Herbert Scarf's Contributions to Economics, Game Theory and Operations Research Volume 4: Applied Equilibrium Analysis

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  • Format: Hardcover
  • Copyright: 2013-09-27
  • Publisher: Palgrave Macmillan

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Herbert Scarf is a highly esteemed distinguished American economist. He is internationally famous for his early epoch-making work on optimal inventory policies and his highly influential study with Andrew Clark on optimal policies for a multi-echelon inventory problem, which initiated the important and flourishing field of supply chain management. Equally, he has gained world recognition for his classic study on the stability of the Walrasian price adjustment processes and his fundamental analysis on the relationship between the core and the set of competitive equilibria (the so-called Edgeworth conjecture). Further achievements include his remarkable sufficient condition for the existence of a core in non-transferable utility games and general exchange economies, his seminal paper with Lloyd Shapley on housing markets, and his pioneering study on increasing returns and models of production in the presence of indivisibilities. All in all, however, the name of Scarf is always remembered as a synonym for the computation of economic equilibria and fixed points. In the early 1960s he invented a path-breaking technique for computing equilibrium prices.

This work has generated a major research field in economics termed Applied General Equilibrium Analysis and a corresponding area in operations research known as Simplicial Fixed Point Methods. This book comprises all his research articles and consists of four volumes. The volume collects Herbert Scarf's papers in the area of Applied Equilibrium Analysis.

Author Biography

Professor Zaifu Yang holds a chair in Economics at the University of York, UK. He has widely published in economics, game theory, operations research and applied mathematics. His articles have appeared in Econometrica, Journal of Economic Theory, Mathematics of Operations Research, Journal of Combinatorial Theory, and SIAM Journal on Control and Optimization among other leading academic journals.

Table of Contents

Preface; Zaifu Yang
1. The Approximation of Fixed Points of a Continuous Mapping
2. An Example of an Algorithm for Calculating General Equilibrium Prices
3. An Algorithm for a Class of Nonconvex Programming Problems 
4. The Solution of Systems of Piecewise Linear Equations
5. The Computation of Equilibrium Prices: An Exposition
6. Mathematical Programming and Economic Theory
7. The Origins of Fixed Point Methods
8. How to Compute Equilibrium Prices in 1891
9. The Computation of Equilibria for the Walrasian Model: A Personal Account

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