Stochastic and Differential Games

Stochastic and Differential Games

Author: Martino Bardi

Publisher: Springer Science & Business Media

ISBN: 0817640290

Category: Mathematics

Page: 380

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The theory of two-person, zero-sum differential games started at the be­ ginning of the 1960s with the works of R. Isaacs in the United States and L. S. Pontryagin and his school in the former Soviet Union. Isaacs based his work on the Dynamic Programming method. He analyzed many special cases of the partial differential equation now called Hamilton­ Jacobi-Isaacs-briefiy HJI-trying to solve them explicitly and synthe­ sizing optimal feedbacks from the solution. He began a study of singular surfaces that was continued mainly by J. Breakwell and P. Bernhard and led to the explicit solution of some low-dimensional but highly nontriv­ ial games; a recent survey of this theory can be found in the book by J. Lewin entitled Differential Games (Springer, 1994). Since the early stages of the theory, several authors worked on making the notion of value of a differential game precise and providing a rigorous derivation of the HJI equation, which does not have a classical solution in most cases; we mention here the works of W. Fleming, A. Friedman (see his book, Differential Games, Wiley, 1971), P. P. Varaiya, E. Roxin, R. J. Elliott and N. J. Kalton, N. N. Krasovskii, and A. I. Subbotin (see their book Po­ sitional Differential Games, Nauka, 1974, and Springer, 1988), and L. D. Berkovitz. A major breakthrough was the introduction in the 1980s of two new notions of generalized solution for Hamilton-Jacobi equations, namely, viscosity solutions, by M. G. Crandall and P. -L.
Differential Games in Marketing
Language: en
Pages: 176
Authors: Steffen Jørgensen, Georges Zaccour
Categories: Business & Economics
Type: BOOK - Published: 2003-11-30 - Publisher: Springer Science & Business Media

Game theory has proven useful to represent and conceptualize problems of conflict and cooperation in a formal way, and to predict the outcome of such situations. Differential games are dynamic games that are particularly designed to study systems where observations and decisions are made in real time. The book conveys
Differential Games in Industrial Economics
Language: en
Pages: 272
Authors: Luca Lambertini
Categories: Business & Economics
Type: BOOK - Published: 2018-04-26 - Publisher:

A comprehensive and self-contained exposition of the applications of optimal control and differential game theory to industrial organisation and trade.
Cooperative Stochastic Differential Games
Language: en
Pages: 242
Authors: David W.K. Yeung, Leon A. Petrosjan
Categories: Business & Economics
Type: BOOK - Published: 2006-05-11 - Publisher: Springer Science & Business Media

Numerical Optimization presents a comprehensive and up-to-date description of the most effective methods in continuous optimization. It responds to the growing interest in optimization in engineering, science, and business by focusing on the methods that are best suited to practical problems. For this new edition the book has been thoroughly
Handbook of Game Theory with Economic Applications
Language: en
Pages: 818
Authors: R.J. Aumann, S. Hart
Categories: Business & Economics
Type: BOOK - Published: 1992 - Publisher: Elsevier

This is the second of three volumes surveying the state of the art in Game Theory and its applications to many and varied fields, in particular to economics. The chapters in the present volume are contributed by outstanding authorities, and provide comprehensive coverage and precise statements of the main results
New Trends in Dynamic Games and Applications
Language: en
Pages: 484
Authors: Jan G. Olsder
Categories: Mathematics
Type: BOOK - Published: 1995-12-01 - Publisher: Springer Science & Business Media

The theory of dynamic games is very rich in nature and very much alive! If the reader does not already agree with this statement, I hope he/she will surely do so after having consulted the contents of the current volume. The activities which fall under the heading of 'dynamic games'