Book Description

This volume presents a collection of papers on game theory dedicated to Michael Maschler. Through his dedication and contributions to game theory, Maschler has become an important figure particularly in the area of cooperative games. Game theory has since become an important subject in operations research, economics and management science. As befits such a volume, the main themes covered are cooperative games, coalitions, repeated games, and a cost allocation games. All the contributions are authoritative surveys of a particular topic, so together they will present an invaluable overview of the field to all those working on game theory problems. ... Read more

Book Description

In recent years game theory has swept through all of the social sciences. Its practioners have great designs for it, claiming that it offers an opportunity to unify the social sciences and that it it the natural foundation of a rational theory of society. Game Theory is for those who are intrigued but baffled by these claims, and daunted by the technical demands of most introductions to the subject. Requiring no more than simple arithmetic, the book: * Traces the origins of Game Theory and its philosophical premises * Looks at its implications for the theory of bargaining and social contract theory * Gives a detailed exposition of all of the major `games' including the famous `prisoner's dilemma' * Analyses cooperative, non cooperative, repeated, evolutionary and experimental games. ... Read more

Book Description

The articles covered in this extraordinary multi-volume set commence game theory from its place in the Enlightenment tradition, through the explosion of literature in the late 1970's, to issues of current and emerging debates. This extensively indexed set will be a valuable reference tool to researchers in sociology and politics, as well as economics. ... Read more

Reviews (1)

Some theoretical papers of a Nobel Prize Winner
This book contains theoretical papers of John C. Harsanyi, published from 1956 through 1980. He was winner of the Nobel Prize in Economics in 1994 (along with John Nash and Reinhard Selten). His contributions to game theory provide a solid basis for dealing with the use of Bayesian methods in economic decision making (that is, basing decisions on subjective assessments of probabilities), and several of the papers presented here provide the theory underlying such methods. Other papers deal with models for bargaining and cooperation in decision making, and they too have been of special importance in applications of game theory in a wide range of contexts, including international negotiation as well as economics. ... Read more

Book Description

This book explains the way in which information and knowledge are treated in contemporary economic theories and, therefore, contributes to our understanding of the importance of the strategic organisation of information and the acquisition of know-how to the behaviour of modern economies. It gathers together contributions of experts on the role of information in the various theories covered: specifically, in system analysis, in game theory, in the 'statistical theory of information', in theories of market pricing, of financial speculation and of bounded rationality decision making, in the evolutionary theory of the firm, in the 'new industrial economics' and in the 'economics of codification'. Economics and Information is divided into three parts. Part One deals with general theories of information. Part Two addresses the role of information in the functioning of markets. Part Three considers the importance of information to the operation of organisations. Conclusions are drawn in Part Four on the implications for the process of economic growth and for economic policies. It, therefore, provides new insights into some of the puzzling features of recent developments in the so called New Economy. ... Read more

Book Description

A major step in differential games is determining an explicit form of the strategies of players who follow a certain optimality principle. To do this, the associated modification of Bellman dynamic programming problems has to be solved; for some differential games this could be Lyapunov functions whose "arsenal" has been supplied by stability theory. This approach, which combines dynamic programming and the Lyapunov function method, leads to coefficient critera, or ratios of the game math model parameters with which optimal strategies of the players not only exist but their analytical form can be specified. In this book coefficient criteria are derived for numerous new and relevant problems in the theory of linear - quadratic multi-player differential games in cases when:
* the player formulate their strategies independently (non co-operative games) and use non-Nash equilibria * the game model recognizes noise, perturbation and other uncertainties of which only their ranges are known (differential games under uncertainty). ... Read more

Book Description

This book presents a carefully selected group of methods for unconstrained and bound constrained optimization problems and analyzes them in depth both theoretically and algorithmically. It focuses on clarity in algorithmic description and analysis rather than generality, and while it provides pointers to the literature for the most general theoretical results and robust software, the author thinks it is more important that readers have a complete understanding of special cases that convey essential ideas. A companion to Kelley’s book, Iterative Methods for Linear and Nonlinear Equations (SIAM, 1995), this book contains many exercises and examples and can be used as a text, a tutorial for self-study, or a reference.

Iterative Methods for Optimization does more than cover traditional gradient-based optimization: it is the first book to treat sampling methods, including the Hooke–Jeeves, implicit filtering, MDS, and Nelder–Mead schemes in a unified way, and also the first book to make connections between sampling methods and the traditional gradient-methods.Thus, readers can experiment with the algorithms in an easy way as well as implement them in other languages. ... Read more

Book Description

The book presents and discusses theoretical and practical developments in the field of optimization. All papers contain new results and the emphasis has been put on the accessibility of each paper for researchers working in optimization. The topics covered in this volume include: - Mathematical programming. - Nonsmooth analysis. - Equilibrium and fixed point theory. - Stochastic programming. - Optimal control. - Global optimization. - Multicriteria optimization. ... Read more

Book Description

In 1984, N. Karmarkar published a seminal paper on algorithmic linear programming. During the subsequent decade, it stimulated a huge outpouring of new algorithmic results by researchers world-wide in many areas of mathematical programming and numerical computation. This book gives an overview of the resulting, dramatic reorganization that has occurred in one of these areas: algorithmic differentiable optimization and equation-solving, or, more simply, algorithmic differentiable programming. The book is aimed at readers familiar with advanced calculus, numerical analysis, in particular numerical linear algebra, the theory and algorithms of linear and nonlinear programming, and the fundamentals of computer science, in particular, computer programming and the basic models of computation and complexity theory.

J.L. Nazareth is a Professor in the Department of Pure and Applied Mathematics at Washington State University. He is the author of two books previously published by Springer-Verlag, DLP and Extensions: An Optimization Model and Decision Support System (2001) and The Newton-Cauchy Framework: A Unified Approach to Unconstrained Nonlinear Minimization (1994). ... Read more

Book Description

Presents the elements of a unified approach to optimization based on "nonsmooth analysis," a term introduced in the 1970s by the author, who is a pioneer in the field. Based on a series of lectures given at a conference at Emory University in 1986, this volume presents its subjects in a self-contained and accessible manner. The topics treated here have been in an active state of development, and this work therefore incorporates more recent results than those presented in 1986.

Focuses mainly on deterministic optimal control, the calculus of variations, and mathematical programming. In addition, it features a tutorial in nonsmooth analysis and geometry and demonstrates that the method of value function analysis via proximal normals is a powerful tool in the study of necessary conditions, sufficient conditions, controllability, and sensitivity analysis. The distinction between inductive and deductive methods, the use of Hamiltonians, the verification technique, and penalization are also emphasized. ... Read more

Book Description

Non-Additive Measure and Integral is the first systematic approach to the subject. Much of the additive theory (convergence theorems, Lebesgue spaces, representation theorems) is generalized, at least for submodular measures which are characterized by having a subadditive integral. The theory is of interest for applications to economic decision theory (decisions under risk and uncertainty), to statistics (including belief functions, fuzzy measures) to cooperative game theory, artificial intelligence, insurance, etc.Non-Additive Measure and Integral collects the results of scattered and often isolated approaches to non-additive measures and their integrals which originate in pure mathematics, potential theory, statistics, game theory, economic decision theory and other fields of application. It unifies, simplifies and generalizes known results and supplements the theory with new results, thus providing a sound basis for applications and further research in this growing field of increasing interest. It also contains fundamental results of -additive and finitely additive measure and integration theory and sheds new light on additive theory.Non-Additive Measure and Integral employs distribution functions and quantile functions as basis tools, thus remaining close to the familiar language of probability theory.In addition to serving as an important reference, the book can be used as a mathematics textbook for graduate courses or seminars, containing many exercises to support or supplement the text. ... Read more

Book Description

The theory of competition has held a central place in economic analysis since the time of Adam Smith. This book, written by one of the most distinguished of contemporary economic theorists, reports on a major research program to provide strategic foundations for the theory of competition. Making use of insights from game theory, search theory and bargaining theory, the author develops a model to explain what actually goes on in markets and how a competitive general equilibrium is achieved. Essential reading for graduate courses in game theory and general equilibrium. ... Read more

Book Description

Progress in the theory of economic equilibria and in game theory has proceeded hand in hand with that of the mathematical tools used in the field, namely nonlinear analysis and, in particular, convex analysis. Jean-Pierre Aubin, one of the leading specialists in nonlinear analysis and its application to economics, has written a rigorous and concise - yet still elementary and self-contained - textbook providing the mathematical tools needed to study optima and equilibria, as solutions to problems, arising in economics, management sciences, operations research, cooperative and non-cooperative games, fuzzy games etc. It begins with the foundations of optimization theory, and mathematical programming, and in particular convex and nonsmooth analysis. Nonlinear analysis is then presented, first game-theoretically, then in the framework of set valued analysis. These results are then applied to the main classes of economic equilibria. The book contains numerous exercises and problems: the latter allow the reader to venture into areas of nonlinear analysis that lie beyond the scope of the book and of most graduate courses. ... Read more

Book Description

The modern theory of threats in bargaining situations is presented in a unified and systematic treatment that puts the existing literature in a new perspective. Harold Houba and Wilko Bolt provide a masterful synthesis of the fundamental results obtained in the rapidly expanding game-theoretic literature. The relative impacts of the fundamental forces on the bargaining outcome are discussed and related to the visions expressed by Nobel-laureate John Nash. Many topics -such as robustness of the results with respect to the diversity of known bargaining procedures, the role of commitment and policy bargaining situations- receive their most extensive treatment to date.

Credible Threats in Negotiations is suitable as a textbook for graduate students in economic theory and other social sciences and a necessity as a resource for scholars interested in bargaining situations. ... Read more

Book Description

Optimal control and differential games continue to attract strong interest from researchers interested in dynamical problems and models in management science. This volume explores the application of these methodologies to new as well as to classical decision problems in management sciences and economics. In Part I, optimal control and dynamical systems approaches are used to analyze problems in areas such as monetary policy, pollution control, relationship marketing, drug control, debt financing, and ethical behavior. In Part II differential games are applied to problems such as oligopolistic competition, common resource management, spillovers in foreign direct investments, marketing channels, incentive strategies, and the computation of Markov perfect Nash equilibria.Optimal Control and Differential Games is an excellent reference for researchers and graduate students covering a wide range of emerging and revisited problems in management science. ... Read more

Book Description

Book Description

This book presents a new approach to global non-convex constrained optimization. Problem dimensionality is reduced via space-filling curves. To economize the search, constraint is accounted separately (penalties are not employed). The multicriteria case is also considered. All techniques are generalized for (non-redundant) execution on multiprocessor systems.Audience: Researchers and students working in optimization, applied mathematics, and computer science. ... Read more