Learning in Economics: Analysis and Application of Genetic Algorithms

ISBN-13: 9783790813845 / Angielski / Miękka / 2001 / 180 str.

Thomas Riechmann

Opis

The book is dedicated to the use of genetic algorithms in theoretical economic research. Genetic algorithms offer the chance of overcoming the limitations traditional mathematical tractability puts on economic research and thus open new horzions for economic theory. The book reveals close relationships between the theory of economic learning via genetic algorithms, dynamic game theory, and evolutionary economics.
Genetic algorithms are here introduced as metaphors for processes of social and individual learning in economics. The book gives a simple description of the basic structures of economic genetic algorithms, followed by an in-depth analysis of their working principles. Several well-known economic models are reconstructed to incorporate genetic algorithms. Genetic algorithms thus help to find genuinely new results of well-known economic problems.

Spis treści

I. Introduction.- 1. Introduction.- 2. The Core Topics; Learning and Computational Economics.- 2.1 Learning.- 2.1.1 A Definition.- 2.1.2 The Necessity of Learning in Economic Models.- 2.1.3 Methods of Describing Economic Learning.- 2.2 Computational Economics.- 2.2.1 Names and Definitions.- 2.2.2 The Role of Computational Economics in Economic Research.- 2.2.3 Agent Based Economics.- 2.2.4 Artificial Economic Agents.- 2.2.5 Differences to Analytical Models.- 2.3 Summary.- 3. An Exemplary Introduction to Structure and Application of Genetic Algorithms in Economic Research.- 3.1 Introduction.- 3.2 The Economic Problem: A Model of Regional Monopolies.- 3.2.1 The General Structure of the Model.- 3.2.2 The Consequences of Bounded Rationality.- 3.3 The Genetic Algorithm.- 3.3.1 Introduction.- 3.3.2 Problem Definition.- 3.3.3 Execution of the Algorithm.- 3.4 A Simple Example.- 3.4.1 Coding and Running the GA.- 3.4.2 Representation of the Results.- 3.4.3 Interpretation.- 3.5 Summary.- II. General Analysis of Genetic Algorithms.- 4. Methods for the General Analysis of Genetic Algorithms as Economic Learning Techniques.- 4.1 Introduction.- 4.1.1 The Schema Theorem.- 4.1.2 Concepts from Population Genetics.- 4.2 Genetic Algorithm Learning as a Markov Process.- 4.2.1 The Basics.- 4.2.2 Markov Chain Analysis.- 4.3 Genetic Algorithm Learning as an Evolutionary Process.- 4.3.1 Populations as Near Nash Equilibria.- 4.3.2 Evolutionary Stability of Genetic Populations.- 4.3.3 Evolutionary Dynamics.- 4.4 Genetic Algorithms as Learning Processes.- 4.4.1 Learning by Imitation.- 4.4.2 Learning by Communication.- 4.4.3 Learning by Experiment.- 4.4.4 GA Learning as a Compound Learning Mechanism.- 4.5 Summary.- 5. Statistical Aspects of the Analysis of Economic Genetic Algorithms.- 5.1 Introduction.- 5.2 Analysis.- 5.3 Summary.- III. Economic Applications and Technical Variations.- 6. Modifications: Election and Meta¡ªLearning.- 6.1 Introduction.- 6.2 Election.- 6.3 Meta Learning.- 6.4 Comparison of Learning Techniques.- 6.5 Summary.- Appendix: Technical Characteristics of the Meta Learning Process.- 7. Extensions: Variable Time Horizon of Selection.- 7.1 Introduction.- 7.2 The Economic Problem: A Cobweb Model with Declining Average Production Costs.- 7.2.1 The General Structure of the Model.- 7.2.2 Theoretical Results.- 7.3 The Genetic Algorithm.- 7.4 Simulation Results.- 7.4.1 Heterogeneities.- 7.4.2 Cycles.- 7.5 Summary.- 8. Algorithms with Real Valued Coding.- 8.1 Introduction.- 8.2 The Economic Model: Consumer Choice.- 8.2.1 The General Structure of the Model.- 8.2.2 The Basic Model.- 8.2.3 The Enhanced Model.- 8.3 The Genetic Algorithm.- 8.3.1 The Basics.- 8.3.2 Coding.- 8.3.3 Standard Operators.- 8.3.4 Enhanced Operators.- 8.3.5 Coping with the Constraints.- 8.4 Simulations and Results.- 8.4.1 Fixed Prices.- 8.4.2 Flexible Prices, High Elasticity.- 8.4.3 Flexible Prices, Low Elasticity.- 8.4.4 Summary of Results.- 8.5 Conclusions.- 8.5.1 The Influence of State Dependency.- 8.5.2 The Influence of Different Learning Schemes.- 8.6 Summary.- Appendix: Statistical Results.- 9. A Multi Population Algorithm.- 9.1 Introduction.- 9.2 The Economic Model: A Basic Overlapping Generations Model with Money.- 9.2.1 The General Structure of the Model.- 9.2.2 Theoretical Results.- 9.3 The Genetic Algorithm.- 9.4 Simulations and Results.- 9.4.1 The Election GA.- 9.4.2 Meta Mutation.- 9.5 An Overlapping Generations Model with Heterogeneous Agents.- 9.5.1 The Extensions to the Basic Model.- 9.5.2 The Role of Bounded Rationality.- 9.5.3 The Credit Market.- 9.5.4 The Money Market.- 9.5.5 The Proceeding of the Model.- 9.5.6 A Walrasian Credit Market.- 9.5.7 Theoretical Conclusions: Stability Properties of the Expec-tations Equilibrium Revisited.- 9.5.8 The Genetic Algorithm.- 9.5.9 Results.- 9.6 Summary.- 10. Final Remarks.