This monograph covers one of the divisions of mathematical theory of control which examines moving objects functionating under conflict and uncertainty conditions. To identify this range of problems we use the term "conflict con trolled processes," coined in recent years. As the name itself does not imply the type of dynamics (difference, ordinary differential, difference-differential, integral, or partial differential equations) the differential games falI within its realms. The problems of search and tracking moving objects are also referred to the field of conflict controlled process. The contents of the monograph is confined to studying classical pursuit-evasion problems which are central to the theory of conflict controlled processes. These problems underlie the theory and are of considerable interest to researchers up to now. It should be noted that the methods of "Line of Sight," "Parallel Pursuit," "Proportional N avigation,""Modified Pursuit" and others have been long and well known among engineers engaged in design of rocket and space technology. An abstract theory of dynamic game problems, in its turn, is based on the methods originated by R. Isaacs, L. S. Pontryagin, and N. N. Krasovskii, and on the approaches developed around these methods. At the heart of the book is the Method of Resolving Functions which was realized within the class of quasistrategies for pursuers and then applied to the solution of the problems of "hand-to-hand," group, and succesive pursuit."

Search Theory is one of the original disciplines within the field of Operations Research. It deals with the problem faced by a Searcher who wishes to minimize the time required to find a hidden object, or "target. " The Searcher chooses a path in the "search space" and finds the target when he is sufficiently close to it. Traditionally, the target is assumed to have no motives of its own regarding when it is found; it is simply stationary and hidden according to a known distribution (e. g. , oil), or its motion is determined stochastically by known rules (e. g. , a fox in a forest). The problems dealt with in this book assume, on the contrary, that the "target" is an independent player of equal status to the Searcher, who cares about when he is found. We consider two possible motives of the target, and divide the book accordingly. Book I considers the zero-sum game that results when the target (here called the Hider) does not want to be found. Such problems have been called Search Games (with the "ze- sum" qualifier understood). Book II considers the opposite motive of the target, namely, that he wants to be found. In this case the Searcher and the Hider can be thought of as a team of agents (simply called Player I and Player II) with identical aims, and the coordination problem they jointly face is called the Rendezvous Search Problem.

The use of the internet for commerce has spawned a variety of auctions, marketplaces, and exchanges for trading everything from bandwidth to books. Mechanisms for bidding agents, dynamic pricing, and combinatorial bids are being implemented in support of internet-based auctions, giving rise to new versions of optimization and resource allocation models. This volume, a collection of papers from an IMA "Hot Topics" workshop in internet auctions, includes descriptions of real and proposed auctions, complete with mathematical model formulations, theoretical results, solution approaches, and computational studies.
This volume also provides a mathematical programming perspective on open questions in auction theory, and provides a glimpse of the growing area of dynamic pricing.

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.

The theory of social choice deals with both the processes and results of col lective decision making. In this book, we explore some issues in the theory of social choice and mechanism design. We examine the premises of this theory, the axiomatic approach, and the mechanism design approach. The main questions are what is collective interest, how is it related to individuals' interests, how should one design social interactions, laws, and in stitutions? These questions are not new. Philosophers, social scientists have indeed pondered upon them for years. And, in fact, the organizational struc tures of many social institutions -courts, parliaments, committees and reg ulatory boards -often lack a sound theoretical base. This is not surprising, as it is, indeed, difficult to provide for a comprehensive formalization of the activities of such organizations. Nevertheless, there has been a definite trend towards providing clear and unambiguous rules for collective decision mak ing. These very rules constitute the body of social choice theory and its main object. The basic problem of social choice We explain here more precisely what a problem of social choice is, what approaches might be used to tackle it, and what kind of solutions it leads to. We introduce a few basic notions in preliminarily fashion and, in doing so, we stress both motivations and explanations."

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.

In the first part of this book, we treat interacting and small open economies. We do this from an historical perspective, starting from the Classical model of the gold standard and the specie-flow mechanism and aim to show there that the Dornbusch IS-LM-PC approach, with or without rational expectations, can still be considered as a (if not the) core contribution to contemporaneous open economy macrodynamics, also on the level of structural macroeconometric model building. In the second part we then extend this analysis to the incorporation of more disequilibrium on the real markets, prominent further feedback channels of the macrodynamic literature and integrated macromodel building. We start from the closed economy, consider large open economies in a fixed exchange rate system, small open economies subject to high capital mobility, and finally two large interacting economies like the USA and Euroland. Our macrofounded approach extends and integrates non-market clearing traditions to macrodynamics and can be usefully compared with the New Keynesian approaches which are generally rigorously microfounded, but often much more limited in scope in capturing full market and agent interactions.

This volume contains several surveys focused on the ideas of approximate solutions, well-posedness and stability of problems in scalar and vector optimization, game theory and calculus of variations. These concepts are of particular interest in many fields of mathematics. The idea of stability goes back at least to J. Hadamard who introduced it in the setting of differential equations; the concept of well-posedness for minimum problems is more recent (the mid-sixties) and originates with A.N. Tykhonov. It turns out that there are connections between the two properties in the sense that a well-posed problem which, at least in principle, is "easy to solve," has a solution set that does not vary too much under perturbation of the data of the problem, i.e. it is "stable." These themes have been studied in depth for minimum problems and now we have a general picture of the related phenomena in this case. But, of course, the same concepts can be studied in other more complicated situations as, e.g. vector optimization, game theory and variational inequalities. Let us mention that in several of these new areas there is not even a unique idea of what should be called approximate solution, and the latter is at the basis of the definition of well posed problem."

The scientific monograph of a survey kind presented to the reader's attention deals with fundamental ideas and basic schemes of optimization methods that can be effectively used for solving strategic planning and operations manage ment problems related, in particular, to transportation. This monograph is an English translation of a considerable part of the author's book with a similar title that was published in Russian in 1992. The material of the monograph embraces methods of linear and nonlinear programming; nonsmooth and nonconvex optimization; integer programming, solving problems on graphs, and solving problems with mixed variables; rout ing, scheduling, solving network flow problems, and solving the transportation problem; stochastic programming, multicriteria optimization, game theory, and optimization on fuzzy sets and under fuzzy goals; optimal control of systems described by ordinary differential equations, partial differential equations, gen eralized differential equations (differential inclusions), and functional equations with a variable that can assume only discrete values; and some other methods that are based on or adjoin to the listed ones."

Non-Additive Measure and Integral is the first systematic approach to the subject. Much of the additive theory (convergence theorems, Lebesgue spaces, representation theorems) is generalized, at least for submodular measures which are characterized by having a subadditive integral. The theory is of interest for applications to economic decision theory (decisions under risk and uncertainty), to statistics (including belief functions, fuzzy measures) to cooperative game theory, artificial intelligence, insurance, etc. Non-Additive Measure and Integral collects the results of scattered and often isolated approaches to non-additive measures and their integrals which originate in pure mathematics, potential theory, statistics, game theory, economic decision theory and other fields of application. It unifies, simplifies and generalizes known results and supplements the theory with new results, thus providing a sound basis for applications and further research in this growing field of increasing interest. It also contains fundamental results of sigma-additive and finitely additive measure and integration theory and sheds new light on additive theory. Non-Additive Measure and Integral employs distribution functions and quantile functions as basis tools, thus remaining close to the familiar language of probability theory. In addition to serving as an important reference, the book can be used as a mathematics textbook for graduate courses or seminars, containing many exercises to support or supplement the text.

These proceedings are from a conference held at the Centre for Regional Science (CERUM) at Umea Umea University, Sweden, 17-18 June 2001. Unlike Un1ike many conference proceedings, this volume contains only on1y invited invited contribu- contribu- tions tions on specified topics so as to make the book coherent and self-contained. The authors and editors hope that this coherence will make the volume use- fu1 fuI also as a text for courses in industrial organisation. To this end two chap- ters on the history of oligopoly theory, from the beginnings with Cournot 1838, to the present day, and one chapter on modem methods for analysing iterated discrete time maps, have been inserted at the beginning ofthe book. Unlike Un1ike most current literature on games and oligopoly, this book is not focused on the usual topics of game theory: optimal strategies, dominance, and equilibrium. Rather it is the evolutionary dynamics, often of a complex type, inc1uding deterministic chaos, which are in focus. The contributions, after the historical and the methodological introductions, represent various segments of the research frontier in this area, though pains have been taken to tie some of the models to a number of most promising contributions from the frugal period 1929-1941, which have suffered from unjust neglect in the following industrial organisation literature.

The ambition of the theory of imperfectly competitive markets is to explain the working of markets in which the issue of strategic interaction among firms is central. Our analysis of this problem will be based on equilibrium concepts borrowed from Game Theory. This research program arises several questions on its feasibility like the empirical relevance of the results, the substantial theoretical insights obtained in this way, etc. Unfortunately, most of these questions can not be answered in the short run. This book is written in the hope that this research strategy is meaningful, but about its final success no body can tell. Another important question is if simpler models could deliver the essential insights offered by the theory of imperfectly competitive mar kets. This Introduction will be devoted to argue that, currently, there is no alternative to the approach presented in this book. Consider the following fact: A square inch of soil in the Explanada of Ali cante (located in front of the sea, right in the middle of downtown) cost several times more than a square inch of soil in San Vicente del Raspeig (located sev eral miles toward the interior of the peninsula). l How can we explain such a thing? First notice that because of the large quantity of possible traders involved in this market, we can safely assume that any agent has to accept the market price, i. e. is a price-taker."

In recent years there is a growing interest in generalized convex fu- tions and generalized monotone mappings among the researchers of - plied mathematics and other sciences. This is due to the fact that mathematical models with these functions are more suitable to describe problems of the real world than models using conventional convex and monotone functions. Generalized convexity and monotonicity are now considered as an independent branch of applied mathematics with a wide range of applications in mechanics, economics, engineering, finance and many others. The present volume contains 20 full length papers which reflect c- rent theoretical studies of generalized convexity and monotonicity, and numerous applications in optimization, variational inequalities, equil- rium problems etc. All these papers were refereed and carefully selected from invited talks and contributed talks that were presented at the 7th International Symposium on Generalized Convexity/Monotonicity held in Hanoi, Vietnam, August 27-31, 2002. This series of Symposia is or- nized by the Working Group on Generalized Convexity (WGGC) every 3 years and aims to promote and disseminate research on the field. The WGGC (http: //www.genconv.org) consists of more than 300 researchers coming from 36 countries

Here, two highly experienced authors present an alternative approach to optimal stopping problems. The basic ideas and techniques of the approach can be explained much simpler than the standard methods in the literature on optimal stopping problems. The monograph will teach the reader to apply the technique to many problems in economics and finance, including new ones. From the technical point of view, the method can be characterized as option pricing via the Wiener-Hopf factorization.

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.

Attractors, Bifurcations, & Chaos - now in its second edition - begins with an introduction to mathematical methods in modern nonlinear dynamics and deals with differential equations. Phenomena such as bifurcations and deterministic chaos are given considerable emphasis, both in the methodological part, and in the second part, containing various applications in economics and in regional science. Coexistence of attractors and the multiplicity of development paths in nonlinear systems are central topics. The applications focus on issues such as business cycles, oligopoly, interregional trade dynamics, and economic development theory.

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.

OndrejMajer, Ahti-VeikkoPietarinen, andTeroTulenheimo 1 Games and logic in philosophy Recent years have witnessed a growing interest in the unifying methodo- gies over what have been perceived as pretty disparate logical 'systems', or else merely an assortment of formal and mathematical 'approaches' to phi- sophical inquiry. This development has largely been fueled by an increasing dissatisfaction to what has earlier been taken to be a straightforward outcome of 'logical pluralism' or 'methodological diversity'. These phrases appear to re ect the everyday chaos of our academic pursuits rather than any genuine attempt to clarify the general principles underlying the miscellaneous ways in which logic appears to us. But the situation is changing. Unity among plurality is emerging in c- temporary studies in logical philosophy and neighbouring disciplines. This is a necessary follow-up to the intensive research into the intricacies of logical systems and methodologies performed over the recent years. The present book suggests one such peculiar but very unrestrained meth- ological perspective over the eld of logic and its applications in mathematics, language or computation: games. An allegory for opposition, cooperation and coordination, games are also concrete objects of formal study.

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.

This volume contains a selection consisting of the best papers presented at the FUR XII conference, held at LUISS in Roma, Italy, in June 2006, organized by John Hey and Daniela Di Cagno. The objectives of the FUR (Foundations of Utility and Risk theory) conferences have always been to bring together leading academics from Economics, Psychology, Statistics, Operations Research, Finance, Applied Mat- matics, and other disciplines, to address the issues of decision-making from a g- uinely multi-disciplinary point of view. This twelfth conference in the series was no exception. The early FUR conferences - like FUR I (organized by Maurice Allais and Ole Hagen) and FUR III (organized by Bertrand Munier) - initiated the move away from the excessively rigid and descriptively-inadequate modelling of beh- iour under risk and uncertainty that was in vogue in conventional economics at that time. More than twenty years later, things have changed fundamentally, and now - novations arising from the FUR conferences, and manifesting themselves in the new behavioural economics, are readily accepted by the profession. Working with new models of ambiguity, and bounded rationality, for example, behavioural decision making is no longer considered a sign of mere non-standard intellectual diversi?- tion. FUR XII was organised with this new spirit. In the sense that the behavioural concerns initiated by the ?rst FUR conferences are now part of conventional e- nomics, and the design and organisation of FUR XII re?ects this integration, FUR XII represents a key turning point in the FUR conference series.

This book systematically presents the main solutions of cooperative games: the core, bargaining set, kernel, nucleolus, and the Shapley value of TU games as well as the core, the Shapley value, and the ordinal bargaining set of NTU games. The authors devote a separate chapter to each solution, wherein they study its properties in full detail. In addition, important variants are defined or even intensively analyzed.

Peter Fishburn has had a splendidly productive career that led to path-breaking c- tributions in a remarkable variety of areas of research. His contributions have been published in a vast literature, ranging through journals of social choice and welfare, decision theory, operations research, economic theory, political science, mathema- cal psychology, and discrete mathematics. This work was done both on an individual basis and with a very long list of coauthors. The contributions that Fishburn made can roughly be divided into three major topical areas, and contributions to each of these areas are identi?ed by sections of this monograph. Section 1 deals with topics that are included in the general areas of utility, preference, individual choice, subjective probability, and measurement t- ory. Section 2 covers social choice theory, voting models, and social welfare. S- tion 3 deals with more purely mathematical topics that are related to combinatorics, graph theory, and ordered sets. The common theme of Fishburn's contributions to all of these areas is his ability to bring rigorous mathematical analysis to bear on a wide range of dif?cult problems.

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.

The present volume contains the proceedings of the workshop on "Minimax Theory and Applications" that was held during the week 30 September - 6 October 1996 at the "G. Stampacchia" International School of Mathematics of the "E. Majorana" Centre for Scientific Cul ture in Erice (Italy) . The main theme of the workshop was minimax theory in its most classical meaning. That is to say, given a real-valued function f on a product space X x Y, one tries to find conditions that ensure the validity of the equality sup inf f(x, y) = inf sup f(x, y). yEY xEX xEX yEY This is not an appropriate place to enter into the technical details of the proofs of minimax theorems, or into the history of the contribu tions to the solution of this basic problem in the last 7 decades. But we do want to stress its intrinsic interest and point out that, in spite of its extremely simple formulation, it conceals a great wealth of ideas. This is clearly shown by the large variety of methods and tools that have been used to study it. The applications of minimax theory are also extremely interesting. In fact, the need for the ability to "switch quantifiers" arises in a seemingly boundless range of different situations. So, the good quality of a minimax theorem can also be judged by its applicability. We hope that this volume will offer a rather complete account of the state of the art of the subject."