This book was written mainly during the Spring periods of 2008 and 2009, when the ?rst author was visiting Maastricht University. Financial s- port both from the Dutch Science Foundation NWO (grants 040. 11. 013 and 0. 40. 11. 082) and from the research institute METEOR (Maastricht Univ- sity) is gratefully acknowledged. Jerusalem Bezalel Peleg Maastricht Hans Peters April 2010 v Contents Preview to this book . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi Part I Representations of constitutions 1 Introduction to Part I. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1. 1 Motivation and summary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1. 2 Arrow's constitution. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1. 3 Arrow's Impossibility Theorem and its implications. . . . . . . . . 4 1. 4 Ga ]rdenfors's model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1. 5 Notes and comments. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2 Constitutions, e?ectivity functions, and game forms . . . . . . 7 2. 1 Motivation and summary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2. 2 Constitutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2. 3 Constitutions and e?ectivity functions . . . . . . . . . . . . . . . . . . . . 12 2. 4 Game forms and a representation theorem. . . . . . . . . . . . . . . . . 16 2. 5 Representation and simultaneous exercising of rights. . . . . . . . 19 2. 6 Notes and comments. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 3 Nash consistent representations. . . . . . . . . . . . . . . . . . . . . . . . . . . 21 3. 1 Motivation and summary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 3. 2 Existence of Nash consistent representations: a general result 22 3. 3 The case of ?nitely many alternatives. . . . . . . . . . . . . . . . . . . . . 24 3. 4 Nash consistent representations of topological e?ectivity functions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 3. 5 Veto functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 3. 5. 1 Finitely many alternatives. . . . . . . . . . . . . . . . . . . . . . . . . 34 3. 5. 2 Topological veto functions. . . . . . . . . . . . . . . . . . . . . . . . . 36 3. 6 Liberalism and Pareto optimality of Nash equilibria. . . . . . . . . 40 3. 7 Notes and comments. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 vii viii Contents 4 Acceptable representations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 4. 1 Motivation and summary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ."

Optimization Theory is becoming a more and more important mathematical as well as interdisciplinary area, especially in the interplay between mathematics and many other sciences like computer science, physics, engineering, operations research, etc.
This volume gives a comprehensive introduction into the theory of (deterministic) optimization on an advanced undergraduate and graduate level. One main feature is the treatment of both continuous and discrete optimization at the same place. This allows to study the problems under different points of view, supporting a better understanding of the entire field.
Audience: The book can be adapted well as an introductory textbook into optimization theory on a basis of a two semester course; however, each of its parts can also be taught separately. Many exercises are included to increase the reader's understanding.

Graph theory is very much tied to the geometric properties of optimization and combinatorial optimization. Moreover, graph theory's geometric properties are at the core of many research interests in operations research and applied mathematics. Its techniques have been used in solving many classical problems including maximum flow problems, independent set problems, and the traveling salesman problem.

Graph Theory and Combinatorial Optimization explores the field's classical foundations and its developing theories, ideas and applications to new problems. The book examines the geometric properties of graph theory and its widening uses in combinatorial optimization theory and application. The field's leading researchers have contributed chapters in their areas of expertise.

This book promotes and describes the application of objective and effective decision making in asset management based on mathematical models and practical techniques that can be easily implemented in organizations. This comprehensive and timely publication will be an essential reference source, building on available literature in the field of asset management while laying the groundwork for further research breakthroughs in this field. The text provides the resources necessary for managers, technology developers, scientists and engineers to adopt and implement better decision making based on models and techniques that contribute to recognizing risks and uncertainties and, in general terms, to the important role of asset management to increase competitiveness in organizations.

Leading expert Paul Booth explores the growth in popularity of board games today, and unpacks what it means to read a board game. What does a game communicate? How do games play us? And how do we decide which games to play and which are just wastes of cardboard? With little scholarly research in this still-emerging field, Board Games as Media underscores the importance of board games in the ever-evolving world of media.

This book describes how evolutionary algorithms (EA), including genetic algorithms (GA) and particle swarm optimization (PSO) can be utilized for solving multi-objective optimization problems in the area of embedded and VLSI system design. Many complex engineering optimization problems can be modelled as multi-objective formulations. This book provides an introduction to multi-objective optimization using meta-heuristic algorithms, GA and PSO and how they can be applied to problems like hardware/software partitioning in embedded systems, circuit partitioning in VLSI, design of operational amplifiers in analog VLSI, design space exploration in high-level synthesis, delay fault testing in VLSI testing and scheduling in heterogeneous distributed systems. It is shown how, in each case, the various aspects of the EA, namely its representation and operators like crossover, mutation, etc, can be separately formulated to solve these problems. This book is intended for design engineers and researchers in the field of VLSI and embedded system design. The book introduces the multi-objective GA and PSO in a simple and easily understandable way that will appeal to introductory readers.

When analyzing systems with a large number of parameters, the dimen sion of the original system may present insurmountable difficulties for the analysis. It may then be convenient to reformulate the original system in terms of substantially fewer aggregated variables, or macrovariables. In other words, an original system with an n-dimensional vector of states is reformulated as a system with a vector of dimension much less than n. The aggregated variables are either readily defined and processed, or the aggregated system may be considered as an approximate model for the orig inal system. In the latter case, the operation of the original system can be exhaustively analyzed within the framework of the aggregated model, and one faces the problems of defining the rules for introducing macrovariables, specifying loss of information and accuracy, recovering original variables from aggregates, etc. We consider also in detail the so-called iterative aggregation approach. It constructs an iterative process, at. every step of which a macroproblem is solved that is simpler than the original problem because of its lower dimension. Aggregation weights are then updated, and the procedure passes to the next step. Macrovariables are commonly used in coordinating problems of hierarchical optimization."

This book brings together historical notes, reviews of research developments, fresh ideas on how to make VC (Vapnik-Chervonenkis) guarantees tighter, and new technical contributions in the areas of machine learning, statistical inference, classification, algorithmic statistics, and pattern recognition. The contributors are leading scientists in domains such as statistics, mathematics, and theoretical computer science, and the book will be of interest to researchers and graduate students in these domains.

Semidefinite and conic optimization is a major and thriving research area within the optimization community. Although semidefinite optimization has been studied (under different names) since at least the 1940s, its importance grew immensely during the 1990s after polynomial-time interior-point methods for linear optimization were extended to solve semidefinite optimization problems.

Since the beginning of the 21st century, not only has research into semidefinite and conic optimization continued unabated, but also a fruitful interaction has developed with algebraic geometry through the close connections between semidefinite matrices and polynomial optimization. This has brought about important new results and led to an even higher level of research activity.

This "Handbook on Semidefinite, Conic and Polynomial Optimization "provides the reader with a snapshot of the state-of-the-art in the growing and mutually enriching areas of semidefinite optimization, conic optimization, and polynomial optimization. It contains a compendium of the recent research activity that has taken place in these thrilling areas, and will appeal to doctoral" "students, young graduates, and experienced researchers alike.

The Handbook's thirty-one chapters are organized into four parts: "Theory," covering significant theoretical developments as well as the interactions between conic optimization and polynomial optimization;"Algorithms," documenting the directions of current algorithmic development;"Software," providing an overview of the state-of-the-art;"Applications," dealing with the application areas where semidefinite and conic optimization has made a significant impact in recent years.

Growing transportation costs and tight delivery schedules mean that good located decisions are more crucial than ever in the success or failure of industrial and puplic projects. The development of realistic location models is an essential phase in every locational decision process. Especially when dealing with geometric representations of continuous (planar) location model problems, the goegraphical reality must be incorporated. This text develops the mathematical implications of barriers to the geometrical and analytical characteristics of continuous location problems. Besides their relevance in the application of location theoretic results, location problems with barriers are also very interesting from a mathematical point of view. The nonconvexity of distance measures in the presence of barriers leads to nonconvex optimization problems. Most of the classical methods in continuous location theory rely heaily on the convexity of the objective function and will thus fail in this context. On the other hand, general methods in global optimization capable of treating nonconvex problems ignore the geometric charateristics of the location problems considered. Theoretic as well as algorithmic approaches are utilized to overcome the described difficulties for the solution of location problems with barriers. Depending on the barrier shapes, the underlying distance measure, and type of objective function, different concepts are conceived to handle the nonconvexity of the problem. This book will appeal to those working in operations research and management science and mathematicians interested in optimization theory and its applications.

This book describes argumentative tools and strategies that can be used to guide policy decisions under conditions of great uncertainty. Contributing authors explore methods from philosophical analysis and in particular argumentation analysis, showing how it can be used to systematize discussions about policy issues involving great uncertainty. The first part of the work explores how to deal in a systematic way with decision-making when there may be plural perspectives on the decision problem, along with unknown consequences of what we do. Readers will see how argumentation tools can be used for prioritizing among uncertain dangers, for determining how decisions should be framed, for choosing a suitable time frame for a decision, and for systematically choosing among different decision options. Case studies are presented in the second part of the book, showing argumentation in practice in the areas of climate geoengineering, water governance, synthetic biology, nuclear waste, and financial markets. In one example, argumentation analysis is applied to proposals to solve the climate problem with various technological manipulations of the natural climate system, such as massive dispersion of reflective aerosols into the stratosphere. Even after a thorough investigation of such a proposal, doubt remains as to whether all the potential risks have been identified. In such discussions, conventional risk analysis does not have much to contribute since it presupposes that the risks have been identified, whereas the argumentative approach to uncertainty management can be used to systematize discussions.

Selected papers submitted by participants of the international Conference "Stochastic Analysis and Applied Probability 2010" ( www.saap2010.org ) make up the basis of this volume.

The SAAP 2010 was held in Tunisia, from 7-9 October, 2010, and was organized by the "Applied Mathematics & Mathematical Physics" research unit of the preparatory institute to the military academies of Sousse (Tunisia), chaired by Mounir Zili.

The papers cover theoretical, numerical and applied aspects of stochastic processes and stochastic differential equations. The study of such topic is motivated in part by the need to model, understand, forecast and control the behavior of many natural phenomena that evolve in time in a random way. Such phenomena appear in the fields of finance, telecommunications, economics, biology, geology, demography, physics, chemistry, signal processing and modern control theory, to mention just a few.

As this book emphasizes the importance of numerical and theoretical studies of the stochastic differential equations and stochastic processes, it will be useful for a wide spectrum of researchers in applied probability, stochastic numerical and theoretical analysis and statistics, as well as for graduate students.

To make it more complete and accessible for graduate students, practitioners and researchers, the editors Mounir Zili and Daria Filatova have included a survey dedicated to the basic concepts of numerical analysis of the stochastic differential equations, written by Henri Schurz.

Alternate Reality Games (ARGs) challenge what players understand as "real." Alternate Reality Games and the Cusp of Digital Gameplay is the first collection to explore and define the possibilities of ARGs. Though prominent examples have existed for more than two decades, only recently have ARGs come to the prominence as a unique and highly visible digital game genre. Adopting many of the same strategies as online video games, ARGs blur the distinction between real and fictional. With ARGs continuing to be an important and blurred space between digital and physical gameplay, this volume offers clear analysis of game design, implementation, and ramifications for game studies. Divided into three distinct sections, the contributions include first hand accounts by leading ARG creators, scholarly analysis of the meaning behind ARGs, and explorations of how ARGs are extending digital tools for analysis. By balancing the voices of designers, players, and researchers, this collection highlights how the Alternate Reality Game genre is transforming the ways we play and interact today.

This book studies storage policies in warehousing systems and maintenance-support strategies for critical operational systems in warehouses, which are the most important issues affecting operational efficiency of warehousing systems. It expands on the theory of class-based storage by considering a finite number of items in store, and also introduces the maintenance-support strategy founded on performance-based contract theory. It is a valuable resource for researchers, practitioners and engineers in the fields of industrial engineering, operations management, operations research and management science.

In February 2002, the Industrial and Systems Engineering (ISE) De partment at the University of Florida hosted a National Science Founda tion Workshop on Collaboration and Negotiation in Supply Chain Man agement and E Commerce. This workshop focused on characterizing the challenges facing leading edge firms in supply chain management and electronic commerce, and identifying research opportunities for de veloping new technological and decision support capabilities sought by industry. The audience included practitioners in the areas of supply chain management and E Commerce, as well as academic researchers working in these areas. The workshop provided a unique setting that has facilitated ongoing dialog between academic researchers and industry practitioners. This book codifies many of the important themes and issues around which the workshop discussions centered. The editors of this book, all faculty members in the ISE Department at the University of Florida, also served as the workshop's coordinators. In addition to workshop participants, we also invited contributions from leading academics and practitioners who were not able to attend. As a result, the chapters herein represent a collection of research contributions, monographs, and case studies from a variety of disciplines and viewpoints. On the aca demic side alone, chapter authors include faculty members in supply chain and operations management, marketing, industrial engineering, economics, computer science, civil and environmental engineering, and building construction departments.

The original edition of this book was celebrated for its coverage of the central concepts of practical optimization techniques. This updated edition expands and illuminates the connection between the purely analytical character of an optimization problem, expressed by properties of the necessary conditions, and the behavior of algorithms used to solve a problem. Incorporating modern theoretical insights, this classic text is even more useful.

Game theory now provides the theoretical underpinning for a multitude of courses in economics worldwide. The speed of these developments has been remarkable and they have constituted something of a revolution. Indeed, the basic tenets of game theory have now begun to colonize other social sciences and its proponents have been unified in claiming its natural basis as a rational theory of society.
But the technical demands of the subject and the lack of clarity of many commentators' explanations have been a problem for many. This second edition of Shaun Hargreaves-Heap and Yanis Varoufakis's classic text strips away the mystique and lets the student make his or her own mind up. This new edition:
* lays bear the philosophy behind game theory and explains all its major concepts
* conducts a clear explanation and careful analysis of all the main 'games', such as repeated games and the prisoner's dilemma, as well as less well-trodden topics such as experimental games and issues of rationality
* introduces and analyses new areas of game theory such as "evolutionary games" and "Psychological games"
Retaining the most popular features from the original edition, this latest version offers improved pedagogy, new questions for discussion, new chapters on the latest developments as well as a host of new examples. A new generation of students of game theory will grow to appreciate this superb text whilst fans of the first edition will eagerly devour this long-awaited update.

The book is a collection of contributed papers in honor of Roy Radner. Reflecting Radner's broad range of research interests, the papers cover quite diverse areas, ranging over general equilibrium analysis of the market mechanism, economies undergoing transition, satisficing behavior, markets with asymmetric information, organizational resource allocation and information processing, incentives and implementation, stable sets and the core, stochastic sequential bargaining games, perfect equilibria in a macro growth model, repeated games, and evolutionary games.

Optimization plainly dominates the design, planning, operation, and c- trol of engineering systems. This is a book on optimization that considers particular cases of optimization problems, those with a decomposable str- ture that can be advantageously exploited. Those decomposable optimization problems are ubiquitous in engineering and science applications. The book considers problems with both complicating constraints and complicating va- ables, and analyzes linear and nonlinear problems, with and without in- ger variables. The decomposition techniques analyzed include Dantzig-Wolfe, Benders, Lagrangian relaxation, Augmented Lagrangian decomposition, and others. Heuristic techniques are also considered. Additionally, a comprehensive sensitivity analysis for characterizing the solution of optimization problems is carried out. This material is particularly novel and of high practical interest. This book is built based on many clarifying, illustrative, and compu- tional examples, which facilitate the learning procedure. For the sake of cl- ity, theoretical concepts and computational algorithms are assembled based on these examples. The results are simplicity, clarity, and easy-learning. We feel that this book is needed by the engineering community that has to tackle complex optimization problems, particularly by practitioners and researchersinEngineering, OperationsResearch, andAppliedEconomics.The descriptions of most decomposition techniques are available only in complex and specialized mathematical journals, di?cult to understand by engineers. A book describing a wide range of decomposition techniques, emphasizing problem-solving, and appropriately blending theory and application, was not previously availabl

Networks of Learning Automata: Techniques for Online Stochastic Optimization is a comprehensive account of learning automata models with emphasis on multiautomata systems. It considers synthesis of complex learning structures from simple building blocks and uses stochastic algorithms for refining probabilities of selecting actions. Mathematical analysis of the behavior of games and feedforward networks is provided. Algorithms considered here can be used for online optimization of systems based on noisy measurements of performance index. Also, algorithms that assure convergence to the global optimum are presented. Parallel operation of automata systems for improving speed of convergence is described. The authors also include extensive discussion of how learning automata solutions can be constructed in a variety of applications.

Practical Goal Programming is intended to allow academics and practitioners to be able to build effective goal programming models, to detail the current state of the art, and to lay the foundation for its future development and continued application to new and varied fields. Suitable as both a text and reference, its nine chapters first provide a brief history, fundamental definitions, and underlying philosophies, and then detail the goal programming variants and define them algebraically. Chapter 3 details the step-by-step formulation of the basic goal programming model, and Chapter 4 explores more advanced modeling issues and highlights some recently proposed extensions.

Chapter 5 then details the solution methodologies of goal programming, concentrating on computerized solution by the Excel Solver and LINGO packages for each of the three main variants, and includes a discussion of the viability of the use of specialized goal programming packages. Chapter 6 discusses the linkages between Pareto Efficiency and goal programming. Chapters 3 to 6 are supported by a set of ten exercises, and an Excel spreadsheet giving the basic solution of each example is available at an accompanying website.

Chapter 7 details the current state of the art in terms of the integration of goal programming with other techniques, and the text concludes with two case studies which were chosen to demonstrate the application of goal programming in practice and to illustrate the principles developed in Chapters 1 to 7. Chapter 8 details an application in healthcare, and Chapter 9 describes applications in portfolio selection.

Network Science, Nonlinear Science and Infrastructure Systems has been written by leading scholars in these areas. Its express purpose is to develop common theoretical underpinnings to better solve modern infrastructural problems. It is felt by many who work in these fields that many modern communication problems, ranging from transportation networks to telecommunications, Internet, supply chains, etc., are fundamentally infrastructure problems. Moreover, these infrastructure problems would benefit greatly from a confluence of theoretical and methodological work done with the areas of Network Science, Dynamical Systems and Nonlinear Science. This book is dedicated to the formulation of infrastructural tools that will better solve these types of infrastructural problems.

A collection of articles summarizing the state of knowledge in a large portion of modern homotopy theory. This welcome reference for many new results and recent methods is addressed to all mathematicians interested in homotopy theory and in geometric aspects of group theory.

The topology optimization method solves the basic engineering problem of distributing a limited amount of material in a design space. The first edition of this book has become the standard text on optimal design, which is concerned with the optimization of structural topology, shape and material. This edition has been substantially revised and updated to reflect progress made in modelling and computational procedures. It also encompasses a comprehensive and unified description of the state of the art of the so-called material distribution method, based on the use of mathematical programming and finite elements. Applications treated include not only structures but also MEMS and materials.