Book Description

Game Theory--the formal modelling of conflict and cooperation--first emerged as a recognized field with the publication of John von Neumann and Oskar Morgenstern's Theory of Games and Economic Behaviour in 1944. Since then, game-theoretic thinking about choice of strategies and the interdependence of people's actions has influenced all the social sciences. However, little is known about the history of the theory of strategic games prior to this publication.

In this volume, the history of strategic games--from its origins up to 1945--is traced through the work of 19th Century economists such as Cournot andEdgeworth; voting theorists, including Lewis Carroll; conflict theorists Richardson and Lanchester; probabilists such as Bertrand, Borel, and Ville; and later economists, notably Stackelberg and Zeuthen. This authoritative account of the history of game theory concludes with a historical perspective on the achievement of von Neumann and Morgenstern and an appraisal of the reception of their book. ... Read more

Book Description

This book provides an integrated treatment of the theory of nonnegative matrices and some related classes of positive matrices, concentrating on connections with game theory, combinatorics, inequalities, optimization and mathematical economics. The authors have chosen the wide variety of applications, which include price fixing, scheduling, and the fair division problem, both for their elegant mathematical content and for their accessibility to students with minimal preparation. They present many new results in matrix theory for the first time in book form, while they present more standard topics in a novel fashion.The treatment is rigorous and almost all results are proved completely. These new results and applications will be of great interest to researchers in linear programming, statistics, and operations research.The minimal prerequisites also make the book accessible to first year graduate students. ... Read more

Book Description

This book should be considered as an introduction to a specialclass of hierarchical systems of optimal control, where subsystems aredescribed by partial differential equations of various types.Optimization is carried out by means of a two-level scheme, where thecenter optimizes coordination for the upper level and subsystems findthe optimal solutions for independent local problems. The mainalgorithm is a method of iterative aggregation. The coordinator solvesthe problem with macrovariables, whose number is less than the numberof initial variables. On the lower level, we have the usual optimalcontrol problems of mathematical physics, which are far simpler thanthe initial statements. Thus, we bridge the gap between twodisciplines: optimization theory of large-scale systems andmathematical physics. The first motivation was a special model ofbranch planning, where the final product obeys a precept assortmentrelation. Audience: The monograph is addressed to specialists inoperations research, optimization, optimal control, and mathematicalphysics. ... Read more

Book Description

This book covers algorithms and discretization procedures for the solution of nonlinear progamming, semi-infinite optimization and optimal control problems. Among the important features included are the theory of algorithms represented as point-to-set maps, the treatment of min-max problems with and without constraints, the theory of consistent approximation which provides a framework for the solution of semi-infinite optimization, optimal control, and shape optimization problems with very general constraints, using simple algorithms that call standard nonlinear programming algorithms as subroutines, the completeness with which algorithms are analysed, and chapter 5 containing mathematical results needed in optimization from a large assortment of sources.

Readers will find of particular interest the exhaustive modern treatment of optimality conditions and algorithms for min-max problems, as well as the newly developed theory of consistent approximations and the treatment of semi-infinite optimization and optimal control problems in this framework.

This book presents the first treatment of optimization algorithms for optimal control problems with state-trajectory and control constraints, and fully accounts for all the approximations that one must make in their solution.It is also the first to make use of the concepts of epi-convergence and optimality fuctions in the construction of consistent approximations to infinite dimensional problems.

Graduate students, university teachers and optimization practitioners in applied mathematics, engineering and economics will find this book useful. ... Read more

Reviews (2)

Optimization : Algorithms and Consistent Approximations
A good book on an important subject!

superbly written ... work of art.
Develops a powerful algorithmic and implementable framework for solving finite and semi-infinite nonlinear optimization problems with a special emphasis on min-max optimization problems. ... Read more

Book Description

The topology of global optimization is treated in detail (Morse Theory, Karush--Kuhn--Tucker points, Chebyshev Approximation). Moreover, three further basic subjects in nonlinear optimization are treated: Stability and sensitivity, gradient- and Newton's differential equations and, finally, parametric aspects.

Audience: Researchers and graduate students working in optimization and operations research. ... Read more

Book Description

The book investigates bargaining between two agents. It presents the history of bargaining analysis from Francis Y. Edgeworth's first formal study, followed by cooperative and noncooperative game-theoretic models, to recent stochastic evolutionary investigations. Connections between the results obtained by different methodology are highlighted. The established theory is generalized with respect to its underlying rationality assumptions. Links between usually neglected psychological factors - e.g. the persistence and capriciousness of an agent - and average bargaining success are identified. Applications of bargaining models contribute to the measurement of decision power and to the discussion of distributive justice. ... Read more

Book Description

This book provides the fundamentals of dynamic optimization which can be used to improve the performance of engineering systems. Most results are derived using the theory of calculus of variations. The methods are illustrated by a number of examples. Numerical implementation of the theory by direct and indirect methods is also described. Computer programs are provided that can be used to work out engineering problems. The book also introduces some new results in dynamic optimization using higher-order approaches. The book is appropriate for undergraduate seniors or first-year graduate students. It should also be of interest to professionals in the areas of automotive, aerospace, or manufacturing engineering. Students and researchers in the areas of systems theory, control, and optimization will benefit from the relatively simple exposition in this book. ... Read more

Book Description

Covering all the essential topics for undergraduate courses, this is the ideal student introduction to game theory. It sets out the basics of the subject in a non-technical way and uses illustrations and examples to show its application to realistic, topical, and interesting problems ranging from strategic decision-making within companies to international environmental policy-making. All explanation is clear, well structured, and entirely accessible to students of both economics and business. ... Read more

Book Description

The book consists of research papers based on results presentedat a conference held in Sweden to celebrate Hoang Tuy's achievementsin Optimization. The collection is dedicated to Professor Tuy on theoccasion of his 70th birthday. The papers appear in alphabetical order by first author and cover awide range of recent results in Mathematical Programming. The work ofHoang Tuy, in particular in Global Optimization, has provideddirections for new algorithmic developments in the field. Audience: Faculty, graduate students, and researchers inmathematical programming, computer science and engineering. ... Read more

Book Description

The aim of the book is to cover the three fundamental aspects of research in equilibrium problems: the statement problem and its formulation using mainly variational methods, its theoretical solution by means of classical and new variational tools, the calculus of solutions and applications in concrete cases. The book shows how many equilibrium problems follow a general law (the so-called user equilibrium condition). Such law allows us to express the problem in terms of variational inequalities. Variational inequalities provide a powerful methodology, by which existence and calculation of the solution can be obtained. Audience: Advanced students and researchers. ... Read more

Book Description

Computational Optimization: A Tribute to Olvi Mangasarianserves as an excellent reference, providing insight into some of themost challenging research issues in the field. This collection of papers covers a wide spectrum of computationaloptimization topics, representing a blend of familiar nonlinearprogramming topics and such novel paradigms as semidefiniteprogramming and complementarity-constrained nonlinear programs. Manynew results are presented in these papers which are bound to inspirefurther research and generate new avenues for applications. Aninformal categorization of the papers includes: Algorithmic advances for special classes of constrainedoptimization problems Analysis of linear and nonlinear programsAlgorithmic advances B- stationary points of mathematicalprograms with equilibrium constraints Applications ofoptimization Some mathematical topics Systems of nonlinearequations. ... Read more

Book Description

An important branch of marketing science is optimal planning of marketing effort, using mathematical modelling and quantitative methods. Here it is important to recognize that the majority of marketing problems are dynamic and involve strategic considerations. Thus, most marketing instruments have impacts that go beyond the current period and the choice of a firm's marketing instruments will affect its competitors.Game theory has proven useful to represent and conceptualize problems of conflict and cooperation in a formal way, and to predict the outcome of such situations. Differential games are dynamic games that are particularly designed to study systems where observations and decisions are made in real time.The book conveys to the reader the state of the art of research in marketing applications of differential game theory. This research started about 25 years ago and the literature has now reached an extent and a maturity that makes it natural to take stock.The book deals with differential games in advertising, pricing, and marketing channels, as well as with marketing-production and pricing-advertising interfaces. It provides also a tutorial on main concepts in differential games. ... Read more

Book Description

In many decision processes there is an hierarchy of decision-makers and decisions are taken at different levels in this hierarchy. Multilevel programming focuses on the whole hierarchy structure. In terms of modeling, the constraint domain associated with a multilevel programming problem is implicitly determined by a series of optimization problems which must be solved in a predetermined sequence. The field of multilevel optimization has become a well-known and important research field. Hierarchical structures can be found in scientific disciplines such as environment, ecology, biology, chemical engineering, mechanics, classification theory, databases, network design, transportation, game theory and economics. Moreover, new applications are constantly being introduced. This has stimulated the development of new theory and efficient algorithms. This volume contains 16 chapters written by various leading researchers and presents a cohesive authoritative overview of developments and applications in their emerging field of optimization.Audience: Researchers whose work involves the application of mathematical programming and optimization to hierarchical structures. ... Read more

Book Description

Vanderschraaf develops a new theory of game theory equilibrium selection in this book. The new theory defends general correlated equilibrium concepts and suggests a new analysis of convention. ... Read more

Reviews (3)

A MUST have!!
I laughed, I cried, I bought three copies. This is one of the most enlightening book you will ever read, please buy as many copies as you can. I have to say he is one of the greatest future brother in laws I can ask for. Great job Pete!

Learning and Coordination: Inductive Deliberation, Equilibri
The author does a great job at making the subject matter clear and understandable. I highly recommend this book.

The most amazing book on this subject I've ever read!
Wow! I can't beleive it. Dr. Vanderschraaf really gets your attention and never lets go throughout the entire book. What a page turner!! I just know that I won't be able to just read this one just once. It's really amazing, and you won't believe the ending! I don't want to spoil it, but be prepared for a major surprise. Kudos to this fine author! He really takes the subject and delivers it to the common reader. Great read! ... Read more

Book Description

Hardbound. This classic work by the late Stefan Banach has been translated into English so as to reach a yet wider audience. It contains the basics of the algebra of operators, concentrating on the study of linear operators, which corresponds to that of the linear forms a1x1 + a2x2 + ... + anxn of algebra.

The book gathers results concerning linear operators defined in general spaces of a certain kind, principally in Banach spaces, examples of which are: the space of continuous functions, that of the pth-power-summable functions, Hilbert space, etc. The general theorems are interpreted in various mathematical areas, such as group theory, differential equations, integral equations, equations with infinitely many unknowns, functions of a real variable, summation methods and orthogonal series.

A new fifty-page section (``Some Aspects of the Present Theory of Banach Spaces'') compl ... Read more

Reviews (1)

Sheldon Axler's review

In 1932 Banach published his famous book Théorie des Opérations Linéaires, based on his Polish version published a year earlier. Remarkably, Théorie des Opérations Linéaires remains in print today more than six decades after its original publication, partly because of its historic value as the first monograph on functional analysis but also because of the clean, modern style with which Banach presents the fundamentals of the subject (as created in good part by him and his collaborators). While a graduate student, I read Théorie des Opérations Linéaires to study for my French exam. I remember the thrill of seeing functional analysis developed by a legendary hero of twentieth century mathematics and my delight in his extraordinarily clear writing. I also remember my amusement that what we today call "Banach spaces" are called "spaces of type (B)" in Banach's book. ... Read more

Book Description

This volume contains the edited texts of the lectures presented at the Workshop on Nonlinear Optimization held in Erice, Sicily, at the `G. Stampacchia' School of Mathematics of the `E. Majorana' Centre for Scientific Culture, June 23--July 2, 1998. In the tradition of these meetings, the main purpose was to review and discuss recent advances and promising research trends concerning theory, algorithms and innovative applications in the field of nonlinear optimization, and of related topics such as convex optimization, nonsmooth optimization, variational inequalities and complementarity problems. ... Read more

Book Description

Game Theory and Applications outlines game theory and proves its validity by examining it alongside the neoclassical paradigm. This book contends that the neoclassical theory is the exceptional case, and that game theory may indeed be the rule. The papers and abstracts collected here explore its recent development and suggest new research directions.

Key Features
* Explains many of the recent central developments in game theory
* Highlights new research directions in economic theory which surpass the neoclassical paradigm
* Includes game-theoretical analyses in economics, political science, and biology
* Written by leading game theorists, economists, political scientists, and biologists ... Read more