Risk has become one of the main topics in fields as diverse as engineering, medicine and economics, and it is also studied by social scientists, psychologists and legal scholars. This Springer Essentials version offers an overview of the in-depth handbook and highlights some of the main points covered in the Handbook of Risk Theory. The topic of risk also leads to more fundamental questions such as: What is risk? What can decision theory contribute to the analysis of risk? What does the human perception of risk mean for society? How should we judge whether a risk is morally acceptable or not? Over the last couple of decades questions like these have attracted interest from philosophers and other scholars into risk theory. This brief offers the essentials of the handbook provides for an overview into key topics in a major new field of research and addresses a wide range of topics, ranging from decision theory, risk perception to ethics and social implications of risk. It aims to promote communication and information among all those who are interested in theoretical issues concerning risk and uncertainty. The Essentials of Risk Theory brings together internationally leading philosophers and scholars from other disciplines who work on risk theory. The contributions are accessibly written and highly relevant to issues that are studied by risk scholars. The Essentials of Risk Theory will be a helpful starting point for all risk scholars who are interested in broadening and deepening their current perspectives.

Predation is an ecological factor of almost universal importance for the biol ogist who aims at an understanding of the habits and structures of animals. Despite its pervasive nature opinions differ as to what predation really is. So far it has been defined only in negative terms; it is thought not to be par asitism, the other great process by which one organism harms another, nor filter-feeding, carrion-eating, or browsing. Accordingly, one could define predation as a process by which an animal spends some effort to locate a live prey and, in addition, spends another effort to mutilate or kill it. Ac cording to this usage of the word a nudibranch, for example, that feeds on hydroids would be a predator inasmuch as it needs some time to locate col onies of its prey which, after being located, scarcely demand more than eating, which differs little from browsing. From the definition just proposed consumption of the prey following its capture has been intentionally omit ted. Indeed, an animal may be disposed of without being eaten. Hence the biological significance of predation may be more than to maintain nutrition al homeostasis. In fact, predation may have something in common with the more direct forms of competition, a facet that will be only cursorily touched upon in this book."

Complementarity theory is a new domain in applied mathematics and is concerned with the study of complementarity problems. These problems represent a wide class of mathematical models related to optimization, game theory, economic engineering, mechanics, fluid mechanics, stochastic optimal control etc. The book is dedicated to the study of nonlinear complementarity problems by topological methods. Audience: Mathematicians, engineers, economists, specialists working in operations research and anybody interested in applied mathematics or in mathematical modeling.

The ?nite-dimensional nonlinear complementarity problem (NCP) is a s- tem of ?nitely many nonlinear inequalities in ?nitely many nonnegative variables along with a special equation that expresses the complementary relationship between the variables and corresponding inequalities. This complementarity condition is the key feature distinguishing the NCP from a general inequality system, lies at the heart of all constrained optimi- tion problems in ?nite dimensions, provides a powerful framework for the modeling of equilibria of many kinds, and exhibits a natural link between smooth and nonsmooth mathematics. The ?nite-dimensional variational inequality (VI), which is a generalization of the NCP, provides a broad unifying setting for the study of optimization and equilibrium problems and serves as the main computational framework for the practical solution of a host of continuum problems in the mathematical sciences. The systematic study of the ?nite-dimensional NCP and VI began in the mid-1960s; in a span of four decades, the subject has developed into a very fruitful discipline in the ?eld of mathematical programming. The - velopments include a rich mathematical theory, a host of e?ective solution algorithms, a multitude of interesting connections to numerous disciplines, and a wide range of important applications in engineering and economics. As a result of their broad associations, the literature of the VI/CP has bene?ted from contributions made by mathematicians (pure, applied, and computational), computer scientists, engineers of many kinds (civil, ch- ical, electrical, mechanical, and systems), and economists of diverse exp- tise (agricultural, computational, energy, ?nancial, and spatial).

During the last decade I have explored the consequences of what I have chosen to call the 'consistent preferences' approach to deductive reasoning in games. To a great extent this work has been done in coop eration with my co-authors Martin Dufwenberg, Andres Perea, and Ylva Sovik, and it has lead to a series of journal articles. This book presents the results of this research program. Since the present format permits a more extensive motivation for and presentation of the analysis, it is my hope that the content will be of interest to a wider audience than the corresponding journal articles can reach. In addition to active researcher in the field, it is intended for graduate students and others that wish to study epistemic conditions for equilibrium and rationalizability concepts in game theory. Structure of the book This book consists of twelve chapters. The main interactions between the chapters are illustrated in Table 0.1. As Table 0.1 indicates, the chapters can be organized into four dif ferent parts. Chapters 1 and 2 motivate the subsequent analysis by introducing the 'consistent preferences' approach, and by presenting ex amples and concepts that are revisited throughout the book. Chapters 3 and 4 present the decision-theoretic framework and the belief operators that are used in later chapters. Chapters 5, 6, 10, and 11 analyze games in the strategic form, while the remaining chapters-Chapters 7, 8, 9, and 12-are concerned with games in the extensive form."

Game Theoretic Risk Analysis of Security Threats introduces reliability and risk analysis in the face of threats by intelligent agents. More specifically, game-theoretic models are developed for identifying optimal and/or equilibrium defense and attack strategies in systems of varying degrees of complexity. The book covers applications to networks, including problems in both telecommunications and transportation. However, the book s primary focus is to integrate game theory and reliability methodologies into a set of techniques to predict, detect, diminish, and stop intentional attacks at targets that vary in complexity.

In this book, Bier and Azaiez highlight work by researchers who combine reliability and risk analysis with game theory methods to create a set of functional tools that can be used to offset intentional, intelligent threats (including the threats of terrorism and war). A comprehensive treatment of such problems must consider two aspects: (1) the structure of the system to be protected; and (2) the adaptive nature of the threat). The book provides a set of tools for applying game theory TO reliability problems in the presence of intentional, intelligent threats. These tools will help to address problems of global security and also facilitate more cost-effective defensive investments.

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STATISTICAL PHYSICS AND ECONOMICS covers systematically and in simple language the physical foundations of evolution equations, stochastic processes, and generalized Master equations applied to complex economic systems. Strong emphasis is placed on concepts, methods, and techniques for modeling, assessment, and solving or estimation of economic problems in an attempt to understand the large variability of financial markets, trading and communication networks, barriers and acceleration of the economic growth as well as the kinetics of product and money flows. The main focus of the book is a clear physical understanding of the self-organizing principles in social and economic systems. This modern introduction will be a useful tool for researchers, engineers, as well as graduate and post-graduate students in econophysics and related topics.

In the case of completely integrable systems, periodic solutions are found by inspection. For nonintegrable systems, such as the three-body problem in celestial mechanics, they are found by perturbation theory: there is a small parameter EURO in the problem, the mass of the perturbing body for instance, and for EURO = 0 the system becomes completely integrable. One then tries to show that its periodic solutions will subsist for EURO -# 0 small enough. Poincare also introduced global methods, relying on the topological properties of the flow, and the fact that it preserves the 2-form L~=l dPi 1\ dqi' The most celebrated result he obtained in this direction is his last geometric theorem, which states that an area-preserving map of the annulus which rotates the inner circle and the outer circle in opposite directions must have two fixed points. And now another ancient theme appear: the least action principle. It states that the periodic solutions of a Hamiltonian system are extremals of a suitable integral over closed curves. In other words, the problem is variational. This fact was known to Fermat, and Maupertuis put it in the Hamiltonian formalism. In spite of its great aesthetic appeal, the least action principle has had little impact in Hamiltonian mechanics. There is, of course, one exception, Emmy Noether's theorem, which relates integrals ofthe motion to symmetries of the equations. But until recently, no periodic solution had ever been found by variational methods.

Since the introduction of electrosurgery the techniques of surgery on the nervous system have passed through further improvements (bipolar coagulation, microscope), even if the procedure was not substantially modified. Today, laser represents a new "discipline," as it offers a new way of performing all basic maneuvers (dissection, demolition, hemostasis, vessel sutures). Furthermore, laser offers the possibility of a special maneuver, namely reduction of the volume of a tumoral mass through vaporization. Its application is not restricted to traditional neurosurgery but extends also to stereotactic and vascular neurosurgery. Laser surgery has also influenced the anesthesiologic techniques. At the same time new instrumentation has been introduced: CUSA ultrasonic aspiration, echotomography, and Doppler flowmeter. I have had the chance to utilize these new technologies all at a time and have come to the conclusion that we are facing the dawn of a new methodology which has already shown its validity and lack of inconveniences, and whose object is to increase the precision of neurological surgery. The technological development is still going on, and some improvements are to be foreseen. Laser scalpel is splitting the initial laser surgery into NO TOUCH and TOUCH surgery with laser. As new instrumentarium will be developed, a variable and tunable beam will become available. For example, in a few years Free Electron Laser will further add to the progress in this field."

Econometric theory, as presented in textbooks and the econometric literature generally, is a somewhat disparate collection of findings. Its essential nature is to be a set of demonstrated results that increase over time, each logically based on a specific set of axioms or assumptions, yet at every moment, rather than a finished work, these inevitably form an incomplete body of knowledge. The practice of econometric theory consists of selecting from, applying, and evaluating this literature, so as to test its applicability and range. The creation, development, and use of computer software has led applied economic research into a new age. This book describes the history of econometric computation from 1950 to the present day, based upon an interactive survey involving the collaboration of the many econometricians who have designed and developed this software. It identifies each of the econometric software packages that are made available to and used by economists and econometricians worldwide.

This work is an exploration of the global market dynamics, their intrinsic natures, common trends and dynamic interlinkages during the stock market crises over the last twelve years. The study isolates different phases of crisis and differentiates between any crisis that remains confined to the region and those that take up a global dimension. The latent structure of the global stock market, the inter-regional and intra-regional stock market dynamics around the crises are analyzed to get a complete picture of the structure of the global stock market. The study further probing into the inherent nature of the global stock market in generating crisis finds the global market to be chaotic thus making the system intrinsically unstable or at best to follow knife-edge stability. The findings have significant bearing at theoretical level and on policy decisions.

This book was originally conceived as a continuation in theme of the collec- tive monograph Limits of Predictability (Yu. A. Kravtsov, Ed. , Springer Series in Synergetics, Vol. 60, Springer-Verlag, Heidelberg, 1993). The main thrust of that book was to examine the various effects and factors (system non- stationarity, measurement noise, predictive model accuracy, and so on) that may limit, in a fundamental fashion, our ability to mathematically predict physical and man-made phenomena and events. Particularly interesting was the diversity of fields from which the papers and examples were drawn, in- cluding climatology, physics, biophysics, cybernetics, synergetics, sociology, and ethnogenesis. Twelve prominant Russian scientists, and one American (Prof. A. J. Lichtman) discussed their philosophical and scientific standpoints on the problem of the limits of predictability in their various fields. During the preparation of that book, the editor (Yu. A. K) had the great pleasure of interacting with world-renowned Russian scientists such as oceanologist A. S. Monin, geophysicist V. I. Keilis-Borok, sociologist I. V. Bestuzhev-Lada, histo- rian L. N. Gumilev, to name a few. Dr. Angela M. Lahee, managing editor of the Synergetics Series at Springer, was enormously helpful in the publishing of that book. In 1992, Prof. H. Haken along with Dr. Lahee kindly supported the idea of publishing a second volume on the theme of nonlinear system predictability, this time with a more international flavor.

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' cannot easily be put into one scientific discipline. On the theoretical side one deals with differential games, difference games (the underlying models are described by differential, respec tively difference equations) and games based on Markov chains, with determin istic and stochastic games, zero-sum and nonzero-sum games, two-player and many-player games - all under various forms of equilibria. On the practical side, one sees applications to economics (stimulated by the recent Nobel prize for economics which went to three prominent scientists in game theory), biology, management science, and engineering. The contents of this volume are primarily based on selected presentations made at the Sixth International Symposium on Dynamic Games and Applica tions, held in St Jovite, Quebec, Canada, 13-15 July 1994. Every paper that appears in this volume has passed through a stringent reviewing process, as is the case with publications for archival technical journals. This conference, as well as its predecessor which was held in Grimentz, 1992, took place under the auspices of the International Society of Dynamic Games (ISDG), established in 1990. One of the activities of the ISDG is the publication of these Annals. The contributions in this volume have been grouped around five themes."

There are problems to whose solution I would attach an infinitely greater import ancf than to those of mathematics, for example touching ethics, or our relation to God, or conceming our destiny and our future; but their solution lies wholly beyond us and completely outside the province 0 f science. J. F. C. Gauss For a1l his prescience in matters physical and mathematieal, the great Gauss apparently did not foresee one development peculiar to OUT own time. The development I have in mind is the use of mathematical reasoning - in partieu lar the axiomatic method - to explicate alternative concepts of rationality and morality. The present bipartite collection of essays (Vol. 11, Nos. 2 and 3 of this journal) is entitled 'Game Theory, Social Choiee, and Ethics'. The eight papers represent state-of-the-art research in formal moral theory. Their intended aim is to demonstrate how the methods of game theory, decision theory, and axiomatic social choice theory can help to illuminate ethical questions central not only to moral theory, but also to normative public policy analysis. Before discussion of the contents of the papers, it should prove helpful to recall a number of pioneering papers that appeared during the decade of the 1950s. These papers contained aseries of mathematical and conceptual break through which laid the basis for much of today's research in formal moral theory. The papers deal with two somewhat distinct topics: the concept of individual and collective rationality, and the concept of social justiee."

In everyday life we must often reach decisions while knowing that the outcome will not only depend on our own choice, but also on the choices of others. These situations are the focus of epistemic game theory. Unlike classical game theory, it explores how people may reason about their opponents before they make their final choice in a game. Packed with examples and practical problems based on stories from everyday life, this is the first textbook to explain the principles of epistemic game theory. Each chapter is dedicated to one particular, natural way of reasoning. The book then shows how each of these ways of reasoning will affect the final choices that can rationally be made and how these choices can be found by iterative procedures. Moreover, it does so in a way that uses elementary mathematics and does not presuppose any previous knowledge of game theory.

Our objectives may be briefly stated. They are two. First, we have sought to provide a compact and digestible exposition of some sub-branches of mathematics which are of interest to economists but which are underplayed in mathematical texts and dispersed in the journal literature. Second, we have sought to demonstrate the usefulness of the mathematics by providing a systematic account of modern neoclassical economics, that is, of those parts of economics from which jointness in production has been excluded. The book is introductory not in the sense that it can be read by any high-school graduate but in the sense that it provides some of the mathematics needed to appreciate modern general-equilibrium economic theory. It is aimed primarily at first-year graduate students and final-year honors students in economics who have studied mathematics at the university level for two years and who, in particular, have mastered a full-year course in analysis and calculus. The book is the outcome of a long correspondence punctuated by periodic visits by Kimura to the University of New South Wales. Without those visits we would never have finished. They were made possible by generous grants from the Leverhulme Foundation, Nagoya City University, and the University of New South Wales. Equally indispensible were the expert advice and generous encouragement of our friends Martin Beckmann, Takashi Negishi, Ryuzo Sato, and Yasuo Uekawa.

This volume records the proceedings of the 22nd Annual International Con ference of the International Simulation and Gaming Association (ISAGA), 15-19 July, 1991, Kyoto, Japan, sponsored by the Science Council of Japan and the Japanese Association of Simulation and Gaming (JASAG). The con ference theme was Global Modeling for Solving Global Problems. The first 2 days of the conference were held in the magnificent Kyoto International Conference Hall; the 3rd day was spent admiring the floats of the famous Gion Festival in the exquisite city of Kyoto and the Daibutsu (or Great Buddha) of the Todaiji Temple in Nara and visiting one of the Sharp factories. During the last 2 days of the conference we were made most welcome in the Faculty of International Relations of Ritsumeikan University. The day after the conference, a number of delegates went to Hiroshima (the Peace Memorial Hall, Museum and Park) and also to one of Japan's "Scenic Trio," the island of Miyajima with its breathtaking views and the Itsukushima Shrine. The conference was attended by some 400 delegates from over 30 different countries. Over 100 sessions, both theoretical and practical, were given: keynote speeches, round-table discussions, workshops, papers. This volume reflects most of those sessions, in the form of either a full paper or a short abstract."

This handbook provides an in-depth examination of important theoretical methods and procedures in applied analysis. It details many of the most important theoretical trends in nonlinear analysis and applications to different fields. These features make the volume a valuable tool for every researcher working on nonlinear analysis.

Distributed Decision Making and Control is a mathematical treatment of relevant problems in distributed control, decision and multiagent systems, The research reported was prompted by the recent rapid development in large-scale networked and embedded systems and communications. One of the main reasons for the growing complexity in such systems is the dynamics introduced by computation and communication delays. Reliability, predictability, and efficient utilization of processing power and network resources are central issues and the new theory and design methods presented here are needed to analyze and optimize the complex interactions that arise between controllers, plants and networks. The text also helps to meet requirements arising from industrial practice for a more systematic approach to the design of distributed control structures and corresponding information interfaces Theory for coordination of many different control units is closely related to economics and game theory network uses being dictated by congestion-based pricing of a given pathway. The text extends existing methods which represent pricing mechanisms as Lagrange multipliers to distributed optimization in a dynamic setting. In Distributed Decision Making and Control, the main theme is distributed decision making and control with contributions to a general theory and methodology for control of complex engineering systems in engineering, economics and logistics. This includes scalable methods and tools for modeling, analysis and control synthesis, as well as reliable implementations using networked embedded systems. Academic researchers and graduate students in control science, system theory, and mathematical economics and logistics will find mcu to interest them in this collection, first presented orally by the contributors during a sequence of workshops organized in Spring 2010 by the Lund Center for Control of Complex Engineering Systems, a Linnaeus Center at Lund University, Sweden.>

This book provides a game theoretic model of interaction among VoIP telecommunications providers regarding their willingness to enter peering agreements with one another. The author shows that the incentive to peer is generally based on savings from otherwise payable long distance fees. At the same time, termination fees can have a countering and dominant effect, resulting in an environment in which VoIP firms decide against peering. Various scenarios of peering and rules for allocation of the savings are considered. The first part covers the relevant aspects of game theory and network theory, trying to give an overview of the concepts required in the subsequent application. The second part of the book introduces first a model of how the savings from peering can be calculated and then turns to the actual formation of peering relationships between VoIP firms. The conditions under which firms are willing to peer are then described, considering the possible influence of a regulatory body.

Birkhauser Boston, Inc., will publish a series of carefully selected mono graphs in the area of mathematical modeling to present serious applications of mathematics for both the undergraduate and the professional audience. Some of the monographs to be selected and published will appeal more to the professional mathematician and user of mathematics, serving to familiarize the user with new models and new methods. Some, like the present monograph, will stress the educational aspect and will appeal more to a student audience, either as a textbook or as additional reading. We feel that this first volume in the series may in itself serve as a model for our program. Samuel Goldberg attaches a high priority to teaching stu dents the art of modeling, that is, to use his words, the art of constructing useful mathematical models of real-world phenomena. We concur. It is our strong conviction as editors that the connection between the actual problems and their mathematical models must be factually plausible, if not actually real. As this first volume in the new series goes to press, we invite its readers to share with us both their criticisms and their constructive suggestions."

Many boundary value problems are equivalent to Au=O (1) where A: X ---+ Y is a mapping between two Banach spaces. When the problem is variational, there exists a differentiable functional 0 and e E X such that lIell > rand inf"

Since the first Congress in Zurich in 1897, the ICM has been an eagerly awaited event every four years. Many of these occasions are celebrated for historie developments and seminal contributions to mathematics. 2002 marks the year of the 24th ICM, the first of the new millennium. Also historie is the first ICM Satellite Conference devoted to game theory and applications. It is one of those rare occasions, in which masters of the field are able to meet under congenial surroundings to talk and share their gathered wisdom. As is usually the case in ICM meetings, participants of the ICM Satellite Conference on Game Theory and Applications (Qingdao, August 2(02) hailed from the four corners of the world. In addition to presentations of high qual ity research, the program also included twelve invited plenary sessions with distinguished speakers. This volume, which gathers together selected papers read at the conference, is divided into four sections: (I) Foundations, Concepts, and Structure. (II) Equilibrium Properties. (III) Applications to the Natural and Social Sciences. (IV) Computational Aspects of Games."

The ?nite-dimensional nonlinear complementarity problem (NCP) is a s- tem of ?nitely many nonlinear inequalities in ?nitely many nonnegative variables along with a special equation that expresses the complementary relationship between the variables and corresponding inequalities. This complementarity condition is the key feature distinguishing the NCP from a general inequality system, lies at the heart of all constrained optimi- tion problems in ?nite dimensions, provides a powerful framework for the modeling of equilibria of many kinds, and exhibits a natural link between smooth and nonsmooth mathematics. The ?nite-dimensional variational inequality (VI), which is a generalization of the NCP, provides a broad unifying setting for the study of optimization and equilibrium problems and serves as the main computational framework for the practical solution of a host of continuum problems in the mathematical sciences. The systematic study of the ?nite-dimensional NCP and VI began in the mid-1960s; in a span of four decades, the subject has developed into a very fruitful discipline in the ?eld of mathematical programming. The - velopments include a rich mathematical theory, a host of e?ective solution algorithms, a multitude of interesting connections to numerous disciplines, and a wide range of important applications in engineering and economics. As a result of their broad associations, the literature of the VI/CP has bene?ted from contributions made by mathematicians (pure, applied, and computational), computer scientists, engineers of many kinds (civil, ch- ical, electrical, mechanical, and systems), and economists of diverse exp- tise (agricultural, computational, energy, ?nancial, and spatial).

This book constitutes the refereed proceedings of the 18th International Symposium Fundamentals of Computation Theory, FCT 2011, held in Oslo, Norway, in August 2011. The 28 revised full papers presented were carefully reviewed and selected from 78 submissions. FCT 2011 focused on algorithms, formal methods, and emerging fields, such as ad hoc, dynamic and evolving systems; algorithmic game theory; computational biology; foundations of cloud computing and ubiquitous systems; and quantum computation.