|
Showing 1 - 5 of
5 matches in All Departments
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.
The paradigms of dynamic games play an important role in the
development of multi-agent models in engineering, economics, and
management science. The applicability of their concepts stems from
the ability to encompass situations with uncertainty, incomplete
information, fluctuating coalition structure, and coupled
constraints imposed on the strategies of all the players. This book
- an outgrowth of the 10th International Symposium on Dynamic Games
- presents current developments of the theory of dynamic games and
its applications to various domains, in particular
energy-environment economics and management sciences. The volume
uses dynamic game models of various sorts to approach and solve
several problems pertaining to pursuit-evasion, marketing, finance,
climate and environmental economics, resource exploitation, as well
as auditing and tax evasions. In addition, it includes some
chapters on cooperative games, which are increasingly drawing
dynamic approaches to their classical solutions. dynamic game
theory and its applications for researchers, practitioners, and
graduate students in applied mathematics, engineering, economics,
as well as environmental and management sciences.
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.
This book provides an integrated treatment of the theory of
nonnegative matrices and some related classes of positive matrices,
concentrating on connections with game theory, combinatorics,
inequalities, optimization and mathematical economics. The authors
have chosen the wide variety of applications, which include price
fixing, scheduling, and the fair division problem, both for their
elegant mathematical content and for their accessibility to
students with minimal preparation. They present many new results in
matrix theory for the first time in book form, while they present
more standard topics in a novel fashion. The treatment is rigorous
and almost all results are proved completely. These new results and
applications will be of great interest to researchers in linear
programming, statistics, and operations research. The minimal
prerequisites also make the book accessible to first year graduate
students.
This book provides an integrated treatment of the theory of
nonnegative matrices and some related classes of positive matrices,
concentrating on connections with game theory, combinatorics,
inequalities, optimization and mathematical economics. The authors
have chosen the wide variety of applications, which include price
fixing, scheduling, and the fair division problem, both for their
elegant mathematical content and for their accessibility to
students with minimal preparation. They present many new results in
matrix theory for the first time in book form, while they present
more standard topics in a novel fashion. The treatment is rigorous
and almost all results are proved completely. These new results and
applications will be of great interest to researchers in linear
programming, statistics, and operations research. The minimal
prerequisites also make the book accessible to first year graduate
students.
|
|