A major step in differential games is determining an explicit form of the strategies of players who follow a certain optimality principle. To do this, the associated modification of Bellman dynamic programming problems has to be solved; for some differential games this could be Lyapunov functions whose "arsenal" has been supplied by stability theory. This approach, which combines dynamic programming and the Lyapunov function method, leads to coefficient criteria, or ratios of the game math model parameters with which optimal strategies of the players not only exist but their analytical form can be specified. In this book coefficient criteria are derived for numerous new and relevant problems in the theory of linear-quadratic multi-player differential games. Those criteria apply when the players formulate their strategies independently (non co-operative games) and use non-Nash equilibria or when the game model recognizes noise, perturbation and other uncertainties of which only their ranges are known (differential games under uncertainty). This text is useful for researchers, engineers and students of applied mathematics, control theory and the engineering sciences.

LQ Dynamic Optimization and Differential Games

LQ Dynamic Optimization and Differential Games
Author: Jacob Engwerda
Publisher: John Wiley & Sons
Total Pages: 514
Release: 2005-06-17
Genre: Business & Economics
ISBN: 9780470015247

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. 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.

Stochastic Differential Games. Theory and Applications

Stochastic Differential Games. Theory and Applications
Author: Kandethody M. Ramachandran
Publisher: Springer Science & Business Media
Total Pages: 253
Release: 2012-01-05
Genre: Mathematics
ISBN: 9491216473

The subject theory is important in finance, economics, investment strategies, health sciences, environment, industrial engineering, etc.