Learning in Economics

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.

Klappentext

It took me over five years to write this book. Finishing my research project and thus finishing this book would not have been possible without the help of many friends of mine. Thus, the first thing to do is to say 'Thanks a lot' . This means at first place the Evangelisches Studienwerk Haus Villigst. They gave me a grant for my work, thus laying the important financial grounds of everything I've done. There is such a large number of friends I worked and lived with over the last few years that I cannot possibly mention them all by name, but I'll try, anyway: So, thanks Christiane, Gilbert, Maik, Karl, and everybody else feeling that his or her name should appear in this list. And, of course, thanks Franz Haslinger, for letting me do whatever I wanted to - and for even encouraging me to stick with it. One more thing I'd like to mention: Although this work is based on very heavy use of computer power, it is my special pride to say that not a single penny (i.e. Deutschmark) had to be spent for software in order to do this work. Instead, all that has been done has been done by free software. Thus, I would like to mention some of my most heavily used software tools in order to let you, the reader, know that nowadays you don't depend on big commercial software packages any more.

Inhalt

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.