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.

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.

This Festschrift is dedicated to Goetz Trenkler on the occasion of his 65th birthday. As can be seen from the long list of contributions, Goetz has had and still has an enormous range of interests, and colleagues to share these interests with. He is a leading expert in linear models with a particular focus on matrix algebra in its relation to statistics. He has published in almost all major statistics and matrix theory journals. His research activities also include other areas (like nonparametrics, statistics and sports, combination of forecasts and magic squares, just to mention afew). Goetz Trenkler was born in Dresden in 1943. After his school years in East G- many and West-Berlin, he obtained a Diploma in Mathematics from Free University of Berlin (1970), where he also discovered his interest in Mathematical Statistics. In 1973, he completed his Ph.D. with a thesis titled: On a distance-generating fu- tion of probability measures. He then moved on to the University of Hannover to become Lecturer and to write a habilitation-thesis (submitted 1979) on alternatives to the Ordinary Least Squares estimator in the Linear Regression Model, a topic that would become his predominant ?eld of research in the years to come.

In June of 2002, over 500 professors, students and researchers met in Boston, Massachusetts for the Fourth International Conference on Complex Systems. The attendees represented a remarkably diverse collection of fields: biology, ecology, physics, engineering, computer science, economics, psychology and sociology, The goal of the conference was to encourage cross-fertilization between the many disciplines represented and to deepen understanding of the properties common to all complex systems.

This volume contains 43 papers selected from the more than 200 presented at the conference. Topics include: cellular automata, neurology, evolution, computer science, network dynamics, and urban planning.

About NECSI: For over 10 years, The New England Complex Systems Institute (NECSI) has been instrumental in the development of complex systems science and its applications. NECSI conducts research, education, knowledge dissemination, and community development around the world for the promotion of the study of complex systems and its application for the betterment of society. NECSI hosts the International Conference on Complex Systems and publishes the NECSI Book Series in conjunction with Springer Publishers.

ALI MINAI is an Affiliate of the New England Complex Systems Institute and an Associate Professor in the Department of Electrical and Computer Engineering and Computer Science at the University of Cincinnati.

YANEER BAR-YAM is President and founder of the New England Complex Systems Institute. He is the author of Dynamics of Complex Systems and Making Things Work: Solving Complex Problems in a Complex World.

Stochastic optimization problems arise in decision-making problems under uncertainty, and find various applications in economics and finance. On the other hand, problems in finance have recently led to new developments in the theory of stochastic control. This volume provides a systematic treatment of stochastic optimization problems applied to finance by presenting the different existing methods: dynamic programming, viscosity solutions, backward stochastic differential equations, and martingale duality methods. The theory is discussed in the context of recent developments in this field, with complete and detailed proofs, and is illustrated by means of concrete examples from the world of finance: portfolio allocation, option hedging, real options, optimal investment, etc. This book is directed towards graduate students and researchers in mathematical finance, and will also benefit applied mathematicians interested in financial applications and practitioners wishing to know more about the use of stochastic optimization methods in finance.

Fundamentals of Convex Analysis offers an in-depth look at some of the fundamental themes covered within an area of mathematical analysis called convex analysis. In particular, it explores the topics of duality, separation, representation, and resolution. The work is intended for students of economics, management science, engineering, and mathematics who need exposure to the mathematical foundations of matrix games, optimization, and general equilibrium analysis. It is written at the advanced undergraduate to beginning graduate level and the only formal preparation required is some familiarity with set operations and with linear algebra and matrix theory. Fundamentals of Convex Analysis is self-contained in that a brief review of the essentials of these tool areas is provided in Chapter 1. Chapter exercises are also provided. Topics covered include: convex sets and their properties; separation and support theorems; theorems of the alternative; convex cones; dual homogeneous systems; basic solutions and complementary slackness; extreme points and directions; resolution and representation of polyhedra; simplicial topology; and fixed point theorems, among others. A strength of this work is how these topics are developed in a fully integrated fashion.

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."

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."

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."

The mechanisms of protest and revolution have been the subject of theoretical research for over a century, yet the lack of data has hindered the empirical validation of conflicting theories. In this book, the author presents a unique new set of sub-daily data from over thirty countries and seven civil wars and uses them to test two models of conflict, the predator-prey model and the competing species model. The dynamic nature of the data modelling and the novelty of the dataset make this work a unique contribution to the field of conflict research. Dynamics of Conflict will help to re-evaluate existing theories and chart a new course towards the formal and statistical modelling of conflict.

Stochastic differential games represent one of the most complex forms of decision making under uncertainty. In particular, interactions between strategic behaviors, dynamic evolution and stochastic elements have to be considered simultaneously. The complexity of stochastic differential games generally leads to great difficulties in the derivation of solutions. Cooperative games hold out the promise of more socially optimal and group efficient solutions to problems involving strategic actions. Despite urgent calls for national and international cooperation, the absence of formal solutions has precluded rigorous analysis of this problem.

The book supplies effective tools for rigorous study of cooperative stochastic differential games. In particular, a generalized theorem for the derivation of analytically tractable "payoff distribution procedure" of subgame consistent solution is presented. Being capable of deriving analytical tractable solutions, the work is not only theoretically interesting but would enable the hitherto intractable problems in cooperative stochastic differential games to be fruitfully explored.

Currently, this book is the first ever volume devoted to cooperative stochastic differential games. It aims to provide its readers an effective tool to analyze cooperative arrangements of conflict situations with uncertainty over time. Cooperative game theory has succeeded in offering many applications of game theory in operations research, management, economics, politics and other disciplines. The extension of these applications to a dynamic environment with stochastic elements should be fruitful. The book will be of interest to game theorists, mathematicians, economists, policy-makers, corporate planners and graduate students.

For quite some time, philosophers, economists, and statisticians have endorsed a view on rational choice known as Bayesianism. The work on this book has grown out of a feeling that the Bayesian view has come to dominate the academic com- nitytosuchanextentthatalternative, non-Bayesianpositionsareseldomextensively researched. Needless to say, I think this is a pity. Non-Bayesian positions deserve to be examined with much greater care, and the present work is an attempt to defend what I believe to be a coherent and reasonably detailed non-Bayesian account of decision theory. The main thesis I defend can be summarised as follows. Rational agents m- imise subjective expected utility, but contrary to what is claimed by Bayesians, ut- ity and subjective probability should not be de?ned in terms of preferences over uncertain prospects. On the contrary, rational decision makers need only consider preferences over certain outcomes. It will be shown that utility and probability fu- tions derived in a non-Bayesian manner can be used for generating preferences over uncertain prospects, that support the principle of maximising subjective expected utility. To some extent, this non-Bayesian view gives an account of what modern - cision theory could have been like, had decision theorists not entered the Bayesian path discovered by Ramsey, de Finetti, Savage, and others. I will not discuss all previous non-Bayesian positions presented in the literature

This is a collection of classic research papers on the Dempster-Shafer theory of belief functions. The book is the authoritative reference in the field of evidential reasoning and an important archival reference in a wide range of areas including uncertainty reasoning in artificial intelligence and decision making in economics, engineering, and management. The book includes a foreword reflecting the development of the theory in the last forty years.

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 book is written by leading scholars in Network Science, Nonlinear Science and Infrastructure Systems, expressly to develop common theoretical underpinnings for better solutions to modern infrastructural problems. The book is dedicated to the formulation of infrastructural tools that will better solve problems from transportation networks to telecommunications, Internet, supply chains and more.

This monograph is an introduction to some aspects of stochastic analysis in the framework of normal martingales, in both discrete and continuous time. The text is mostly self-contained, except for Section 5.7 that requires some background in geometry, and should be accessible to graduate students and researchers having already received a basic training in probability. Prereq- sites are mostly limited to a knowledge of measure theory and probability, namely?-algebras,expectations,andconditionalexpectations.Ashortint- duction to stochastic calculus for continuous and jump processes is given in Chapter 2 using normal martingales, whose predictable quadratic variation is the Lebesgue measure. There already exists several books devoted to stochastic analysis for c- tinuous di?usion processes on Gaussian and Wiener spaces, cf. e.g. [51], [63], [65], [72], [83], [84], [92], [128], [134], [143], [146], [147]. The particular f- ture of this text is to simultaneously consider continuous processes and jump processes in the uni?ed framework of normal martingales.

In the following chapters, I offer an evolutionary account of morality and from that extrapolate a version of contractarianism I call consent theory. Game theory helps to highlight the evolution of morality as a resolution of interpersonal conflicts under strategic negotiation. It is this emphasis on strategic negotiation that underwrites the idea of consent. Consent theory differs from other contractarian models by abandoning reliance on rational self-interest in favour of evolutionary adaptation. From this, more emphasis will be placed on consent as natural convergence rather than consent as an idealization. My picture of contractarianism, then, ends up looking more like the relativist model offered by Harman, rather than the rational (or pseudo-rational) model offered by Gauthier, let alone the Kantian brands of Rawls or Scanlon. So at least some of my discussion will dwell on why it is no loss to abandon hope for the universal, categorical morality that rational models promise. In the introduction, I offer the betting analogy that underwrites the remaining picture. There are some bets where the expected utility is positive, though the odds of winning on this particular occasion are exceedingly low. In such cases, we cannot hope to give an argument that taking the bet is rational. The only thing we can say is that those predisposed to take this kind of bet on these kinds of occasions will do better than those with other dispositions, so long as such games occur often enough.

Game theory has already proved its tremendous potential for con?ict resolution problems in the ?elds of Decision Theory and Economics. In the recent past, there have been attempts to extend the results of crisp game theory to those con?ict resolution problems which are fuzzy in nature e.g. Nishizaki and Sakawa [61] and references cited there in. These developments have lead to the emergence of a new area in the literature called fuzzy games. Another area in the fuzzy decision theory, which has been growing very fast is the area of fuzzy mathematical programming and its applications to various branches of sciences, Engineering and Management. In the crisp scenario, there exists a beautiful relationship between two person zero sum matrix game theory and duality in linear p- gramming. It is therefore natural to ask if something similar holds in the fuzzy scenario as well. This discussion essentially constitutes the core of our presentation. The objective of this book is to present a systematic and focussed study of the application of fuzzy sets to two very basic areas of decision theory, namely Mathematical Programming and Matrix Game Theory.

"Deals with pricing and hedging financial derivatives.... Computational methods are introduced and the text contains the Excel VBA routines corresponding to the formulas and procedures described in the book. This is valuable since computer simulation can help readers understand the theory....The book...succeeds in presenting intuitively advanced derivative modelling... it provides a useful bridge between introductory books and the more advanced literature." --MATHEMATICAL REVIEWS

The project of writing this monograph was conceived in August 2006. It is a m- ter of delight and satisfaction that this monograph would be published during the centenary year (May 27, 2008 - May 26, 2009) of our dear alma mater, the Indian Institute of Science, which is truly a magni cent temple and an eternal source of inspiration, with a splendid ambiance for research. Studying the rational behavior of entities interacting with each other in or- nized or ad-hoc marketplaces has been the bread and butter of our research group here at the Electronic Commerce Laboratory, Department of Computer Science and Automation, Indian Institute of Science. Speci cally, the application of game th- retic modeling and mechanism design principles to the area of network economics was an area of special interest to the authors. In fact, the dissertations of the s- ond, third, and fourth authors (Dinesh Garg, Ramasuri Narayanam, and Hastagiri Prakash) were all in this area. Dinesh Garg's Doctoral Thesis, which later won the Best Dissertation Award at the Department of Computer Science and Automation, Indian Institute of Science for the academic year 2006-07, included an interesting chapter on applying the brilliant work of Roger Myerson (Nobel laureate in E- nomic Sciences in 2007) to the topical problem of sponsored search auctions on the web. Ramasuri's Master's work applied mechanism design to develop robust broadcastprotocolsin wireless adhoc networkswhile Hastagiri's Master's work - veloped resource allocation mechanisms for computational grids.

Cooperative game theory is a booming research area with many new developments in the last few years. So, our main purpose when prep- ing the second edition was to incorporate as much of these new dev- opments as possible without changing the structure of the book. First, this o?ered us the opportunity to enhance and expand the treatment of traditional cooperative games, called here crisp games, and, especially, that of multi-choice games, in the idea to make the three parts of the monograph more balanced. Second, we have used the opportunity of a secondeditiontoupdateandenlargethelistofreferencesregardingthe threemodels of cooperative games. Finally, we have bene?ted fromthis opportunity by removing typos and a few less important results from the ?rst edition of the book, and by slightly polishing the English style and the punctuation, for the sake of consistency along the monograph. The main changes are: (1) Chapter 3 contains an additional section, Section 3. 3, on the - erage lexicographic value, which is a recent one-point solution concept de?ned on the class of balanced crisp games. (2) Chapter 4 is new. It o?ers a brief overview on solution c- cepts for crisp games from the point of view of egalitarian criteria, and presents in Section 4. 2 a recent set-valued solution concept based on egalitarian considerations, namely the equal split-o? set. (3)Chapter5isbasicallyanenlargedversionofChapter4ofthe?rst edition because Section 5. 4 dealing with the relation between convex games and clan games with crisp coalitions is new.

This is the fourth edition of a book that, after circulating in the form of l- ture notes at the universities of Rome (now La Sapienza University of Rome) and Siena in the late 1960s, was originally published in 1971 under the titleMat- maticalMethodsandModelsinEconomicDynamics. Inthosefortyoddyearstwo main developments have occurred in economic dynamics. The ?rst is the much greater amount of advanced mathematics that is being used today with respect to the past. The second is the increasing importance of non-linear modelling as contrastedwiththelinearapproach(which,however,hasnotgoneoutoffashion). This fourth edition re?ects both developments. It contains additional advanced mathematical tools, and a larger amount of non-linear mathematics and appli- tions. These developments are re?ected especially in Part III, that now accounts forwellover50%ofthebook. ItgoeswithoutsayingthatIhavemadeeverye?ort topreservetheuser-friendlyfeatureofthepreviouseditions: thespiritofthebook hasremainedthesame, namelytogiveacomprehensive, butsimple, treatmentof the mathematical methods commonly used in dynamical economics, and to show how they are applied to build and analyse economic models. Accordingly, the focus is on methods, and every mathematical technique - troduced is followed by its application to selected economic models that serve as examples. Theunifyingprincipleintheexpositionofthedi?erenteconomicm- els is then seen to be the common mathematical technique. This process will enable the readers not only to understand the basic literature, but also to build and analyse their own models.

The present third edition of The Statistical Mechanics of Financial Markets is published only four years after the ?rst edition. The success of the book highlights the interest in a summary of the broad research activities on the application of statistical physics to ?nancial markets. I am very grateful to readers and reviewers for their positive reception and comments. Why then prepare a new edition instead of only reprinting and correcting the second edition? The new edition has been signi?cantly expanded, giving it a more pr- tical twist towards banking. The most important extensions are due to my practical experience as a risk manager in the German Savings Banks' As- ciation (DSGV): Two new chapters on risk management and on the closely related topic of economic and regulatory capital for ?nancial institutions, - spectively, have been added. The chapter on risk management contains both the basics as well as advanced topics, e. g. coherent risk measures, which have not yet reached the statistical physics community interested in ?nancial m- kets. Similarly, it is surprising how little research by academic physicists has appeared on topics relating to Basel II. Basel II is the new capital adequacy framework which will set the standards in risk management in many co- tries for the years to come. Basel II is responsible for many job openings in banks for which physicists are extemely well quali?ed. For these reasons, an outline of Basel II takes a major part of the chapter on capital.

A former Harvard professor of decision science and game theory draws on those disciplines in this review of controversial strategic and tactical decisions of World War II. Allied leadership-although outstanding in many ways-sometimes botched what now is termed meta-decision making or deciding how to decide. Operation Jubilee, a single-division amphibious raid on Dieppe in August 1942, illustrates the pitfalls of groupthink. Prior to the invasion of North Africa in November, American and British leaders fell victim to the planning fallacy, going in with rosy expectations for easily achievable objectives. In the conquest of Sicily, they violated the millennia-old principle of command unity-now re-endorsed and elaborated on by modern theorists. Had Allied tacticians understood the game-theoretic significance of the terrain and conditions for success at Anzio, they might well not have and landed two-plus divisions there to fight a months-long stalemate in the first half of 1944.

Elfi Ettinger focuses her research on how financial consultants perceive, explain, and interpret their commitment at work based on their collective reality of actions and behavior. She analyzes which organizational performance variables consultants associate with their commitment at work, and how consultants' commitment behavior is linked with organizational performance.