Handbook of Mathematical Economics Volume 4 1st Edition by Hildenbrand, Sonnenschein ISBN 0444874615 9780444874610

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ISBN 10: 0444874615
ISBN 13: 9780444874610
Author: Hildenbrand, Sonnenschein

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.

Handbook of Mathematical Economics Volume 4 1st Edition Table of contents:

Part I: Market Theory and General Equilibrium

1. Market Structures and Perfect Competition

   • Perfect Competition and Welfare Optimality
   • Imperfect Competition: Oligopoly and Monopoly
   • The Theory of Contestable Markets
   • Market Power and Price Discrimination

2. General Equilibrium Theory: Foundations and Applications

   • The Arrow-Debreu Model of General Equilibrium
   • Existence, Uniqueness, and Stability in Equilibrium
   • Welfare Theorems and the Role of Government
   • The Walrasian Auctioneer and Market Clearing

3. Multi-Market Equilibrium and Applications

   • Multi-Market Models in International Trade
   • Global Supply and Demand Systems
   • Environmental and Natural Resource Economics
   • Computational General Equilibrium Models

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Part II: Welfare Economics and Social Choice

4. Social Choice Theory

   • Arrow’s Impossibility Theorem and Its Extensions
   • Fairness and Equity in Social Choice Models
   • Voting Mechanisms and Majority Rule
   • Mechanisms for Public Goods Allocation

5. Welfare Economics and Income Distribution

   • Pareto Efficiency and Equity Considerations
   • The Theory of Optimal Taxation
   • Income Redistribution and Social Welfare Functions
   • The Role of Government in Achieving Social Welfare

6. Intertemporal Choice and Social Welfare

   • Discounting and the Time Value of Welfare
   • Sustainability and Intergenerational Equity
   • Social Planning in a Dynamic Context
   • Long-Term Welfare Optimization

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Part III: Dynamic Models and Economic Growth

7. Dynamic General Equilibrium Models

   • Recursive and Overlapping Generations Models
   • Growth and Technological Change in Dynamic Systems
   • Real Business Cycle Models
   • Endogenous Growth and Technological Innovation

8. Optimal Growth and Resource Allocation

   • Solow Growth Model and Extensions
   • The Role of Capital Accumulation in Growth
   • Optimal Consumption and Investment Decisions
   • Resource Allocation under Uncertainty

9. Economic Fluctuations and the Business Cycle

   • Dynamic Stochastic General Equilibrium (DSGE) Models
   • The Role of Monetary and Fiscal Policy
   • Financial Markets and Macroeconomic Instability
   • Applications of Cyclical Models in Policy Design

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Part IV: Game Theory and Strategic Interaction

10. Non-Cooperative Game Theory and Applications

    • Nash Equilibrium and Its Extensions
    • Bargaining and Negotiation Models
    • Auctions and Mechanism Design
    • Strategic Behavior in Competitive Markets

11. Cooperative Game Theory and Resource Allocation

    • The Core, Shapley Value, and Cooperative Solutions
    • Applications in Network Design and Resource Sharing
    • Fairness and Efficiency in Cooperative Games
    • Stable Matching and Allocation Problems

12. Evolutionary Game Theory and Applications

    • Evolutionarily Stable Strategies (ESS)
    • Replicator Dynamics in Population Models
    • Social and Economic Applications of Evolutionary Game Theory
    • Behavioral Economics and Evolutionary Models

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Part V: Econometrics and Applied Mathematical Methods

13. Statistical Methods in Economics

    • Econometrics of Generalized Linear Models
    • Non-Parametric and Semi-Parametric Methods
    • Structural Estimation and Model Selection
    • Econometric Approaches to Forecasting

14. Time Series and Dynamic Econometrics

    • Autoregressive and Vector Autoregressive Models
    • Cointegration and Error Correction Models
    • Non-Stationary Data and Unit Root Analysis
    • Forecasting and Economic Policy Simulations

15. Computational Economics and Data Analysis

    • Computational Methods for Market and General Equilibrium
    • Optimization Algorithms in Economic Modeling
    • Agent-Based Modeling and Simulation
    • Data Mining and Machine Learning in Economics

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