Book Description

This book is on applications of game theory. It contains a lot of examples of applications of game theory together with the background of those games considered and a list of unsolved problems. Also we consider only the game where the optimal strategies of the players are found in closed form. For example, the following games are investigated: (a) games of protection of a channel from infiltration of a submarine, (b) the submarine versus helicopter game, (c) the matrix search games, (d) allocation search and economics games, where players face up an alternative either not to come into contest if the cost of efforts seems too high, or come into it, (e) dynamic infiltration games where the infiltrator tries to penetrate zone uncaught, (f) duels and (g) parlour games. ... Read more

Book Description

Book Description

Concepts similar to fuzzy measure have been introduced independently in many domains: in non-expected utility theory, cooperative game theory, complexity analysis, measure theory, etc. This book reflects all these facets. It gathers survey papers written by leading researchers in the field, covering a selection of most significant topics. The first part is devoted to fundamental and theoretical material, while the second part deals with more applied topics such as decision making and pattern recognition. The book is of interest to researchers in decision making, artificial intelligence, applied mathematics, mathematical social sciences, etc. ... Read more

Book Description

Most of the books in optimization are devoted to details of one or two aspect of the subject e.g. linear and nonlinear programming, stochastic programming, optimal control, stochastic dynamic programming, mixed integer programming, heuristic methods, or multi-objective programming etc., or are written for a specific discipline. The wide scope of optimization mandates extensive interaction between various disciplines in the development of the methods and algorithms, and in their fruitful application to real world problems. This book presents a discipline independent view of optimization for scientists, researchers, and analysts in various fields. It provides them opportunities to identify and apply algorithms, methods and tools from the diverse areas of optimization to their own field without getting into too much detail about the underlying theories.Audience: Researchers in various fields as well as undergraduate and graduate students in engineering, sciences, management science, and decision science. ... Read more

Book Description

This is a textbook for a course in the theory of games. It is intended for advanced undergraduates and graduate students in mathematics and other quantitative disciplines, e.g., statistics, operations research, etc. It treats the central topics in game theory and is meant to give students a basis from which they can go on to more advanced topics. The subject matter is approached in a mathematically rigorous way, but , within this constraint, an effort is made to keep it interesting and lively. New definitions and topics are motivated as thoroughly as possible. The mathematical prerequisites for understanding the book are modest: basic probability together with a little calculus and linear algebra.

Among others, two topics of great current interest are discussed in this book. The idea of iterated Prisoner's Dilemma (super games) is considered. It is specially of great interest to biologists, sociologists and others who use it in studying the evolution of cooperative behavior both in nature and in human society. Also covered are challenging game-playing computer programs. ... Read more

Reviews (2)

A good read, and I learned something.
This is an enjoyable book even if you don't know much about mathematics. I took it with me to Capri last summer, and got a sunburn when I was too absorbed in the text to move into the shade! The plot moves quickly, there are plenty of interesting characters and exotic locales, and though the equations can be hard to follow (for me, anyway!), the author never lets you get bogged down in them. Like Lewis Carroll, another author/mathematician, Morris knows how to make you think without realizing you're thinking. That sounds like exalted company, but I, for one, am anxious for the sequel.

An excellent book to be used in introductory courses of GT
Though it is an excellent introductory book to be used in Game Theory courses, it is not suggested for self study in case the reader lacks on a mathematics background. The provided material seems to be the result of the author's hard work on issues related to teaching GT. The final chapter devoted to Programming algorithms and techniques sounds more as an addendum or appendix, than as a "sine qua non" component of the book. Adamantios Koumpis BSc in Computer Science Institute of Computer Science, Foundation for Research and Technology-Hellas Crete, Greece ... Read more

Book Description

The ideal primer for those deterred by the technical nature of many textbooks, this title provides a clear explanation for the enduring popularity of game theory and its increasing centralityto the teaching of economics. ... Read more

Book Description

This monograph is the first book in the study of necessary conditions of an extremum in which topological connectedness plays a major role. Many new and original results are presented here. The synthesis of the well-known Dybrovitskii--Milyutin approach, based on functional analysis, and topological methods permits the derivation of the so-called alternative conditions of an extremum: if the Euler equation has the trivial solution only at an extreme point, then some inclusion is valid for the functionals belonging to the dual space. Also, the present approach gives a transparent answer to the question why the Kuhn--Tucker theorem establishes the restrictions on the signs of the Lagrange multipliers for the inequality constraints but why this theorem does not establish any analogous restrictions on the multipliers for the equality constraints.Examples from mathematical economics illustrate the alternative conditions of any extremum. Parallels are drawn between these examples and the problems of static equilibrium in classical mechanics.Audience: This volume will be of use to mathematicians and graduate students interested in the areas of optimization, optimal control and mathematical economics. ... Read more

Book Description

From whatever domain they come, engineers are faced daily with optimization problems that requires conflicting objectives to be met. This monograph systematically presents several multiobjective optimization methods accompanied by many analytical examples. Each method or definition is clarified, when possible, by an illustration. Multiobjective Optimization treats not only engineering problems, e.g in mechanics, but also problems arising in operations research and management. It explains how to choose the most suitable method to solve a given problem and uses three primary application examples: optimization of the numerical simulation of an industrial process; sizing of a telecommunication network; and decision-aid tools for the sorting of bids. This book is intended for engineering students, and those in applied mathematics, algorithmics, economics (operational research), production management, and computer scientists. ... Read more

Reviews (1)

A long awaited book
The importance of multiobjective optimization is significantly increasing in biology, economy etc... An updated introductory book is long overdue. The problem is it has disappeared shortly after it has been published!! ... Read more

Book Description

Genetic Algorithms (GAs) have become a highly effective tool for solving hard optimization problems. As their popularity has increased, the number of GA applications has grown in more than equal measure. Genetic Algorithm theory, however, has not kept pace with the growing use and application of GAs. Most book-length treatments of GAs provide only a cursory discussion of theory and this discussion primarily focuses on the traditional view, which depends heavily on the concept of a "schema".Genetic Algorithms: Principles and Perspectives: A Guide to GA Theory is a survey of some important theoretical contributions, many of which have been proposed and developed in the Foundations of Genetic Algorithms series of workshops. However, this theoretical work is still rather fragmented, and the authors believe that it is the right time to provide the field with a systematic presentation of the current state of theory in the form of a set of theoretical perspectives. The authors do this in the interest of providing students and researchers with a balanced foundational survey of some recent research on GAs. The scope of the book includes chapter-length discussions of Basic Principles, Schema Theory, "No Free Lunch", GAs and Markov Processes, Dynamical Systems Model, Statistical Mechanics Approximations, Predicting GA Performance, Landscapes and Test Problems.The authors have worked hard to make the book as accessible as possible for students and researchers. An undergraduate-level mathematical understanding of linear algebra and stochastic processes is assumed. For those readers who have not encountered GAs before, a comprehensive survey of GA concepts is provided and the variety of ways in which GAs can be implemented is outlined. Exercises are provided at the ends of the chapters with the express purpose of aiding understanding of the concepts discussed and to whet the reader's appetite for pursuing theoretical research in GAs. ... Read more

Book Description

The IMA Workshop on Evolutionary Algorithms brought together many of the top researchers in the area of Evolutionary Computation for a week of intensive interaction. The field of Evolutionary Computation has developed significantly over the past 30 years and today consists of a variety of subfields such as genetic algorithms, evolution strategies, evolutionary programming, and genetic programming, each with its own algorithmic perspectives and goals. The workshop did a great deal to clarify the current state of the theory of Evolutionary Algorithms. The existing theory might be characterized as deriving from two principal approaches. There is a high level macro-theory that looks at the processing of "building blocks" and "schemata" that are shared by many good solutions when searching a problem space. There is also a low level micro-theory that builds exact Markov models of the search process. It is sometimes hard for researchers working at such different levels of abstraction to interact. The IMA workshop allowed researchers working at these different levels to present their points of view and to move toward common ground. There was real progress in communication between theorists and practitioners in the evolutionary computation field. Speakers presented applications across a wide range of problem areas. In some of those cases, theoretically motivated methods work quite well. In other cases, practitioners used domain-based methods to obtain better performance than could be achieved by using a "pure" evolutionary algorithm. Individuals on both sides went away with a better appreciation of the successes and failures of current theory. ... Read more

Book Description

A collection of work from top researchers in the field, this book covers all aspects of self-similar network traffic. Readers will gain a better understanding of these networks through a broad introduction to the topic, as well as suggestions for future research. ... Read more

Reviews (3)

Good compilation of recent results in the field
This book is a compilation of articles written for the performance analyst and network modeler who is needing an overview of the recent results in this area. The book does include articles on both the theoretical and experimental results in self-similar network traffic and this makes it useful from a model validation viewpoint. Each article also has numerous up-to-date references for the reader who needs more in-depth information. The first article gives a general overview of the subject along with relevant definitions for those who may be approaching it for the first time. Theorems are stated but not proved but references are given for the proofs. Wavelets are discussed in Chapter 2; the most useful part of this chapter is the discussion on how to generate fractional Brownian motion time series using wavelet expansions. Chapter 3 gives a very quick overview of network simulations with heavy-tailed distributions. This chapter is a little disappointing in that the authors do not discuss how to deal with heavy-tailed distributions (with their large moments) computationally. This is important for developing network simulations and models using these distributions.A discussion of approximations of heavy-tailed distributions by other more manageable distributions would have been helpful here. The next chapter talks about fractional Brownian motion and could be viewed as a first glance at the theory of large deviations. The author does a good job of showing that analytical results are available in these kinds of processes. More general results in Gaussian input processes are discussed in Chapter 5, with asymptotics of queue length distributions characterized in some detail. The M/G/1 model is discussed in Chapter 6, where it is assumed that the service time is heavy-tailed. The most interesting part of this chapter is the discussion of the limit theorems. Chapter 7 gives a good overview of performance degradation under heavy-tail sources; the authors show, interestingly, that the expected time for overflow is polynomially fast. The authors in Chapter 8, give asymptotic bounds for the buffer overflow probability given a self-similar source They do take the time to prove many of their results. M/G/Infinity input processes are discussed in Chapter 9 and the authors do a good job of using large deviations to give asymptotic bounds on these kinds of queuing models. In Chapter 10, the author discusses subexponential distributions. These results were very new to me but the author did I think do a good job of explaining them. Queuing with on/off sources is discussed in Chapter 11, and the author derives many of the results using the Mellin transform. Most importantly he does compare his results with simulation experiments. I did not read the next chapter on VBR so I will omit its review. Just perusing though it seems as though the author holds that long-range dependence is irrelevant for VBR. Chapter 13 discusses transient losses and the impact on performance. The authors do a great job of comparing the difference in performance between Markov and long-range dependent processes. Actually the most interesting part of this chapter is the use of integral equations to prove some of the results. The results in Chapter 14 are more practical, where the authors use network simulations to study the problem of file size distributions drawn from heavy-tailed distributions in client-server models. The most useful part of this chapter is the comparison between the UDP and TCP as a moderator of the degradation experienced when self-similarity is increased. The best chapter for me was Chapter 15, which discusses TCP connection arrivals and their self-similar nature. The author does show how to model empirical distributions, particularly the Weibull distribution. I did not read the rest of the chapters so I will omit their review. This book is recommended for those involved in network modeling and performance. It is somewhat expensive, but worth it both as an introduction and as a reference source.

Book for new researchers
Teletraffic Theory was laid the foundation by A.K.Erlang at the beginning of 20 century (1908-1918). It's a voice traffic theory. How do you guess,since then anything changed? Undoubtedly. In the modern networks prevail packet traffic. It gave rise requirement to research new form of one - self-similar. Corresponding measurements, collecting statistics and following investigations was reflected in the papers, articles, projects. And, finally, book is being published. It summarized done work. But this book isn't only summarizing, but also excellent assistant for young researchers, devoting himself to study and development new derection of Teletraffic Theory.

The comprehensive book in the field!
This is one of those books thats very comprehensive and the only one of its kind available in the new area of Self similar traffic modeling in Communication networks.

Self Similar traffic came to view in 1995 after the publishing of the "Self Similar Nature of Ethernet" paper by one of the authors of the book. Since then there have been a number of papers and book articles on self similarity and long range dependence, but not a single book fully devoted to this.

The book is very well organised and is a good handbook for all references to self similar network traffic. The first chapter provides a comprehensive introduction, which also serves as a pointer to the exact material one is looking for his research. The further chapters are well written.

As a graduate student doing research in this field, I find this book very useful. ... Read more

Book Description

An easy-to-read, and enjoyable introduction to game theory! This clearly written book shows readers how to set up and solve games, particularly those in economics and business, using game theory. Gardener's innovative approach helps readers develop strong modeling skills by using proven applications and examples of setups. The book also features a variety of examples, including many from business, politics, economics, and history. ... Read more

Reviews (1)

A must-have to anyone learning the first steps in Game T.
Anybody looking for an easy to read book about game theory, don't search no more, this is the one. It covers all the main subjects of game theory in a very simple way, not sacrificing its technical qualities. It is richly filled with real world examples and all mathematical questions are covered in a step-by-step way. This should be the first text to anyone seriously thinking of learning Game Theory ... Read more

Book Description

This book is a spectacular introduction to the modern mathematical discipline known as the Theory of Games. Harold Kuhn first presented these lectures at Princeton University in 1952. They succinctly convey the essence of the theory, in part through the prism of the most exciting developments at its frontiers half a century ago. Kuhn devotes considerable space to topics that, while not strictly the subject matter of game theory, are firmly bound to it. These are taken mainly from the geometry of convex sets and the theory of probability distributions.

The book opens by addressing "matrix games," a name first introduced in these lectures as an abbreviation for two-person, zero-sum games in normal form with a finite number of pure strategies. It continues with a treatment of games in extensive form, using a model introduced by the author in 1950 that quickly supplanted von Neumann and Morgenstern's cumbersome approach. A final section deals with games that have an infinite number of pure strategies for the two players.

Throughout, the theory is generously illustrated with examples, and exercises test the reader's understanding. A historical note caps off each chapter. For readers familiar with the calculus and with elementary matrix theory or vector analysis, this book offers an indispensable store of vital insights on a subject whose importance has only grown with the years.

Reviews (1)

Be there when the field of game theory was born
Princeton University Press is doing the mathematical world a favor by publishing their annals of mathematics series. It is designed to make available to all some of the seminal papers and lectures in many areas of mathematics. This book contains a republication of the lectures in the introductory theory of games that Harold Kuhn presented to a group of upper level undergraduate and graduate students in 1952. For these reasons, reading them will not only teach you the basic theory of games, but also give you some of the historical perspective on how the theory arose. The level of presentation is just right, and Kuhn does not have the ensuing fifty years of game theory analysis to fall back on in his explanations, so he is very clear in his statements.
The topics are the standard ones for introductory game theory: the representation of a game as a matrix, computation of optimal strategies by employing matrix operations, algorithms used in the analysis of games, strategies for infinite games with decision trees and games with perfect information. None of it was new to me, but it still held my attention, which is a high compliment.
Time has not dimmed the light on these lectures, and this is a book that can still be used in basic game theory classes.

Published in the recreational mathematics e-mail newsletter, reprinted with permission. ... Read more

Book Description

Is Nine-Men's Morris, in the hands of perfect players, a win for white or for black--or a draw? Can king, rook, and knight always defeat king and two knights in chess? What can Go players learn from economists? What are nimbers, tinies, switches, minies? This book deals with combinatorial games, that is, games not involving chance or hidden information. Their study is at once old and young: though some games, such as chess, have been analyzed for centuries, the first full analysis of a nontrivial combinatorial game (Nim) only appeared in 1902. This book deals with combinatorial games, that is, games not involving chance or hidden information. Their study is at once old and young: though some games, such as chess, have been analyzed for centuries, the first full anlaysis of a nontrivial combinatorial game (Nim) only appeared in 1902. The first part of this book will be accessible to anyone, regardless of background: it contains introductory expositions, reports of unusual contest between an angel and a devil. For those who want to delve more deeply, the book also contains combinatorial studies of chess and Go; reports on computer advances such as the solution of Nine-Men's Morris and Pentominoes; and new theoretical approaches to such problems as games with many players.If you have read and enjoyed Martin Gardner, or if you like to learn and analyze new games, this book is for you. ... Read more

Reviews (3)

Fascinating
I don't have read all the book, but I read most of the scientific papers it is composed by. I think they are very interesting and puzzling, on the border line between serious mathematics (game theory and all this stuff) and "recreational math" (like the angel problem). It would be a good read also for people interested in computer games.

great book
This book is full of beatiful work. Every section is an investigation into some combinatorial game, or some idea in combinatorial game theory. Most of the material is clearly presented and all should be accessible to undergrads, but be warned: this is not simple stuff. But, as we all know, beautiful mathematics isn't always simple. The book also includes a section with 52 unsolved problems, which should be of considerable interest to the curious.

MAA Online review
See Ed Sandifer's MAA Online review at: http://www.maa.org/reviews/nochance.htm ... Read more

Reviews (1)

My Optimisation Companion
Practical Optimization Methods - M.Asghar Bhatti

This is my favorite optimisation book. I recommend it to anyone interested in the application of optimisation techniques, in particular for those in industry. This book has been a constant companion in my optimisation adventure and unlike other books; it has helped me firmly establish a solid foundation and understanding on the various optimisation techniques and the theories behind them. Believe me, I can even read those books which I have shelved in the past because they were complicated with too many cryptic mathematical statements. They don't scare me anymore.

Bhatti wisely used Mathematica as the teaching platform and the accompanying OptimizationToolbox software allows one to brush aside the cryptic mathematical statements. The reader can now concentrate on the concepts, relegating the mathematics manipulations to Mathematica and the functions of the OptimisationToolbox. What I like about this book is that it also shows how the Taylor Series, the Quadratic Form and convexity requirements are put into practice to create an iterative scheme to solve a system of non-linear equations. The OptimisationToolbox and the internal Mathematica functions seamlessly pace the reader through the mathematical preliminaries. By the end of Chapter 3, the reader should now be a good shape to go to the more serious stuffs.

Chapter 4 deals with the subject of optimality conditions starting first with the optimality conditions for unconstrained optimisation problems. These conditions, albeit slightly more involved in computation, are essentially the same as the optimality conditions for single variable functions of the high school days. The "slightly involved" computations are those of the Grad (1st Order and Necessary Condition) and the Hessian (2nd Order and Necessary). Mathematica graphics are put to great effect to help visualize the meaning of these conditions.

The additive property of constraints, which was dealt with in graphic detail, extends the earlier ideas behind the optimality conditions for an unconstrained optimisation to that for constrained optimisation problems.

The introduction to Chapter 5 gives an excellent overview of issues in solving unconstrained problems. Basically, all solution schemes covered in this chapter involve two steps. The first step is a simple iterative scheme, which requires a direction and a step length. The second step is a termination condition, taken as when the gradient of objective function, which should be zero at the optimal point, is sufficiently close to within a specified tolerance to zero.

The process of computing the step length in for a particular search direction is known as the line search. The line search methods (including Mathematica algorithms) covered include analytical line search, equal interval search, section search, the Golden Section search, the Quadratic Interpolation Method and the Approximate Line Search based on Amigo's rule.

As for the search direction, one obvious choice would be along the direction of greatest negative change - the Steepest Descent Method. The performance of this method can suffer badly as it zigzag search scheme slows down to a crawl as it approaches the optimal point. One improvement would be to retain some potion of the previous search direction, so the resultant search pattern is not successively perpendicular to each other but somewhere in between. This approach of adding some potion of the previous direction is known as the Conjugate Gradient Method. The two "some previous direction potion" schemes covered and included as Mathematica functions are the Fletcher-Reeves and the Polak-Ribiere schemes. Other numerical methods covered include the Modified Newton and the Quais-Newton Methods. One drawback of latter approach is the computation of the Hessian Matrix at each iteration step. The Quasi-Newton Methods do not require the computation of the Hessian Matrix. Instead they use some inverse Hessian update methods. Two such methods covered are the DFP (Davidon, Fletcher, and Powel) Update and the BFGS (Broyden, Fletcher, Goldfarb, and Shannon) Update. Don't be intimidated by all these jargons, Mathematica functions including graphic functions are provided to provide a step-by-step explanation and presentations of the various concepts are provided.

The section on Linear Programming is extensive, in comparison to other chapters. I was tempted to skim over this LP section because the technique is well known and there are many industry standard LP algorithms on the market so why spend too much time on it. However, my curiosity got the better of me and I must confess that the combination of the accompanying OptimisationToolbox and Mathematica Graphics makes the revision on Linear Programming entertaining and interesting. The section started with an overview of issues involved in solving an underdetermined system of linear equations; going over the Gauss-Jordan, LU decomposition and introduction of slack variables to convert the LP problem into its standard form. The simplex algorithm is introduced in three styles: Simplex Tableau, Basic Simplex and Revised Simplex. The first two simplex styles, as Mathematica functions by the way, are intended to show the sequence of steps of the simplex algorithm. For large problems, however, the above LP methods may take a long time and researchers have developed better search methods such as the interior point method. The interior point method, as its name implies, starts from an interior feasible point and takes appropriate steps alone descent directions towards the optimal point.

Chapters 8 & 9 adequately covered the subject of quadratic programming and constrained nonlinear problems. However, they concentrated only on local optimisation techniques. Inclusion of global optimisation methods such as Simulated Annealing (SA), Genetic Algorithms (GA), Discrete Gradient Methods (DGM), Hooke-Jeeves, Nelder and Mead, and Powell methods would have made the book a complete guide to practical optimisation.

My favorite Optimisation Book - Clear and Useful ... Read more

Book Description

This text, intended for a first course in performance evaluation, provides a self-contained treatment of all aspects of queueing theory. It starts by introducing readers to the terminology and usefulness of queueing theory and continues by considering Markovian queues in equilibrium, Little's law, reversibility, transient analysis and computation, and the M/G/1 queueing system. Subsequent chapters treat the theory of networks of queues and computational algorithms for networks of queues. Stochastic Petri networks, including those whose solutions can be given in product form, are covered in detail. A chapter on discrete-time queueing systems, which are of recent interest, discusses arrival processes, Geom/Geom/m queueing models, and case studies of discrete-time queueing networks arising in industrial applications.This third edition includes a new chapter on current models of network traffic as well as sixteen new homework problems on discrete-time models and a revised and updated set of references. The discussion of network traffic models includes a survey of continuous and discrete time models, a detailed discussion of burstiness, a complete introduction to self-similar traffic and a presentation of solution techniques. Solutions for all of the homework problems in this text are available in a separate volume. ... Read more

Book Description

Edited by three leading figures in the field, this exciting volume presents cutting-edge work in decision theory by a distinguished international roster of contributors. These mostly unpublished papers address a host of crucial areas in the contemporary philosophical study of rationality and knowledge. Topics include causal versus evidential decision theory, game theory, backwards induction, bounded rationality, counterfactual reasoning in games and in general, analyses of the famous common knowledge assumptions in game theory, and evaluations of the normal versus extensive form formulations of complex decision problems. ... Read more