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Books > Science & Mathematics > Mathematics > Optimization > Game theory
We all played tag when we were kids. What most of us don't
realize is that this simple chase game is in fact an application of
pursuit theory, and that the same principles of games like tag,
dodgeball, and hide-and-seek are also at play in military strategy,
high-seas chases by the Coast Guard, and even romantic pursuits. In
"Chases and Escapes," Paul Nahin gives us the first complete
history of this fascinating area of mathematics, from its classical
analytical beginnings to the present day.
Drawing on game theory, geometry, linear algebra,
target-tracking algorithms, and much more, Nahin also offers an
array of challenging puzzles with their historical background and
broader applications. "Chases and Escapes" includes solutions to
all problems and provides computer programs that readers can use
for their own cutting-edge analysis.
Now with a gripping new preface on how the Enola Gay escaped the
shock wave from the atomic bomb dropped on Hiroshima, this book
will appeal to anyone interested in the mathematics that underlie
pursuit and evasion.
The advent of noncooperative game theory over the past two decades has brought about a mild revolution in economics. This book presents an accessible, non-technical discussion of the basic concepts from noncooperative theory, and explores the strengths, weaknesses, and future of the theory as a tool for economists.
Despite the growing consensus on the need for action to counteract
climate change, complex economic and political forces have so far
prevented international actors from making much headway toward
resolving the problem. Most approaches to climate change are based
in economics and environmental science; in this book, Parkash
Chander argues that we can make further progress on the climate
change impasse by considering a third approach-game theory. Chander
shows that a game-theoretic approach, which offers insight into the
nature of interactions between sovereign countries behaving
strategically and the kinds of outcomes such interactions produce,
can illuminate how best to achieve international agreements in
support of climate-change mitigation strategies. Game Theory and
Climate Change develops a conceptual framework with which to
analyze climate change as a strategic or dynamic game, bringing
together cooperative and noncooperative game theory and providing
practical analyses of international negotiations. Chander offers
economic and game-theoretic interpretations of both the Kyoto
Protocol and the Paris Agreement and argues that the Paris
Agreement may succeed where the Kyoto Protocol failed. Finally,
Chander discusses the policy recommendations his framework
generates, including a global agreement to support development of
cleaner technologies on a global scale.
Simple games are mathematical structures inspired by voting
systems in which a single alternative, such as a bill, is pitted
against the status quo. The first in-depth mathematical study of
the subject as a coherent subfield of finite combinatorics--one
with its own organized body of techniques and results--this book
blends new theorems with some of the striking results from
threshold logic, making all of it accessible to game theorists.
Introductory material receives a fresh treatment, with an emphasis
on Boolean subgames and the Rudin-Keisler order as unifying
concepts. Advanced material focuses on the surprisingly wide
variety of properties related to the weightedness of a game.
A desirability relation orders the individuals or coalitions of
a game according to their influence in the corresponding voting
system. As Taylor and Zwicker show, acyclicity of such a relation
approximates weightedness--the more sensitive the relation, the
closer the approximation. A trade is an exchange of players among
coalitions, and robustness under such trades is equivalent to
weightedness of the game. Robustness under trades that fit some
restrictive exchange pattern typically characterizes a wider class
of simple games--for example, games for which some particular
desirability order is acyclic. Finally, one can often describe
these wider classes of simple games by weakening the total
additivity of a weighting to obtain what is called a
pseudoweighting. In providing such uniform explanations for many of
the structural properties of simple games, this book showcases
numerous new techniques and results.
What is a game? Classically, a game is perceived as something
played by human beings. Its mathematical analysis is
human-centered, explores the structures of particular games,
economic or social environments and tries to model supposedly
'rational' human behavior in search of appropriate 'winning
strategies'. This point of view places game theory into a very
special scientific corner where mathematics, economics and
psychology overlap and mingle.This book takes a novel approach to
the subject. Its focus is on mathematical models that apply to game
theory in particular but exhibit a universal character and thus
extend the scope of game theory considerably.This textbook
addresses anyone interested in a general game-theoretic view of the
world. The reader should have mathematical knowledge at the level
of a first course in real analysis and linear algebra. However,
possibly more specialized aspects are further elaborated and
pointers to relevant supplementary literature are given. Moreover,
many examples invite the reader to participate 'actively' when
going through the material. The scope of the book can be covered in
one course on Mathematical Game Theory at advanced undergraduate or
graduate level.
This book offers a gentle introduction to Hex, the classic board
game created by Piet Hein and popularized by John Nash and Martin
Gardner. The first three chapters cover rules, basic strategy, and
history. The remaining eight chapters cover a variety of topics:
mathematical properties (there are no draws, the first player can
win, the acute corner is a losing first move), the related game of
Y, winning strategies for small boards, how computers play Hex, an
analysis of Random-Move Hex (where one or both players move
randomly) and Dark Hex (the imperfect information version of the
game, where you can't see your opponent's moves). Did we mention
puzzles? There are puzzles in every chapter, with solutions. This
book is intended for anyone interested in playing board games or
learning some recreational mathematics. It is written for a wide
audience and will be enjoyed equally by general readers and
professional mathematicians. The book could be used as a textbook
or companion resource for a topics course on recreational
mathematics or game theory or as a source for undergraduate
research questions.
A host of digital affordances, including reduced cost production
tools, open distribution platforms, and ubiquitous connectivity,
have engendered the growth of indie games among makers and users,
forcing critics to reconsider the question of who makes games and
why. Taking seriously this new mode of cultural produciton compells
analysts to reconsider the blurred boundaries and relations of
makers, users and texts as well as their respective relationship to
cultural power and hierarchy. The contributions to Indie Games in
the Digital Age consider these questions and examine a series of
firms, makers, games and scenes, ranging from giants like Nintendo
and Microsoft to grassroots games like Cards Against Humanity and
Stardew Valley, to chart more precisely the productive and
instructive disruption that this new site of cultural production
offers.
The genre of adventure games is frequently overlooked. Lacking the
constantly-evolving graphics and graphic violence of their
counterparts in first-person and third-person shooters or
role-playing games, they are often marketed to and beloved by
players outside of mainstream game communities. While often
forgotten by both the industry and academia, adventure games have
had (and continue to have) a surprisingly wide influence on
contemporary games, in categories including walking simulators,
hidden object games, visual novels, and bestselling titles from
companies like Telltale and Campo Santo. In this examination of
heirs to the genre's legacy, the authors examine the genre from
multiple perspectives, connecting technical analysis with critical
commentary and social context. This will be the first book to
consider this important genre from a comprehensive and
transdisciplinary perspective. Drawing upon methods from platform
studies, software studies, media studies, and literary studies,
they reveal the genre's ludic and narrative origins and patterns,
where character (and the player's embodiment of a character) is
essential to the experience of play and the choices within a game.
A deep structural analysis of adventure games also uncovers an
unsteady balance between sometimes contradictory elements of story,
exploration, and puzzles: with different games and creators
employing a multitude of different solutions to resolving this
tension.
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