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There has been an increase in attention toward systems involving
large numbers of small players, giving rise to the theory of mean
field games, mean field type control and nonlinear Markov games.
Exhibiting various real world problems involving major and minor
agents, this book presents a systematic continuous-space
approximation approach for mean-field interacting agents models and
mean-field games models. After describing Markov-chain methodology
and a modeling of mean-field interacting systems, the text presents
various structural conditions on the chain to yield respective
socio-economic models, focusing on migration models via binary
interactions. The specific applications are wide-ranging -
including inspection and corruption, cyber-security,
counterterrorism, coalition building and network growth, minority
games, and investment policies and optimal allocation - making this
book relevant to a wide audience of applied mathematicians
interested in operations research, computer science, national
security, economics, and finance.
There has been an increase in attention toward systems involving
large numbers of small players, giving rise to the theory of mean
field games, mean field type control and nonlinear Markov games.
Exhibiting various real world problems involving major and minor
agents, this book presents a systematic continuous-space
approximation approach for mean-field interacting agents models and
mean-field games models. After describing Markov-chain methodology
and a modeling of mean-field interacting systems, the text presents
various structural conditions on the chain to yield respective
socio-economic models, focusing on migration models via binary
interactions. The specific applications are wide-ranging -
including inspection and corruption, cyber-security,
counterterrorism, coalition building and network growth, minority
games, and investment policies and optimal allocation - making this
book relevant to a wide audience of applied mathematicians
interested in operations research, computer science, national
security, economics, and finance.
Steadily growing applications of game theory in modern science
(including psychology, biology and economics) require sources to
provide rapid access in both classical tools and recent
developments to readers with diverse backgrounds. This book on game
theory, its applications and mathematical methods, is written with
this objective in mind.The book gives a concise but wide-ranging
introduction to games including older (pre-game theory) party games
and more recent topics like elections and evolutionary games and is
generously spiced with excursions into philosophy, history,
literature and politics. A distinguished feature is the clear
separation of the text into two parts: elementary and advanced,
which makes the book ideal for study at various levels.Part I
displays basic ideas using no more than four arithmetic operations
and requiring from the reader only some inclination to logical
thinking. It can be used in a university degree course without any
(or minimal) prerequisite in mathematics (say, in economics,
business, systems biology), as well as for self-study by school
teachers, social and natural scientists, businessmen or laymen.Part
II is a rapid introduction to the mathematical methods of game
theory, suitable for a mathematics degree course of various levels.
It includes an advanced material not yet reflected in standard
textbooks, providing links with the exciting modern developments in
financial mathematics (rainbow option pricing), tropical
mathematics, statistical physics (interacting particles) and
discusses structural stability, multi-criteria differential games
and turnpikes.To stimulate the mathematical and scientific
imagination, graphics by a world-renowned mathematician and
mathematics imaging artist, A T Fomenko, are used. The carefully
selected works of this artist fit remarkably into the many ideas
expressed in the book.
Steadily growing applications of game theory in modern science
(including psychology, biology and economics) require sources to
provide rapid access in both classical tools and recent
developments to readers with diverse backgrounds. This book on game
theory, its applications and mathematical methods, is written with
this objective in mind.The book gives a concise but wide-ranging
introduction to games including older (pre-game theory) party games
and more recent topics like elections and evolutionary games and is
generously spiced with excursions into philosophy, history,
literature and politics. A distinguished feature is the clear
separation of the text into two parts: elementary and advanced,
which makes the book ideal for study at various levels.Part I
displays basic ideas using no more than four arithmetic operations
and requiring from the reader only some inclination to logical
thinking. It can be used in a university degree course without any
(or minimal) prerequisite in mathematics (say, in economics,
business, systems biology), as well as for self-study by school
teachers, social and natural scientists, businessmen or laymen.
Part II is a rapid introduction to the mathematical methods of game
theory, suitable for a mathematics degree course of various
levels.To stimulate the mathematical and scientific imagination,
graphics by a world-renowned mathematician and mathematics imaging
artist, A T Fomenko, are used. The carefully selected works of this
artist fit remarkably into the many ideas expressed in the
book.This new edition has been updated and enlarged. In particular,
two new chapters were added on statistical limit of games with many
agents and on quantum games, reflecting possibly the two most
stunning trends in the game theory of the 21st century.
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