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.

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."

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 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.

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.

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."

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 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.

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."

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.

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.

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.

In recent decades game theory-the mathematics of rational decision-making by interacting individuals-has assumed a central place in our understanding of capitalist markets, the evolution of social behavior in animals, and even the ethics of altruism and fairness in human beings. With game theory's ubiquity, however, has come a great deal of misunderstanding. Critics of the contemporary social sciences view it as part of an unwelcome trend toward the marginalization of historicist and interpretive styles of inquiry, and many accuse its proponents of presenting a thin and empirically dubious view of human choice. The World the Game Theorists Made seeks to explain the ascendency of game theory, focusing on the poorly understood period between the publication of John von Neumann and Oscar Morgenstern's seminal Theory of Games and Economic Behavior in 1944 and the theory's revival in economics in the 1980s. Drawing on a diverse collection of institutional archives, personal correspondence and papers, and interviews, Paul Erickson shows how game theory offered social scientists, biologists, military strategists, and others a common, flexible language that could facilitate wide-ranging thought and debate on some of the most critical issues of the day.

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.

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 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.

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.

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.

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.

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.

Andreas Schertzinger identifies determinants of successful transactions, such as transaction timing and diversifying transaction strategy, through a multivariate statistical analysis. Two case studies illustrate success factors specifically related to the conduct of transactions in greater detail.

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.