Handbook of Mathematical Economics Volume 3 1st Edition by Michael Intriligator, Kenneth Arrow ISBN 0444861289 9780444861283

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.

Handbook of Mathematical Economics Volume 3 1st Edition Table of contents:

Part I: Advanced Topics in Economic Theory

1. Advanced General Equilibrium Models

   • The Core and the Shapley Value
   • Existence and Uniqueness in Dynamic Equilibrium Models
   • Advanced Topics in Edgeworth Box and Pareto Efficiency
   • General Equilibrium with Production and Taxes

2. Cooperative Game Theory

   • The Shapley Value in Cooperative Games
   • The Core and Core Convergence
   • Applications of Cooperative Game Theory in Economics
   • Bargaining and Negotiation Theory

3. Non-Equilibrium and Disequilibrium Economics

   • Disequilibrium Models of Markets
   • Adaptive Dynamics and Evolutionary Equilibrium
   • Market Clearing and Price Adjustment Processes
   • Non-Linear Price Adjustment and Policy Implications

Part II: Economic Dynamics and Growth

4. Advanced Growth Theory

   • Endogenous Growth with Technological Change
   • Growth Models with Human Capital
   • The Role of Innovation and R&D in Economic Growth
   • Globalization and Convergence in Growth Models

5. Economic Fluctuations and Business Cycles

   • Dynamic Stochastic General Equilibrium (DSGE) Models
   • The Role of Shocks in Business Cycle Theory
   • Economic Policy and Stabilization
   • Applications of Cyclical Models to Monetary and Fiscal Policy

6. Population Economics and Economic Demography

   • Models of Population Growth and Economic Development
   • Intergenerational Transfers and Human Capital
   • The Economics of Aging and Demographic Transition
   • Population Dynamics in Development Economics

Part III: Advanced Topics in Game Theory

7. Stochastic Games and Evolutionary Strategies

   • Stochastic Dynamic Games
   • Evolutionary Stable Strategies (ESS) in Games
   • Applications in Biological Economics and Social Choice
   • Cooperative vs Non-Cooperative Games in Dynamic Settings

8. Mechanism Design and Implementation Theory

   • The Theory of Mechanism Design
   • Auctions, Voting Mechanisms, and Social Choice
   • The Vickrey-Clarke-Groves (VCG) Mechanism
   • Implementation in Economic Models

9. Behavioral Game Theory

   • Rational vs Behavioral Models in Game Theory
   • Experimental Economics and Behavioral Game Theory
   • Trust, Fairness, and Cooperation in Games
   • Applications of Behavioral Game Theory in Policy Design

Part IV: Mathematical Methods in Economics

10. Advanced Optimization Techniques

    • Nonlinear and Stochastic Optimization Methods
    • Dynamic and Recursive Optimization
    • Optimal Control in Economic Models
    • Algorithms and Computational Methods for Optimization

11. Stochastic Processes in Economics

    • Brownian Motion and Random Walks in Economics
    • Stochastic Differential Equations in Finance
    • Stochastic Processes in Macroeconomics
    • Markov Chains and Their Economic Applications

12. Statistical Methods and Econometrics

    • Econometric Models and Estimation Methods
    • Time Series Analysis in Economics
    • Panel Data and Longitudinal Models
    • Structural Econometrics and Model Selection

Part V: Applications of Mathematical Economics

13. Financial Economics: Pricing and Risk Management

    • The Efficient Market Hypothesis and Asset Pricing
    • Stochastic Models for Pricing Derivatives
    • Risk Management in Financial Economics
    • Hedging and Portfolio Optimization

14. Macroeconomic Models and Policy Analysis

    • The IS-LM Model and Extensions
    • The New Keynesian Model and Its Applications
    • Fiscal and Monetary Policy in Dynamic Models
    • Policy Simulations and Forecasting Models

15. International Economics and Trade

    • The Theory of Comparative Advantage
    • Trade Models with Multiple Goods and Countries
    • International Finance and Exchange Rate Dynamics
    • Global Trade Agreements and Policy Analysis

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