This book describes the latest advances in the theory of mean field games, which are optimal control problems with a continuum of players, each of them interacting with the whole statistical distribution of a population. While it originated in economics, this theory now has applications in areas as diverse as mathematical finance, crowd phenomena, epidemiology, and cybersecurity. Because mean field games concern the interactions of infinitely many players in an optimal control framework, one expects them to appear as the limit for Nash equilibria of differential games with finitely many players as the number of players tends to infinity. This book rigorously establishes this convergence, which has been an open problem until now. The limit of the system associated with differential games with finitely many players is described by the so-called master equation, a nonlocal transport equation in the space of measures. After defining a suitable notion of differentiability in the space of measures, the authors provide a complete self-contained analysis of the master equation. Their analysis includes the case of common noise problems in which all the players are affected by a common Brownian motion. They then go on to explain how to use the master equation to prove the mean field limit. This groundbreaking book presents two important new results in mean field games that contribute to a unified theoretical framework for this exciting and fast-developing area of mathematics.

Optimization is one of the most important areas of modern applied mathematics, with applications in fields from engineering and economics to finance, statistics, management science, and medicine. While many books have addressed its various aspects, "Nonlinear Optimization" is the first comprehensive treatment that will allow graduate students and researchers to understand its modern ideas, principles, and methods within a reasonable time, but without sacrificing mathematical precision. Andrzej Ruszczynski, a leading expert in the optimization of nonlinear stochastic systems, integrates the theory and the methods of nonlinear optimization in a unified, clear, and mathematically rigorous fashion, with detailed and easy-to-follow proofs illustrated by numerous examples and figures.

The book covers convex analysis, the theory of optimality conditions, duality theory, and numerical methods for solving unconstrained and constrained optimization problems. It addresses not only classical material but also modern topics such as optimality conditions and numerical methods for problems involving nondifferentiable functions, semidefinite programming, metric regularity and stability theory of set-constrained systems, and sensitivity analysis of optimization problems.

Based on a decade's worth of notes the author compiled in successfully teaching the subject, this book will help readers to understand the mathematical foundations of the modern theory and methods of nonlinear optimization and to analyze new problems, develop optimality theory for them, and choose or construct numerical solution methods. It is a must for anyone seriously interested in optimization.

Information is a central concept in economics, and The Knowledge We Have Lost in Information explores its treatment in modern economics. The study of information, far from offering enlightenment, resulted in all matter of confusion for economists and the public. Philip Mirowski and Edward Nik-Khah argue that the conventional wisdom suggesting "economic rationality" was the core of modern economics is incomplete. In this trenchant investigation, they demonstrate that the history of modern microeconomics is better organized as a history of the treatment of information. The book begins with a brief primer on information, and then shows how economists have responded over time to successive developments on the concept of information in the natural sciences. Mirowski and Nik-Khah detail various intellectual battles that were fought to define, analyze, and employ information in economics. As these debates developed, economists progressively moved away from pure agent conscious self-awareness as a non-negotiable desideratum of economic models toward a focus on markets and their design as information processors. This has led to a number of policies, foremost among them: auction design of resources like the electromagnetic spectrum crucial to modern communications. The Knowledge We Have Lost in Information provides insight into the interface between disputes within the economics discipline and the increasing role of information in contemporary society. Mirowski and Nik-Shah examine how this intersection contributed to the dominance of neoliberal approaches to economics, politics, and other realms.

This book introduces one of the most powerful tools of modern economics to a wide audience: those who will later construct or consume game-theoretic models. Robert Gibbons addresses scholars in applied fields within economics who want a serious and thorough discussion of game theory but who may have found other works overly abstract. Gibbons emphasizes the economic applications of the theory at least as much as the pure theory itself; formal arguments about abstract games play a minor role. The applications illustrate the process of model building--of translating an informal description of a multi-person decision situation into a formal game-theoretic problem to be analyzed. Also, the variety of applications shows that similar issues arise in different areas of economics, and that the same game-theoretic tools can be applied in each setting. In order to emphasize the broad potential scope of the theory, conventional applications from industrial organization have been largely replaced by applications from labor, macro, and other applied fields in economics. The book covers four classes of games, and four corresponding notions of equilibrium: static games of complete information and Nash equilibrium, dynamic games of complete information and subgame-perfect Nash equilibrium, static games of incomplete information and Bayesian Nash equilibrium, and dynamic games of incomplete information and perfect Bayesian equilibrium.

The Great War is an immense, confusing and overwhelming historical conflict - the ideal case study for teaching game theory and international relations. Using thirteen historical puzzles, from the outbreak of the war and the stability of attrition, to unrestricted submarine warfare and American entry into the war, this book provides students with a rigorous yet accessible training in game theory. Each chapter shows, through guided exercises, how game theoretical models can explain otherwise challenging strategic puzzles, shedding light on the role of individual leaders in world politics, cooperation between coalitions partners, the effectiveness of international law, the termination of conflict, and the challenges of making peace. Its analytical history of World War I also surveys cutting edge political science research on international relations and the causes of war. Written by a leading game theorist known for his expertise of the war, this textbook includes useful student features such as chapter key terms, contemporary maps, a timeline of events, a list of key characters and additional end-of-chapter game-theoretic exercises.

When John Nash won the Nobel prize in economics in 1994, many people were surprised to learn that he was alive and well. Since then, Sylvia Nasar's celebrated biography "A Beautiful Mind," the basis of a new major motion picture, has revealed the man. "The Essential John Nash" reveals his work--in his own words. This book presents, for the first time, the full range of Nash's diverse contributions not only to game theory, for which he received the Nobel, but to pure mathematics--from Riemannian geometry and partial differential equations--in which he commands even greater acclaim among academics. Included are nine of Nash's most influential papers, most of them written over the decade beginning in 1949.

From 1959 until his astonishing remission three decades later, the man behind the concepts "Nash equilibrium" and "Nash bargaining"--concepts that today pervade not only economics but nuclear strategy and contract talks in major league sports--had lived in the shadow of a condition diagnosed as paranoid schizophrenia. In the introduction to this book, Nasar recounts how Nash had, by the age of thirty, gone from being a wunderkind at Princeton and a rising mathematical star at MIT to the depths of mental illness.

In his preface, Harold Kuhn offers personal insights on his longtime friend and colleague; and in introductions to several of Nash's papers, he provides scholarly context. In an afterword, Nash describes his current work, and he discusses an error in one of his papers. A photo essay chronicles Nash's career from his student days in Princeton to the present. Also included are Nash's Nobel citation and autobiography.

"The Essential John Nash" makes it plain why one of Nash's colleagues termed his style of intellectual inquiry as "like lightning striking." All those inspired by Nash's dazzling ideas will welcome this unprecedented opportunity to trace these ideas back to the exceptional mind they came from.

Born of a belief that economic insights should not require much mathematical sophistication, this book proposes novel and parsimonious methods to incorporate ignorance and uncertainty into economic modeling, without complex mathematics. Economics has made great strides over the past several decades in modeling agents' decisions when they are incompletely informed, but many economists believe that there are aspects of these models that are less than satisfactory. Among the concerns are that ignorance is not captured well in most models, that agents' presumed cognitive ability is implausible, and that derived optimal behavior is sometimes driven by the fine details of the model rather than the underlying economics. Compte and Postlewaite lay out a tractable way to address these concerns, and to incorporate plausible limitations on agents' sophistication. A central aspect of the proposed methodology is to restrict the strategies assumed available to agents.

This innovative textbook makes the tools and applications of game theory and strategic reasoning both fascinating and easy to understand. Each chapter focuses a specific strategic situation as a way of introducing core concepts informally at first, then more fully, with a minimum of mathematics. At the heart of the book is a diverse collection of strategic scenarios, not only from business and politics, but from history, fiction, sports, and everyday life as well. With this approach, students don't just learn clever answers to puzzles, but instead acquire genuine insights into human behaviour. Written for major courses in economics, business, political science, and international relations, this textbook is accessible to students across the undergraduate spectrum.

When should you adopt an aggressive business strategy? How do we make decisions when we don't have all the information? What makes international environmental cooperation possible? Game theory is the study of how we make a decision when the outcome of our moves depends on the decisions of someone else. Economists Ivan and Tuvana Pastine explain why, in these situations, we sometimes cooperate, sometimes clash, and sometimes act in a way that seems completely random. Stylishly brought to life by award-winning cartoonist Tom Humberstone, Game Theory will help readers understand behaviour in everything from our social lives to business, global politics to evolutionary biology. It provides a thrilling new perspective on the world we live in.

How to Divide When There Isn't Enough develops a rigorous yet accessible presentation of the state-of-the-art for the adjudication of conflicting claims and the theory of taxation. It covers all aspects one may wish to know about claims problems: the most important rules, the most important axioms, and how these two sets are related. More generally, it also serves as an introduction to the modern theory of economic design, which in the last twenty years has revolutionized many areas of economics, generating a wide range of applicable allocations rules that have improved people's lives in many ways. In developing the theory, the book employs a variety of techniques that will appeal to both experts and non-experts. Compiling decades of research into a single framework, William Thomson provides numerous applications that will open a large number of avenues for future research.

The world's best negotiators have moved beyond the conventional wisdom by utilising cutting-edge studies and real-world results. It's time you did too. For over twenty years, David Sally has been teaching the art of negotiation at leading business schools and to executives at top companies. Now, using insights from social psychology and game theory, he delivers the proven, clear, actionable advice you need to stay one step ahead. By studying great examples, from Machiavelli to Wall Street, Xi Jinping and Barack Obama, he explores how the game's masters navigate the field strategically, craftily, even emotionally. The best know every negotiation is different and that your tactics are, in part, determined by your opponent. One Step Ahead will make sure that you have what it takes to come out on top, no matter who you are facing across the table.

It is widely held that Bayesian decision theory is the final word on how a rational person should make decisions. However, Leonard Savage--the inventor of Bayesian decision theory--argued that it would be ridiculous to use his theory outside the kind of small world in which it is always possible to "look before you leap." If taken seriously, this view makes Bayesian decision theory inappropriate for the large worlds of scientific discovery and macroeconomic enterprise. When is it correct to use Bayesian decision theory--and when does it need to be modified? Using a minimum of mathematics, "Rational Decisions" clearly explains the foundations of Bayesian decision theory and shows why Savage restricted the theory's application to small worlds.

The book is a wide-ranging exploration of standard theories of choice and belief under risk and uncertainty. Ken Binmore discusses the various philosophical attitudes related to the nature of probability and offers resolutions to paradoxes believed to hinder further progress. In arguing that the Bayesian approach to knowledge is inadequate in a large world, Binmore proposes an extension to Bayesian decision theory--allowing the idea of a mixed strategy in game theory to be expanded to a larger set of what Binmore refers to as "muddled" strategies.

Written by one of the world's leading game theorists, "Rational Decisions" is the touchstone for anyone needing a concise, accessible, and expert view on Bayesian decision making.

This book provides a timely overview of fuzzy graph theory, laying the foundation for future applications in a broad range of areas. It introduces readers to fundamental theories, such as Craine's work on fuzzy interval graphs, fuzzy analogs of Marczewski's theorem, and the Gilmore and Hoffman characterization. It also introduces them to the Fulkerson and Gross characterization and Menger's theorem, the applications of which will be discussed in a forthcoming book by the same authors. This book also discusses in detail important concepts such as connectivity, distance and saturation in fuzzy graphs. Thanks to the good balance between the basics of fuzzy graph theory and new findings obtained by the authors, the book offers an excellent reference guide for advanced undergraduate and graduate students in mathematics, engineering and computer science, and an inspiring read for all researchers interested in new developments in fuzzy logic and applied mathematics.

Was hat Hamlet falsch gemacht? In diesem Buch lernen Sie Instrumente kennen, mit denen Sie dieser Frage systematisch nachgehen koennen - die Ihnen helfen, Entscheidungssituationen zu durchdenken, die sich durch Konflikte und Koordinationsprobleme auszeichnen. Mit Hilfe spieltheoretischer Konzepte und Ansatze werden Sie Ihre Antwort darauf finden, was Hamlet falsch gemacht hat, warum der Kalte Krieg "kalt" blieb und warum Michelin seinen Eintritt in den US-Markt besser vermieden hatte. Die Spieltheorie ist aus der heutigen OEkonomik nicht mehr wegzudenken. Auch in der Politikwissenschaft, Soziologie und Philosophie findet sich inzwischen ein breites Band sehr unterschiedlicher Anwendungen. Diese Einfuhrung in die Spieltheorie liefert die theoretischen Grundlagen und schult beim Leser die spieltheoretische Argumentationsweise. Fur die vorliegende 8. Auflage wurden grosse Teile der Kapitel 1 bis 4 grundlich uberarbeitet und erganzt. Das neue Kapitel 9 bietet unterhaltsame Einblicke in die spannende (Vor-)Geschichte der Spieltheorie. Eine gut lesbare Einfuhrung!

This book is a spectacular introduction to the modern mathematical discipline known as the Theory of Games. Harold Kuhn first presented these lectures at Princeton University in 1952. They succinctly convey the essence of the theory, in part through the prism of the most exciting developments at its frontiers half a century ago. Kuhn devotes considerable space to topics that, while not strictly the subject matter of game theory, are firmly bound to it. These are taken mainly from the geometry of convex sets and the theory of probability distributions.

The book opens by addressing "matrix games," a name first introduced in these lectures as an abbreviation for two-person, zero-sum games in normal form with a finite number of pure strategies. It continues with a treatment of games in extensive form, using a model introduced by the author in 1950 that quickly supplanted von Neumann and Morgenstern's cumbersome approach. A final section deals with games that have an infinite number of pure strategies for the two players.

Throughout, the theory is generously illustrated with examples, and exercises test the reader's understanding. A historical note caps off each chapter. For readers familiar with the calculus and with elementary matrix theory or vector analysis, this book offers an indispensable store of vital insights on a subject whose importance has only grown with the years.

Focusing on recent advances in option pricing under the SABR model, this book shows how to price options under this model in an arbitrage-free, theoretically consistent manner. It extends SABR to a negative rates environment, and shows how to generalize it to a similar model with additional degrees of freedom, allowing simultaneous model calibration to swaptions and CMSs. Since the SABR model is used on practically every trading floor to construct interest rate options volatility cubes in an arbitrage-free manner, a careful treatment of it is extremely important. The book will be of interest to experienced industry practitioners, as well as to students and professors in academia. Aimed mainly at financial industry practitioners (for example quants and former physicists) this book will also be interesting to mathematicians who seek intuition in the mathematical finance.

In diesem Buch finden Studierende aller wirtschaftswissenschaftlichen Studiengange eine verstandliche Einfuhrung in die fur sie relevanten mathematischen Methoden. Der Text ist in drei Teile gegliedert: Grundlagen Lineare Algebra mit den Schwerpunkten lineare Gleichungssysteme und lineare Optimierung Analysis mit den Schwerpunkten Finanzmathematik und Differentialrechnung Neben einer praxisnahen Motivation der Inhalte bietet das Buch auch zahlreiche Beispiele und UEbungen mit Loesungen. Ausserdem wird die klassische Anwendung der mathematischen Verfahren durch die Anwendung des Open-Source-Programms Scilab erganzt und veranschaulicht. Die einzelnen Schritte dazu sind im Text beschrieben, was einen leichten Zugang zu dem Programm ermoeglicht. Die 4. uberarbeitete und erganzte Auflage ist nun um einen Abschnitt uber ganzzahlige lineare Optimierung erganzt.

This monograph develops a method of creating convenient coordinate systems for game theory that will allow readers to more easily understand, analyze, and create games at various levels of complexity. By identifying the unique characterization of games that separates the individual's strategic interests from the group's collective behavior, the authors construct a single analytical methodology that readers will be able to apply to a wide variety of games. With its emphasis on practicality and approachability, readers will find this book an invaluable tool, and a viable alternative to the ad hoc analytical approach that has become customary for researchers utilizing game theory. The introductory chapters serve two important purposes: they review several games of fundamental importance, and also introduce a dynamic that is inherent in games, but has gone unexplored until now. After this has been established, readers will advance from simple 2 x 2 games to games with more player strategies and dynamics. For interested readers, a rigorous treatment of the underlying mathematics is conveniently gathered at the end of the book. Additional topics of interest, such as extensive form and coalitional games, are presented to help readers visualize more complex settings that will be vital in aiding the understanding of advanced topics, such as coalition-free Nash points, multi-player repeated games, and more. Coordinate Systems for Games is ideal for a wide variety of researchers interested in game theory, including social scientists, economists, mathematicians, computer scientists, and more. The authors' approachable style also makes this accessible to an audience at any scale of experience, from beginning non-specialists to more practiced researchers.

The newest addition to our Influential Video Game Designers series explores the work of Todd Howard, executive producer at Bethesda Studios, known for how he consistently pushes the boundaries of open-world gaming and player agency. Howard’s games create worlds in which players can design their own characters and tell their own stories. While many games tell the story of the game’s main character, Todd Howard’s worldbuilding approach to game design focuses more on telling the story of the game’s world, whether it be the high fantasy environments of the Elder Scrolls series or the post-apocalyptic wasteland of the Fallout series. This focus on sculpting the world allows for remarkable amounts of player freedom and choice in an expansive game environment by creating a landscape rich with open opportunity. Drawing on both academic discussions of narrative, world design, and game design, as well as on officially released interviews, speeches, and presentations given by Howard and other designers at Bethesda Games, Wendi Sierra highlights three core areas set Howard’s design perspective apart from other designers: micronarratives, iterative design, and the sharing of design tools. Taken as a whole, these three elements demonstrate how Howard has used a worldbuilding perspective to shape his games. In doing so, he has impacted not only Bethesda Studios, but also the landscape of game design itself.

Sebastian Rhein untersucht den bilateralen Dialog zwischen Unternehmen und internationalen zivilgesellschaftlichen Organisationen (ZGOs). Ausgehend davon, dass Stakeholder-Dialoge ein wichtiges Instrument fur die Strategieentwicklung und Nachhaltigkeit von Unternehmen sind, untersucht er empirisch die institutionellen Bedingungen dieser Dialoge aus Sicht der ZGOs. Dabei wertet der Autor funf Interviews mit der quantitativen Methode GABEK (R) aus und diskutiert bestehende Konflikte und Regeln innerhalb dieser Dialoge. Mithilfe der ordonomischen Wirtschaftsethik leitet er Handlungsempfehlungen ab und zeigt, wie Interessenskonflikte uberwunden und durch individuelle und kollektive Selbstbindungen Win-Win-Situationen erreicht werden koennen.

Praktische Anwendung und wissenschaftliche Analyse in den Wirtschaftswissenschaften basieren zunehmend auf dem Einsatz empirischer Methoden. Dieses Buch fuhrt Studierende der Wirtschaftswissenschaften und benachbarter Facher in die wichtigsten Methoden der angewandten Wirtschaftsforschung einschliesslich der OEkonometrie ein. Inhaltlich umfasst das Buch die Bereiche Daten (Grundlage und Aufbereitung), Wirtschaftsindikatoren, Input-Output-Analyse, oekonometrische Verfahren, Trend- und Saisonbereinigung sowie Simulation und Prognose. Dabei wird stets ein enger Bezug zu praktischen Anwendungen und ein intuitiver Zugang angestrebt, ohne auf eine formale Darstellung der Methoden zu verzichten. Die Methoden werden gut verstandlich erlautert. Illustrierende Fallbeispiele und der Bezug zu praxisrelevanten Themen machen das Buch besonders anschaulich und interessant fur den Leser. Die 4. Auflage wurde aktualisiert und in Teilen erganzt.

Mathematics is not, and never will be, an empirical science, but mathematicians are finding that the use of computers and specialized software allows the generation of mathematical insight in the form of conjectures and examples, which pave the way for theorems and their proofs. In this way, the experimental approach to pure mathematics is revolutionizing the way research mathematicians work. As the first of its kind, this book provides material for a one-semester course in experimental mathematics that will give students the tools and training needed to systematically investigate and develop mathematical theory using computer programs written in Maple. Accessible to readers without prior programming experience, and using examples of concrete mathematical problems to illustrate a wide range of techniques, the book gives a thorough introduction to the field of experimental mathematics, which will prepare students for the challenge posed by open mathematical problems.