Books in Mathematical economics and game theory

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Discrete Dynamical Systems, Bifurcations and Chaos in Economics

• 1st Edition
• Volume 204
• January 5, 2006
• Wei-Bin Zhang
• English
• eBook 978-0-08-046246-2

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This book is a unique blend of difference equations theory and its exciting applications to economics. It deals with not only theory of linear (and linearized) difference equations, but also nonlinear dynamical systems which have been widely applied to economic analysis in recent years. It studies most important concepts and theorems in difference equations theory in a way that can be understood by anyone who has basic knowledge of calculus and linear algebra. It contains well-known applications and many recent developments in different fields of economics. The book also simulates many models to illustrate paths of economic dynamics.

A Mathematical Treatment of Economic Cooperation and Competition Among Nations, with Nigeria, USA, UK, China, and the Middle East Examples

• 1st Edition
• Volume 203
• September 30, 2005
• Ethelbert N. Chukwu
• English
• eBook 978-0-08-045952-3

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The book presents a careful mathematical study of Economic Cooperation and Competition among Nations. It appropriates the principles of Supply and Demand and of Rational Expectations to build the dynamic model of the Gross Domestic Products of two groups of nations which are linked up together. The first group consists of Nigeria, the US, the UK and China. The second group is made up of Egypt, the US, Jordan and Israel. The link connecting the four nations of each group is mirrored in the net export function which is broadened to include trade, debts and the inflow or the outflow of wealth from the competing and cooperating nations. This realistic models of the four interacting GDP's, a hereditary differential game of pursuit are validated with historical data from International Financial Statistic Year Book. The Mathematical model is then studied for controllability: from a current initial GDPs a better state can be attained using government and private strategies which are carefully identified. We use regression and differential equation methods to test whether the four countries are competing or cooperating. The consequences of competition or cooperation are explored. Cooperation can be realized and the growth of wealth assured because the system is controllable and we can increase the growth of GDP and then increase the coefficient of cooperation. The outcome may be unbounded growth of wealth for all concerned – the triumph of cooperation. With analogous simple examples the book shows that sufficiently cooperating systems grow unbounded and competing ones are either bounded at best, or become extinct in finite time. If competition is small, i.e., limited, or regulated the GDP's need not be extinct even after a long time. This results are in contrast with popular opinion which advocate competition over cooperation. The detailed policy implication of the cooperation analysis at one time or the other were advocated by Pope John Paul II, President Clinton and President Bush. The mathematical message is clear: the strategy of cooperation is the best way in an Interconnected World: Cooperation triumphs over competition. The same type of analysis allows the book to argue through modeling that prosperity, internal peace and harmony can flourish in Nigeria among the old three regions and the newer six geopolitical regions. The same is true for the four powerful states in the Middle East.Thus the author’s refreshing approach is the "scientific" treatment of cooperation and competition models of the gross-domestic product of two groups of nations – Nigeria, the USA, the UK, and China, and the USA, Egypt, Jordan and Israel. Attempts are made to provide "scientific" answers to broad national policies. It allows predictions of growth to be made with some degree of accuracy for up to 4 years. MATLAB and Maple programs in accompanied CD are provided. The author's individual nations economic models are cited. The dynamics are ordinary and hereditary games of pursuit also cited from the original earlier writings of the author are models of the economic state of each nation – a vector of six things – the gross domestic product (GDP) (y), interest rate R; employment (or unemployment) (L), value of capital stock (k), prices p(t), and therefore inflation and cumulative balance of payment (E). Each economic state is isolated except the impact of export function on aggregate demand.The main difference between this earlier contributions and this book is the link and its apparent policy implications and consequences.Key features:* Study of Cooperation and Competition among Nations with real life examples from the World Bank, the IMF data of Nigeria, the US; the UK, China, Egypt, Jordan and Israel.* Complete MATLAB or MAPLE program with data output and graphs, and possible realistic prediction of economic growth.* Including a comprehensive CD presenting each program in an easy and accessible way.* Realistic Model – comparison of real data and diagram of output. Duplicatable results.* With the CD and IMF data and generic programs, other groups of nations' economies can be studied as well as the economy of all UN members as a group.

Handbook of Game Theory with Economic Applications

• 1st Edition
• Volume 3
• August 19, 2002
• R.J. Aumann + 1 more
• English
• Hardback 978-0-444-89428-1

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This is the third volume of the Handbook of Game Theory with Economic Applications. Since the publication of multi-Volume 1 a decade ago, game theory has continued to develop at a furious pace, and today it is the dominant tool in economic theory. The three volumes together cover the fundamental theoretical aspects, a wide range of applications to economics, several chapters on applications to political science and individual chapters on applications to disciplines as diverse as evolutionary biology, computer science, law, psychology and ethics. The authors are the most eminent practitioners in the field, including three Nobel Prize winners.The topics covered in the present volume include strategic ("Nash") equilibrium; incomplete information; two-person non-zero-sum games; noncooperative games with a continuum of players; stochastic games; industrial organization; bargaining, inspection; economic history; the Shapley value and its applications to perfectly competitive economies, to taxation, to public goods and to fixed prices; political science; law mechanism design; and game experimentation.

Game Theory

• 1st Edition
• December 1, 2000
• A. J. Jones
• English
• Paperback 978-1-898563-14-3

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• eBook 978-0-85709-969-3

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Written engagingly and with agreeable humour, this book balances a light touch with a rigorous yet economical account of the theory of games and bargaining models. It provides a precise interpretation, discussion and mathematical analysis for a wide range of “game-like” problems in economics, sociology, strategic studies and war.There is first an informal introduction to game theory, which can be understood by non-mathematicians, which covers the basic ideas of extensive form, pure and mixed strategies and the minimax theorem. The general theory of non-cooperative games is then given a detailed mathematical treatment in the second chapter. Next follows a “first class” account of linear programming, theory and practice, terse, rigorous and readable, which is applied as a tool to matrix games and economics from duality theory via the equilibrium theorem, with detailed explanations of computational aspects of the simplex algorithm.The remaining chapters give an unusually comprehensive but concise treatment of cooperative games, an original account of bargaining models, with a skillfully guided tour through the Shapley and Nash solutions for bimatrix games and a carefully illustrated account of finding the best threat strategies.

Handbook of Game Theory with Economic Applications

• 1st Edition
• Volume 2
• December 21, 1994
• R.J. Aumann + 1 more
• English
• Hardback 978-0-444-89427-4

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This is the second of three volumes surveying the state of the art in Game Theory and its applications to many and varied fields, in particular to economics. The chapters in the present volume are contributed by outstanding authorities, and provide comprehensive coverage and precise statements of the main results in each area. The applications include empirical evidence. The following topics are covered: communication and correlated equilibria, coalitional games and coalition structures, utility and subjective probability, common knowledge, bargaining, zero-sum games, differential games, and applications of game theory to signalling, moral hazard, search, evolutionary biology, international relations, voting procedures, social choice, public economics, politics, and cost allocation. This handbook will be of interest to scholars in economics, political science, psychology, mathematics and biology.For more information on the Handbooks in Economics series, please see our home page on http://www.elsevier.nl/locate/hes

Handbook of Game Theory with Economic Applications

• 1st Edition
• Volume 1
• November 19, 1992
• R.J. Aumann + 1 more
• English
• Hardback 978-0-444-88098-7

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This is the first volume of the Handbook of Game Theory with Economic Applications, to be followed by two additional volumes. Game Theory has developed greatly in the last decade, and today it is an essential tool in much of economic theory. The three volumes will cover the fundamental theoretical aspects, a wide range of applications to economics, several chapters on applications to political science, and individual chapters on relations with other disciplines.The topics covered in the present volume include chess-playing computers, an introduction to the non-cooperative theory, repeated games, bargaining theory, auctions, location, entry deterrence, patents, the cooperative theory and its applications, and the relation between Game Theory and ethics.For more information on the Handbooks in Economics series, please see our home page on http://www.elsevier.nl/locate/hes

Handbook of Mathematical Economics

• 1st Edition
• Volume 4
• August 27, 1991
• W. Hildenbrand + 1 more
• English
• Hardback 978-0-444-87461-0

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The Handbook of Mathematical Economics aims to provide a definitive source, reference, and teaching supplement for the field of mathematical economics. It surveys, as of the late 1970's the state of the art of mathematical economics. This is a constantly developing field and all authors were invited to review and to appraise the current status and recent developments in their presentations. In addition to its use as a reference, it is intended that this Handbook will assist researchers and students working in one branch of mathematical economics to become acquainted with other branches of this field.The emphasis of this fourth volume of the Handbook of Mathematical Economics is on choice under uncertainty, general equilibrium analysis under conditions of uncertainty, economies with an infinite number of consumers or commodities, and dynamical systems. The book thus reflects some of the ideas that have been most influential in mathematical economics since the appearance of the first three volumes of the Handbook.Researchers, students, economists and mathematicians will all find this Handbook to be an indispensable reference source. It surveys the entire field of mathematical economics, critically reviewing recent developments. The chapters (which can be read independently) are written at an advanced level suitable for professional, teaching and graduate-level use. For more information on the Handbooks in Economics series, please see our home page on http://www.elsevier.nl/locate/hes

Handbook of Mathematical Economics

• 1st Edition
• Volume 3
• February 1, 1986
• Michael D. Intriligator + 3 more
• English
• Hardback 978-0-444-86128-3

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The Handbook of Mathematical Economics aims to provide a definitive source, reference, and teaching supplement for the field of mathematical economics. It surveys, as of the late 1970's the state of the art of mathematical economics. This is a constantly developing field and all authors were invited to review and to appraise the current status and recent developments in their presentations. In addition to its use as a reference, it is intended that this Handbook will assist researchers and students working in one branch of mathematical economics to become acquainted with other branches of this field. Volume I deals with Mathematical Methods in Economics, including reviews of the concepts and techniques that have been most useful for the mathematical development of economic theory. Volume II elaborates on Mathematical Approaches to Microeconomic Theory, including consumer, producer, oligopoly, and duality theory, as well as Mathematical Approaches to Competitive Equilibrium including such aspects of competitive equilibrium as existence, stability, uncertainty, the computation of equilibrium prices, and the core of an economy.

Economic Analysis in Historical Perspective

• 1st Edition
• March 27, 1984
• J. Creedy + 1 more
• English
• eBook 978-1-4831-6359-8

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Economic Analysis in Historical Perspective offers a wide discussion on economics and its history. One of the book’s main principles is to place the several major areas of economic analysis in historical perspective. The book’s first topic is about monetary economics; it includes subtopics such as concepts of money, supply and demand of money, monetary control, and rate of interest. The next chapter highlights the economics of welfare, including its nature, modern issues, classical paradigm, and advancements. In Chapter 4, the main topics are public finance, taxes, and the government’s role in all of it. This chapter also elaborates on public expenditure, taxation, and income redistribution. In the last remaining chapters, the discussion circles around the topic’s relevant theories, metrics, and statistics. The text serves as a valuable reference to undergraduates or postgraduates of economics.

Handbook of Mathematical Economics

• 1st Edition
• Volume 1
• January 1, 1984
• Kenneth J. Arrow + 1 more
• English
• Hardback 978-0-444-86126-9

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The Handbook of Mathematical Economics aims to provide a definitive source, reference, and teaching supplement for the field of mathematical economics. It surveys, as of the late 1970's the state of the art of mathematical economics. This is a constantly developing field and all authors were invited to review and to appraise the current status and recent developments in their presentations. In addition to its use as a reference, it is intended that this Handbook will assist researchers and students working in one branch of mathematical economics to become acquainted with other branches of this field.Volume 1 deals with Mathematical Methods in Economics, including reviews of the concepts and techniques that have been most useful for the mathematical development of economic theory.For more information on the Handbooks in Economics series, please see our home page on http://www.elsevier.nl/locate/hes