The book compiles research on Condorcet's Paradox over some two centuries. It begins with a historical overview of the discovery of Condorcet's Paradox in the 18th Century, reviews numerous studies conducted to find actual occurrences of the paradox, and compiles research that has been done to develop mathematical representations for the probability that the paradox will be observed. Combines all approaches that have been used to study this very interesting phenomenon.

Efficiency and Equity of Climate Change Policy is a comprehensive assessment of the economic effects of climate change policy, addressing the issues with a quantitative modelling approach. The book thus goes beyond the usual statements on the efficiency of economic instruments to identify the way gains and losses are distributed; who gains and who loses. Both the costs and benefits of climate change policies are analyzed. Most papers also provide useful information on the economic features of the Kyoto Protocol, its possible extensions, and the effect of different implementation strategies (such as the debate on emissions trading ceilings). Readership: Scientists and policy makers, students and specialists in climate related industries, members of NGOs, and policy advisors.

Social computing concerns the study of social behavior and context based on computational systems. Behavioral modeling reproduces the social behavior, and allows for experimenting with and deep understanding of behavior, patterns, and potential outcomes. The pervasive use of computer and Internet technologies provides an unprecedented environment where people can share opinions and experiences, offer suggestions and advice, debate, and even conduct experiments. Social computing facilitates behavioral modeling in model building, analysis, pattern mining, anticipation, and prediction. The proceedings from this interdisciplinary workshop provide a platform for researchers, practitioners, and graduate students from sociology, behavioral and computer science, psychology, cultural study, information systems, and operations research to share results and develop new concepts and methodologies aimed at advancing and deepening our understanding of social and behavioral computing to aid critical decision making.

Linear programming attracted the interest of mathematicians during and after World War II when the first computers were constructed and methods for solving large linear programming problems were sought in connection with specific practical problems for example, providing logistical support for the U.S. Armed Forces or modeling national economies. Early attempts to apply linear programming methods to solve practical problems failed to satisfy expectations. There were various reasons for the failure. One of them, which is the central topic of this book, was the inexactness of the data used to create the models. This phenomenon, inherent in most pratical problems, has been dealt with in several ways. At first, linear programming models used "average" values of inherently vague coefficients, but the optimal solutions of these models were not always optimal for the original problem itself. Later researchers developed the stochastic linear programming approach, but this too has its limitations. Recently, interest has been given to linear programming problems with data given as intervals, convex sets and/or fuzzy sets. The individual results of these studies have been promising, but the literature has not presented a unified theory. Linear Optimization Problems with Inexact Data attempts to present a comprehensive treatment of linear optimization with inexact data, summarizing existing results and presenting new ones within a unifying framework."

Over the past decade, rational agency has come to be recognised as a central theme in artificial intelligence. Drawing upon research on rational action and agency in philosophy, logic, game theory, decision theory, and the philosophy of language, this volume represents an advanced, comprehensive state-of-the-art survey of the field of rational agency as it stands today. It covers the philosophical foundations of rational agency, logical and decision-theoretic approaches to rational agency, multi-agent aspects of rational agency (including speech acts, joint plans, and cooperation protocols), and, finally, describes a number of approaches to programming rational agents. Although written from the standpoint of artificial intelligence, this interdisciplinary text will be of interest to researchers in logic, mainstream computer science, the philosophy of rational action and agency, and economics.

This Report contains a Consensus Report and the papers submitted to the April 6 -10, 1995 NATO Advanced Research Workshop on Strategic Stability In The Post-Cold War World And The Future Of Nuclear Disarmament, held in Washington D. C., United States Of America of at The Airlie Conference Center. The workshop was sponsored by the NATO Division Scientific and Environmental Affairs as part of its ongoing outreach programme to widen and deepen scientific contacts between NATO member countries and the Cooperation Partner countries of the former Warsaw Treaty Organization. The participants recognize that the collapse of the former Soviet Union has left a conceptual vacuum in the definition of a new world order. Never before have the components of world order all changed so rapidly, so deeply, or so globally. As Henry Kissinger points out, the emergence of the new world order will have answered three fundamental questions: " What are the basic units of the international order? What are their means of interacting? and What are the goals on behalf of which they interact? " The main question is whether the establishment and maintenance of an international system will turn out to be a conscious design, or the outgrowth of a test of strength. The concept of a planning framework that could shape or govern these interactions is emerging and may now be at hand. Capturing this emerging framework is the thrust of this NATO-sponsored Advanced Research Workshop.

This book consists of five acts and two interludes, which are all written as dialogues between three main characters and other supporting characters. Each act discusses the epistemological, institutional and methodological foundations of game theory and economics, while using various stories and examples. A featured aspect of those discussions is that many forms of mutual misunderstanding are involved in social situations as well as in those fields themselves. One Japanese traditional comic story called the Konnyaku Mondo is representative and gives hints of how our thought is constrained by incorrect beliefs. Each dialogue critically examines extant theories and common misunderstanding in game theory and economics in order to find possible future developments of those fields.

In many industries the tariffs are not strictly proportional to the quantity purchased, i. e, they are nonlinear. Examples of nonlinear tariffs include railroad and electricity schedules and rental rates for durable goods and space. The major justification for the nonlinear pricing is the existence of private information on the side of consumers. In the early papers on the subject, private information was captured either by assuming a finite number of types (e. g. Adams and Yellen, 1976) or by a unidimensional continuum of types (Mussa and Rosen, 1978). Economics of the unidimen sional problems is by now well understood. The unidimensional models, however, do not cover all the situations of practical interest. Indeed, often the nonlinear tariffs specify the payment as a function of a variety of characteristics. For example, railroad tariffs spec ify charges based on weight, volume, and distance of each shipment. Dif ferent customers may value each of these characteristics differently, hence the customer's type will not in general be captured by a unidimensional characteristic and a problem of multidimensional screening arises. In such models the consumer's private information (her type) is captured by an m-dimensional vector, while the good produced by the monopolist has n quality dimensions."

This text examines new research at the interface of operations research, behavioral and cognitive sciences, and decision analysis. From the cognitive behaviorist who collects empirical evidence as to how people make decisions to the engineer and economist who are the consumers of such understanding, the reader encounters the familiar Traveling Salesman Problem and Prisoner's dilemma, how agricultural decisions are made in Argentina's Pampas region, and some social goals that come into play as an element of rational decision-making.

In these 14 self-contained chapters, broad topics covered include the integration of decision analysis and behavioral models, innovations in behavioral models, exploring descriptive behavior models, and experimental studies.

In this book, different quantitative approaches to the study of electoral systems have been developed: game-theoretic, decision-theoretic, statistical, probabilistic, combinatorial, geometric, and optimization ones. All the authors are prominent scholars from these disciplines. Quantitative approaches offer a powerful tool to detect inconsistencies or poor performance in actual systems. Applications to concrete settings such as EU, American Congress, regional, and committee voting are discussed.

This work systematically investigates a large number of oscillatory network configurations that are able to describe many real systems such as electric power grids, lasers or even the heart muscle, to name but a few. The book is conceived as an introduction to the field for graduate students in physics and applied mathematics as well as being a compendium for researchers from any field of application interested in quantitative models.

Agent systems are being used to model complex systems like societies, markets and biological systems. In this book we investigate issues of agent systems related to convergence and interactivity using techniques from agent based modelling to simulate complex systems, and demonstrate that interactivity/exchange and convergence in multi-agent systems are issues that are significantly interrelated.

Topic and features: - Introduces the state of the art in multi-agent systems, with an emphasis on agent-based computational economics. - Sheds light on the fundamental concepts behind the stability of multi-agent systems. - Investigates knowledge exchange among agents, the rationale behind it and its effects on the ecosystem. - Explores how information provided through interaction with the system can be used to optimise its performance. - Describes a pricing strategy for a realistic large-scale distributed system.

This book supplies a comprehensive resource and will be invaluable reading for researchers and postgraduates studying this topic.

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.

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 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.

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."

Due to the ability to handle specific characteristics of economics and finance forecasting problems like e.g. non-linear relationships, behavioral changes, or knowledge-based domain segmentation, we have recently witnessed a phenomenal growth of the application of computational intelligence methodologies in this field.

In this volume, Chen and Wang collected not just works on traditional computational intelligence approaches like fuzzy logic, neural networks, and genetic algorithms, but also examples for more recent technologies like e.g. rough sets, support vector machines, wavelets, or ant algorithms. After an introductory chapter with a structural description of all the methodologies, the subsequent parts describe novel applications of these to typical economics and finance problems like business forecasting, currency crisis discrimination, foreign exchange markets, or stock markets behavior.

After a decade's development, evolutionary computation (EC) proves to be a powerful tool kit for economic analysis. While the demand for this equipment is increasing, there is no volume exclusively written for economists. This volume for the first time helps economists to get a quick grasp on how EC may support their research. A comprehensive coverage of the subject is given, that includes the following three areas: game theory, agent-based economic modelling and financial engineering. Twenty leading scholars from each of these areas contribute a chapter to the volume. The reader will find himself treading the path of the history of this research area, from the fledgling stage to the burgeoning era. The results on games, labour markets, pollution control, institution and productivity, financial markets, trading systems design and derivative pricing, are new and interesting for different target groups. The book also includes informations on web sites, conferences, and computer software.

Graph algorithms are easy to visualize and indeed there already exists a variety of packages to animate the dynamics when solving problems from graph theory. Still it can be difficult to understand the ideas behind the algorithm from the dynamic display alone.

CATBox consists of a software system for animating graph algorithms and a course book which we developed simultaneously. The software system presents both the algorithm and the graph and puts the user always in control of the actual code that is executed. In the course book, intended for readers at advanced undergraduate or graduate level, computer exercises and examples replace the usual static pictures of algorithm dynamics.

For this volume we have chosen solely algorithms for classical problems from combinatorial optimization, such as minimum spanning trees, shortest paths, maximum flows, minimum cost flows, weighted and unweighted matchings both for bipartite and non-bipartite graphs.

Find more information at http: //schliep.org/CATBox/.

Modern option pricing theory was developed in the late sixties and early seventies by F. Black, R. e. Merton and M. Scholes as an analytical tool for pricing and hedging option contracts and over-the-counter warrants. How ever, already in the seminal paper by Black and Scholes, the applicability of the model was regarded as much broader. In the second part of their paper, the authors demonstrated that a levered firm's equity can be regarded as an option on the value of the firm, and thus can be priced by option valuation techniques. A year later, Merton showed how the default risk structure of cor porate bonds can be determined by option pricing techniques. Option pricing models are now used to price virtually the full range of financial instruments and financial guarantees such as deposit insurance and collateral, and to quantify the associated risks. Over the years, option pricing has evolved from a set of specific models to a general analytical framework for analyzing the production process of financial contracts and their function in the financial intermediation process in a continuous time framework. However, very few attempts have been made in the literature to integrate game theory aspects, i. e. strategic financial decisions of the agents, into the continuous time framework. This is the unique contribution of the thesis of Dr. Alexandre Ziegler. Benefiting from the analytical tractability of contin uous time models and the closed form valuation models for derivatives, Dr."

The Bachelier Society for Mathematical Finance held its first World Congress in Paris last year, and coincided with the centenary of Louis Bacheliers thesis defence. In his thesis Bachelier introduces Brownian motion as a tool for the analysis of financial markets as well as the exact definition of options. The thesis is viewed by many the key event that marked the emergence of mathematical finance as a scientific discipline. The prestigious list of plenary speakers in Paris included two Nobel laureates, Paul Samuelson and Robert Merton, and the mathematicians Henry McKean and S.R.S. Varadhan. Over 130 further selected talks were given in three parallel sessions. .

This book introduces the student to numerous modern applications of mathematics in technology. The authors write with clarity and present the mathematics in a clear and straightforward way making it an interesting and easy book to read. Numerous exercises at the end of every section provide practice and reinforce the material in the chapter. An engaging quality of this book is that the authors also present the mathematical material in a historical context and not just the practical one.

Mathematics and Technology is intended for undergraduate students in mathematics, instructors and high school teachers. Additionally, its lack of calculus centricity as well as a clear indication of the more difficult topics and relatively advanced references make it suitable for any curious individual with a decent command of high school math.

The fourth edition is augmented by more than 70 new formulas. In particular, we have included some key concepts and results from trade theory, games of incomplete information and combinatorics. In addition there are scattered additions of new formulas in many chapters. Again we are indebted to a number of people who has suggested corrections, - provements and new formulas. In particular, we would like to thank Jens-Henrik Madsen, Larry Karp, Harald Goldstein, and Geir Asheim. In a reference book, errors are particularly destructive. We hope that readers who ?nd our remaining errors will call them to our attention so that we may purge them from future editions. Oslo and Berkeley, May 2005 Knut Sydsaeter, Arne Strom, Peter Berck From the preface to the third edition Thepracticeofeconomicsrequiresawide-rangingknowledgeofformulasfrommat- matics, statistics, andmathematicaleconomics. Withthisvolumewehopetopresent a formulary tailored to the needs of students and working professionals in economics. In addition to a selection of mathematical and statistical formulas often used by economists, this volume contains many purely economic results and theorems. It containsjusttheformulasandtheminimumcommentaryneededtorelearnthema- ematics involved. We have endeavored to state theorems at the level of generality economists might ?nd useful. In contrast to the economic maxim, "everything is twice more continuously di?erentiable than it needs to be," we have usually listed theregularityconditionsfortheoremstobetrue.Wehopethatwehaveachieveda level of explication that is accurate and useful without being pedantic."

Each concept is discussed from the basics and supported by sufficient mathematical background and worked examples.

Suitable for individual or group learning, the book offers numerous end-of-chapter problems for study and review.