Book Description

Chapters in Game Theory has been written on the occasion of the 65th birthday of Stef Tijs, who can be regarded as the godfather of game theory in the Netherlands. The contributors all are indebted to Stef Tijs, as former Ph.D. students or otherwise. The book contains fourteen chapters on a wide range of subjects. Some of these can be considered surveys while other chapters present new results: most contributions can be positioned somewhere in between these categories. The topics covered include: cooperative stochastic games; noncooperative stochastic games; sequencing games; games arising form linear (semi-) infinite programming problems; network formation, costs and potential games; potentials and consistency in transferable utility games; the nucleolus and equilibrium prices; population uncertainty and equilibrium selection; cost sharing; centrality in social networks; extreme points of the core; equilibrium sets of bimatrix games; game theory and the market; and transfer procedures for nontransferable utility games. Both editors did their Ph.D with Stef Tijs, while he was affiliated with the mathematics department of the University of Nijmegen. ... Read more

Book Description

Meta-heuristics have developed dramatically since their inception in the early 1980s. They have had widespread success in attacking a variety of practical and difficult combinatorial optimization problems. These families of approaches include, but are not limited to greedy random adaptive search procedures, genetic algorithms, problem-space search, neural networks, simulated annealing, tabu search, threshold algorithms, and their hybrids. They incorporate concepts based on biological evolution, intelligent problem solving, mathematical and physical sciences, nervous systems, and statistical mechanics. Since the 1980s, a great deal of effort has been invested in the field of combinatorial optimization theory in which heuristic algorithms have become an important area of research and applications.This volume is drawn from the first conference on Meta-Heuristics and contains 41 papers on the state-of-the-art in heuristic theory and applications. The book treats the following meta-heuristics and applications: Genetic Algorithms, Simulated Annealing, Tabu Search, Networks & Graphs, Scheduling and Control, TSP, and Vehicle Routing Problems. It represents research from the fields of Operations Research, Management Science, Artificial Intelligence and Computer Science. ... Read more

Book Description

Dynamic game theory has found applications in almost every scientific discipline that uses mathematical modeling tools to investigate ideas and solve problems. Growing from a rich assortment of theoretical concepts, applications abound to other areas of mathematics as well as to economics, biology, management science, engineering and many other fields of study. The papers included in this volume demonstrate this diversity in dynamical games, both with respect to theory and applications and are grouped in five areas: -Zero-sum games: minimax control - H-infinity aspects, incomplete (deterministic) information, problems with slow and fast dynamics -Zero-sum games: pursuit evasion - Air control problems, relationship with symbolic programming, neural networks - Zero-sum games: solution methods - Numerical approaches via clever discretization schemes and viscosity solutions - Nonzero-sum games: theory - Turnpike theorems, Riccati equations for Nash solutions, dynamic bargaining, cooperative games - Nonzero-sum games: applications - economic, management, and biological games

Research workers and graduate students will find in this volume a rich source of ideas and information relating to their work and study in dynamic games. ... Read more

Book Description

This compact book, through the simplifying perspective it presents, will take a reader who knows little of interior-point methods to within sight of the research frontier, developing key ideas that were over a decade in the making by numerous interior-point method researchers. It aims at developing a thorough understanding of the most general theory for interior-point methods, a class of algorithms for convex optimization problems. The study of these algorithms has dominated the continuous optimization literature for nearly 15 years. In that time, the theory has matured tremendously, but much of the literature is difficult to understand, even for specialists. By focusing only on essential elements of the theory and emphasizing the underlying geometry, A Mathematical View of Interior-Point Methods in Convex Optimization makes the theory accessible to a wide audience, allowing them to quickly develop a fundamental understanding of the material.

The author begins with a general presentation of material pertinent to continuous optimization theory, phrased so as to be readily applicable in developing interior-point method theory. This presentation is written in such a way that even motivated Ph.D. students who have never had a course on continuous optimization can gain sufficient intuition to fully understand the deeper theory that follows. Renegar continues by developing the basic interior-point method theory, with emphasis on motivation and intuition. In the final chapter, he focuses on the relations between interior-point methods and duality theory, including a self-contained introduction to classical duality theory for conic programming; an exploration of symmetric cones; and the development of the general theory of primal-dual algorithms for solving conic programming optimization problems.

Rather than attempting to be encyclopedic, A Mathematical View of Interior-Point Methods in Convex Optimization gives the reader a solid understanding of the core concepts and relations, the kind of understanding that stays with a reader long after the book is finished. ... Read more

Reviews (1)

A simplifying perspective of IPM's in Convex Optimization
At last, we find a book which develops a thorough understanding
of the most general theory of interior point methods for
convex optimization, and is easily accessible. As the author
himself remarks "Much of the literature on the general
theory of interior point methods is difficult to understand,
even for specialists. My hope is that this book will make
the most general theory accessible to a wide audience -
especially Ph.D. students, the next generation of optimizers".
The book covers basic interior point theory including
the theory of self concordant functionals. There is a chapter
on conic programming covering the relationship between interior point
methods and duality theory, and the development
of primal dual interior point algorithms for solving conic
optimization problems (Conic programming includes linear,
semidefinite and second order cone programming as special
cases!).

One can then "perhaps" take on Nesterov and Nemirovskii's
seminal treatise on Interior Point Polynomial Algorithms
in Convex Programming, one of the most widely cited references
in optimization, which I must confess is not exactly
an easy read.

To summarize, conic optimization and efficient interior point
methods to solve them are certainly one of the most exciting
areas in optimization recently, and Renegar's excellent,
intuitive and short book is a welcome addition to the
bookshelf of any serious optimizer!. Strongly recommended! ... Read more

Book Description

"This comprehensive and immensely readable volume takes the reader to the cutting edge of the field. Like the conference from which it stems, the book has extremely broad coverage in terms of the topics addressed, the disciplines from which the authors come and to which their papers contribute, and the geographic sites of origin of the ideas and findings. The conference presentations, of a high quality in their initial form, have been wonderfully crafted by the authors with the excellent guidance of the editors. It is a timely addition to the literature and belongs on every gamer's bookshelf." --Cathy Stein Greenblat, Professor of Sociology, Rutgers University, New Jersey With contributions from leading international researchers in simulation and gaming, this book provides readers with up-to-date coverage of simulation and gaming as a professional endeavor rather than just as a set of subject-relevant techniques. Organized into four parts (applications, policy exercises, research, and professional matters), the book covers such topics as the application of simulation/games to specific purposes (such as international conflict, citizen participation, etc.); research in the areas of business performance and discourse analysis; and debriefing, ethics, and the state of simulation/gaming in various countries. Simulation and Gaming Across Disciplines and Cultures offers readers a cohesive picture of the breadth and richness of the field of simulation and gaming. ... Read more

Book Description

Containing detailed references, appendices, questions and answers, this book uses algebra, geometry, combinatorics, number theory, graph theory, and other branches of mathematics to tell a player how to win, or not to lose, mathematical games. It covers solitaires, games for two players, a theory of games, and rankings. For sophisticated mathematicians as well as aspiring mathematicians. ... Read more

Book Description

This book brings together papers of well-known specialists in game theory and adjacent problems. It presents the basic results in dynamic games, stochastic games, applications of game theoretical methods in ecology and economics and methodological aspects of game theory. ... Read more

Book Description

Statistics help guide us to optimal decisions under uncertainty. A large variety of statistical problems are essentially solutions to optimization problems. The mathematical techniques of optimization are fundamentalto statistical theory and practice. In this book, Jagdish Rustagi provides full-spectrum coverage of these methods, ranging from classical optimization and Lagrange multipliers, to numerical techniques using gradients or direct search, to linear, nonlinear, and dynamic programming using the Kuhn-Tucker conditions or the Pontryagin maximal principle. Variational methods and optimization in function spaces are also discussed, as are stochastic optimization in simulation, including annealing methods.
The text features numerous applications, including:
Finding maximum likelihood estimates
Markov decision processes
Programming methods used to optimize monitoring of patients in hospitals
Derivation of the Neyman-Pearson lemma
The search for optimal designs
Simulation of a steel mill
Suitable as both a reference and a text, this book will be of interest to advanced undergraduate or beginning graduate students in statistics, operations research, management and engineering sciences, and related fields. Most of the material can be covered in one semester by students with a basic background in probability and statistics.

Key Features
* Covers optimization from traditional methods to recent developments such as Karmarkars algorithm and simulated annealing
* Develops a wide range of statistical techniques in the unified context of optimization
* Discusses applications such as optimizing monitoring of patients and simulating steel mill operations
* Treats numerical methods and applications
Includes exercises and references for each chapter
* Covers topics such as linear, nonlinear, and dynamic programming, variational methods, and stochastic optimization ... Read more

Book Description

This book is dedicated to Jack Edmonds in appreciation of his ground breaking work that laid the foundations for a broad variety of subsequent results achieved in combinatorial optimization. The main part consists of 13 revised full papers on current topics in combinatorial optimization, presented at Aussois 2001, the Fifth Aussois Workshop on Combinatorial Optimization, March 5-9, 2001, and dedicated to Jack Edmonds. Additional highlights in this book are an account of an Aussois 2001 special session dedicated to Jack Edmonds including a speech given by William R. Pulleyblank as well as newly typeset versions of three up-to-now hardly accessible classical papers: - Submodular Functions, Matroids, and Certain Polyhedra   by Jack Edmonds - Matching: A Well-Solved Class of Integer Linear Programs   by Jack Edmonds and Ellis L. Johnson - Theoretical Improvements in Algorithmic Efficiency for Network Flow Problems   by Jack Edmonds and Richard M. Karp. ... Read more

Book Description

Issues relating to the emergence, persistence, and stability of cooperation among social agents of every type are widely recognized to be of paramount importance. They are also analytically difficult and intellectually challenging. This book, arising from a NATO Advanced Study Institute held at SUNY in 1994, is an up-to-date presentation of the contribution of game theory to the subject. The contributors are leading specialists who focus on the problem from the many different angles of game theory, including axiomatic bargaining theory, the Nash program of non-cooperative foundations, game with complete information, repeated and sequential games, bounded rationality methods, evolutionary theory, experimental approaches, and others. Together they offer significant progress in understanding cooperation. ... Read more

Book Description

Strategic interaction occurs whenever it depends on others what one finally obtains: on markets, in firms, in politics etc. Game theorists analyse such interaction normatively, using numerous different methods. The rationalistic approach assumes perfect rationality whereas behavioral theories take into account cognitive limitations of human decision makers. In the animal kingdom one usually refers to evolutionary forces when explaining social interaction. The volume contains innovative contributions, surveys of previous work and two interviews which shed new light on these important topics of the research agenda. The contributions come from highly regarded researchers from all over the world who like to express in this way their intellectual inspiration by the Nobel-laureate Reinhard Selten. ... Read more

Book Description

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. ... Read more

Book Description

This new book, organized by editors representing a wide degree of interests in dynamic games, is aimed at control engineers, applied mathematicians, operations research specialists, and research workers.

It contains survey papers on such diverse topics as pursuit-evasion games, viscosity solutions, gambling theory, discounted stochastic games, optimal routing, numerical methods, and others. The volume consists of two parts, with the first dealing with zero-sum differential games and numerical methods, and the second with stochastic and nonzero-sum games, and applications.

Topics and Features:

state-of-the-art surveys, new results, and algorithms.viscosity solutions.gambling theory and stochastic games.optimal routing.viability kernel algorithm and discriminating kernal algorithm.

Researchers, professionals and advanced graduate students will find the book an essential resource for current work in dynamic games and applications. ... Read more