Equilibrium Problems and Applications
Equilibrium Problems and Applications

Author: Gábor Kassay

Publisher: Academic Press

Published: 2018-10-09

Total Pages: 442

ISBN-13: 0128110309

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Equilibrium Problems and Applications develops a unified variational approach to deal with single-valued, set-valued and quasi-equilibrium problems. The authors promote original results in relationship with classical contributions to the field of equilibrium problems. The content evolved in the general setting of topological vector spaces and it lies at the interplay between pure and applied nonlinear analysis, mathematical economics, and mathematical physics. This abstract approach is based on tools from various fields, including set-valued analysis, variational and hemivariational inequalities, fixed point theory, and optimization. Applications include models from mathematical economics, Nash equilibrium of non-cooperative games, and Browder variational inclusions. The content is self-contained and the book is mainly addressed to researchers in mathematics, economics and mathematical physics as well as to graduate students in applied nonlinear analysis. - A rigorous mathematical analysis of Nash equilibrium type problems, which play a central role to describe network traffic models, competition games or problems arising in experimental economics - Develops generic models relevant to mathematical economics and quantitative modeling of game theory, aiding economists to understand vital material without having to wade through complex proofs - Reveals a number of surprising interactions among various equilibria topics, enabling readers to identify a common and unified approach to analysing problem sets - Illustrates the deep features shared by several types of nonlinear problems, encouraging readers to develop further this unifying approach from other viewpoints into economic models in turn

Problems in Equilibrium Theory
Problems in Equilibrium Theory

Author: Charalambos D. Aliprantis

Publisher: Springer Science & Business Media

Published: 2013-03-09

Total Pages: 257

ISBN-13: 3662032333

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This is the first book to teach the basic methods of proof and problem solving in General Equilibrium Theory at graduate level. The problems cover the entire spectrum of difficulty: some are routine, while others require a good grasp of the material involved, and some are even challenging. In searching for the basic required techniques, students will discover a wealth of new material, and are encouraged to arrive at solutions different from the ones presented in the book. Complete solutions to two hundred problems are provided.

Finding Equilibrium
Finding Equilibrium

Author: Till Düppe

Publisher: Princeton University Press

Published: 2014-07-21

Total Pages: 302

ISBN-13: 0691156646

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The remarkable story and personalities behind one of the most important theories in modern economics Finding Equilibrium explores the post–World War II transformation of economics by constructing a history of the proof of its central dogma—that a competitive market economy may possess a set of equilibrium prices. The model economy for which the theorem could be proved was mapped out in 1954 by Kenneth Arrow and Gerard Debreu collaboratively, and by Lionel McKenzie separately, and would become widely known as the "Arrow-Debreu Model." While Arrow and Debreu would later go on to win separate Nobel prizes in economics, McKenzie would never receive it. Till Düppe and E. Roy Weintraub explore the lives and work of these economists and the issues of scientific credit against the extraordinary backdrop of overlapping research communities and an economics discipline that was shifting dramatically to mathematical modes of expression. Based on recently opened archives, Finding Equilibrium shows the complex interplay between each man's personal life and work, and examines compelling ideas about scientific credit, publication, regard for different research institutions, and the awarding of Nobel prizes. Instead of asking whether recognition was rightly or wrongly given, and who were the heroes or villains, the book considers attitudes toward intellectual credit and strategies to gain it vis-à-vis the communities that grant it. Telling the story behind the proof of the central theorem in economics, Finding Equilibrium sheds light on the changing nature of the scientific community and the critical connections between the personal and public rewards of scientific work.

General Equilibrium Theory
General Equilibrium Theory

Author: Ross M. Starr

Publisher: Cambridge University Press

Published: 1997-07-13

Total Pages: 280

ISBN-13: 9780521564731

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General Equilibrium Theory: An Introduction treats the classic Arrow-Debreu general equilibrium model in a form accessible to graduate students and advanced undergraduates in economics and mathematics. Topics covered include mathematical preliminaries, households and firms, existence of general equilibrium, Pareto efficiency of general equilibrium, the First and Second Fundamental Theorems of Welfare Economics, the core and core convergences, future markets over time and contingent commodity markets under uncertainty. Demand, supply, and excess demand appear first as (point-valued) functions, then optionally as (set-valued) correspondences. The mathematics presented (with elementary proofs of the theorems) includes a real analysis, the Brouwer fixed point theorem, and separating and supporting hyperplane theorems. Optional chapters introduce the existence of equilibrium with set-valued supply and demand, the mathematics of upper and lower hemicontinuous correspondences, and the Kakutani fixed point theorem. The treatment emphasizes clarity and accessibility to the student through use of examples and intuition.

Nonsmooth Approach to Optimization Problems with Equilibrium Constraints
Nonsmooth Approach to Optimization Problems with Equilibrium Constraints

Author: Jiri Outrata

Publisher: Springer Science & Business Media

Published: 2013-06-29

Total Pages: 281

ISBN-13: 1475728255

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In the early fifties, applied mathematicians, engineers and economists started to pay c10se attention to the optimization problems in which another (lower-Ievel) optimization problem arises as a side constraint. One of the motivating factors was the concept of the Stackelberg solution in game theory, together with its economic applications. Other problems have been encountered in the seventies in natural sciences and engineering. Many of them are of practical importance and have been extensively studied, mainly from the theoretical point of view. Later, applications to mechanics and network design have lead to an extension of the problem formulation: Constraints in form of variation al inequalities and complementarity problems were also admitted. The term "generalized bi level programming problems" was used at first but later, probably in Harker and Pang, 1988, a different terminology was introduced: Mathematical programs with equilibrium constraints, or simply, MPECs. In this book we adhere to MPEC terminology. A large number of papers deals with MPECs but, to our knowledge, there is only one monograph (Luo et al. , 1997). This monograph concentrates on optimality conditions and numerical methods. Our book is oriented similarly, but we focus on those MPECs which can be treated by the implicit programming approach: the equilibrium constraint locally defines a certain implicit function and allows to convert the problem into a mathematical program with a nonsmooth objective.

Variational Inequalities and Network Equilibrium Problems
Variational Inequalities and Network Equilibrium Problems

Author: F. Giannessi

Publisher: Springer Science & Business Media

Published: 2013-06-29

Total Pages: 304

ISBN-13: 1489913580

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This volume brings forth a set of papers presented at the conference on "Varia tional Inequalities and network equilibrium problems", held in Erice at the "G. Stam pacchia" School of the "E. Majorana" Centre for Scientific Culture in the period 19~25 June 1994. The meeting was conceived to contribute to the exchange between Variational Analysis and equilibrium problems, especially those related to network design. Most of the approaches and viewpoints of these fields are present in the volume, both as concerns the theory and the applications of equilibrium problems to transportation, computer and electric networks, to market behavior, and to bi~level programming. Being convinced of the great importance of equilibrium problems as well as of their complexity, the organizers hope that the merging of points of view coming from differ ent fields will stimulate theoretical research and applications. In this context Variational and Quasi~Variational Inequalities have shown them selves to be very important models for equilibrium problems. As a consequence in the last two decades they have received a lot of attention both as to mathematical inves tigation and applications. The proof that the above mentioned equilibrium problems can be expressed, in terms of Variational or Quasi~Variational Inequalities also in the non~standard and non~symmetric cases, has been a crucial improvement.

Equilibrium Problems: Nonsmooth Optimization and Variational Inequality Models
Equilibrium Problems: Nonsmooth Optimization and Variational Inequality Models

Author: F. Giannessi

Publisher: Springer Science & Business Media

Published: 2006-04-11

Total Pages: 304

ISBN-13: 0306480263

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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.

General Equilibrium Analysis
General Equilibrium Analysis

Author: Monique Florenzano

Publisher: Springer Science & Business Media

Published: 2003-08-31

Total Pages: 198

ISBN-13: 140207512X

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General Equilibrium Analysis is a systematic exposition of the Walrasian model of economic equilibrium with a finite number of agents, as formalized by Arrow, Debreu and McKenzie at the beginning of the fifties and since then extensively used, worked and studied. Existence and optimality of general equilibrium are developed repeatedly under different sets of hypothesis which define some general settings and delineate different approaches to the general equilibrium existence problem. The final chapter is devoted to the extension of the general equilibrium model to economies defined on an infinite dimensional commodity space. The objective of General Equilibrium Analysis is to give to each problem in each framework the most general solution, at least for the present state of art. The intended readers are graduate students, specialists and researchers in economics, especially in mathematical economics. The book is appropriate as a class text, or for self-study.

General Equilibrium, Overlapping Generations Models, and Optimal Growth Theory
General Equilibrium, Overlapping Generations Models, and Optimal Growth Theory

Author: Truman F. Bewley

Publisher: Harvard University Press

Published: 2009-07-01

Total Pages: 615

ISBN-13: 0674020928

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This book presents an original exposition of general equilibrium theory for advanced undergraduate and graduate-level students of economics. It contains detailed discussions of economic efficiency, competitive equilibrium, the first and second welfare theorems, the Kuhn-Tucker approach to general equilibrium, the Arrow-Debreu model, and rational expectations equilibrium and the permanent income hypothesis. Truman Bewley also treats optimal growth and overlapping generations models as special cases of the general equilibrium model. He uses the model and the first and second welfare theorems to explain the main ideas of insurance, capital theory, growth theory, and social security. It enables him to present a unified approach to portions of macro- as well as microeconomic theory. The book contains problems sets for most chapters.

General Equilibrium
General Equilibrium

Author: W. D. A. Bryant

Publisher: World Scientific

Published: 2010

Total Pages: 492

ISBN-13: 9812818340

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"This book focuses on the foundations of general equilibrium theory, more specifically on the existence, uniqueness, stability, optimality and comparative static properties of equilibrium states. It also explores the question of the empirical relevance of equilibrium states. It highlights a series of 'relationship conditions' which are essential for the existence of equilibrium, but appear in optimality results." -- PUBLISHER WEBSITE.