The Evolution of Expectations in Boundedly Rational Agents Edmund Chattoe (Lady Margaret Hall) This thesis was submitted for the degree of DPHIL in the Department of Economics at the University of Oxford on 23rd January 2003. It is 75297 words long and contains 23168 additional words in 3 appendices. The Evolution of Expectations in Boundedly Rational Agents Edmund Chattoe (Lady Margaret Hall) Submitted for the degree of DPHIL, Hilary 2003. Abstract This thesis develops an analogy between biological evolution and the adaptation of firm decision processes under oligopoly and uses it to build a computer simulation involving the technique of Genetic Programming. The decision processes and operating procedures of the firm represent the “genes” which produce particular actions (such as price setting) in the “body” (phenotype) of the firm. Decision processes are varied by processes analogous to recombination and mutation and firms are selected - though bankruptcy or having an inadequate share of the market - according to the effectiveness of their decision strategies in setting prices that produce profits. Over time, less successful decision processes (which yield less profit) are weeded out and more successful ones are modified and recombined to produce even greater effectiveness. The result is that markets “self-organise” in a way that would be very hard for rational or adaptive learning processes to achieve. The simulation model replicates existing work in this field and is then extended to investigate the evolution of expectations and heterogeneity of firm goals. The results cast light on the importance of expectations in market co-ordination and the important role of different firm goals in determining market structure. The model also provides insights into the importance of salient choices in speculative markets and possible mechanisms for tacit collusion between firms. The objective of the thesis is to show that simulations based on Genetic Programming are plausible, feasible and able to produce results of interest to economics. Acknowledgements I dedicate this thesis to my parents, without whom... I am very grateful to my supervisor Michael Bacharach (1936-2002) for his constant help and inspiration. I wish he were still here to see the thesis accepted. Thanks are also due to my examiners for their helpful suggestions concerning revisions. Finally, thanks to Adrienne, who has had to put up with a lot in the last year. Table of Contents Chapter 1 A Short Introduction 1 Chapter 2 Biology 6 2.1 The Development of Evolutionary Biology 2.1.1 2.1.2 2.1.3 2.1.4 Why Study Biological Evolution? Darwinian Selection Mendelian Genetics Neo-Darwinism and Contemporary Genetics 6 6 8 15 19 2.2 Some Evolutionary Fallacies 25 2.3 A Formal Description of Evolution 34 2.3.1 2.3.2 The Four Process Description Illustrative Example: A Simple Evolutionary Game 34 36 Chapter 3 Economics 41 3.1 Introduction 41 3.2 The Prehistory of Evolutionary Economics 42 3.2.1 3.2.2 3.3 Sociobiology, Social Darwinism and EEM Marshall, Veblen and Schumpeter The History of Evolutionary Economics 3.3.1 3.3.2 3.4 Alchian Penrose Bounded Rationality and Behavioural Economics 3.4.1 3.4.2 3.5 Two Interpretations of Bounded Rationality Bounded Rationality as an Empirical Theory of Process Contemporary Evolutionary Economics 3.5.1 3.5.2 3.5.3 3.6 The Nelson and Winter Approach The Nelson and Winter Models Evaluating the Nelson and Winter Approach Conclusions Chapter 4 Artificial Intelligence 42 45 51 51 66 81 82 87 96 97 100 104 108 110 4.1 The Artificial Intelligence Perspective 110 4.1.1 4.1.2 4.1.3 What is Artificial Intelligence? Instrumental and Descriptive Models The Difficulties of Search 111 116 119 4.2 Genetic Algorithms, Classifier Systems and Genetic Programming 122 4.2.1 The Basic Genetic Algorithm 122 4.2.1.1 4.2.1.2 4.2.1.3 4.2.1.4 4.2.1.5 4.2.1.6 What is a Genetic Algorithm? The Problem Representation and Initial Population The Fitness Function The Process of Reproduction The Genetic Operators Convergence 122 126 128 129 132 136 4.2.2 Developing the Genetic Algorithm 137 4.2.2.1 4.2.2.2 4.2.2.3 Generalising the Solution Representation The Formal Analysis of Genetic Algorithms Making the Process of Evolution Endogenous 138 140 141 4.2.3 Genetic Programming 145 4.3 Models of Firm Decision Making Using Evolutionary Algorithms 153 4.3.1 4.3.2 4.3.3 4.3.4 The Advantages of Simulation EEM Using Genetic Algorithms EEM Using Classifier Systems EEM Using Genetic Programming 154 155 164 172 Chapter 5 A Basic Model of Price Adaptation Under Oligopoly 177 5.1 Introduction 177 5.2 Setting Out the Basic Model 180 5.2.1 5.2.2 5.2.3 5.2.4 5.3 A Description of the Basic Model Clarifications and Modifications of the Dosi et al. Model Technical Specifications for the Basic Model The Status of the Model Replication and Discussion of the Basic Model 180 185 192 195 199 5.3.1 5.3.2 The Monopoly Case The Oligopoly Case 199 219 Chapter 6 Three Case Studies in Evolutionary Adaptation 227 6.1 Introduction 227 6.2 The Interpretation of Strategies 230 6.3 The Evolution of Firm Goals 238 6.4 The Evolution of Expectations 248 6.5 Conclusions 258 6.5.1 6.5.2 6.5.3 6.5.4 The Interpretation of Strategies The Empirical Study of Firm Genotypes Extending the Model Extending the Representation Appendix 1 Bibliography Appendix 2 Programme Code – The Oligopoly Model Appendix 3 Programme Code – The Tree Interpreter 259 261 262 264 1-21 1-70 1-6 Detailed Chapter Summary The first chapter provides a brief introduction to the contents and arguments of the thesis. The second chapter describes the biological theory of evolution in detail, showing how it serves as a powerful adaptive mechanism for uncertain environments. The purpose of this section is to make the clearest possible statement of the biological theory so that the quality of the proposed analogy between biological evolution and economic change can be evaluated fairly. The next section of the chapter examines and refutes several “folk” misunderstandings of evolution that are important because they have affected economic applications of evolutionary ideas. The final part of the chapter provides a formal description of evolutionary processes. This is applied to a simple evolutionary game to demonstrate its applicability and heuristic value for subsequent use. The third chapter reviews key applications of evolutionary ideas to firm decision-making. The first section situates evolutionary economics in historical and intellectual terms. The second section provides a detailed discussion of work by Alchian, the first economist to provide a framework for evolutionary firm adaptation explicit enough to form the basis for modelling. This paper specifies the detailed analogy between biological and economic evolution. The third section analyses an extensive critique of this work by Penrose. The fourth section deals with an interpretation of Bounded Rationality suitable for evolutionary economics and its modelling implications. The fifth section reviews how Alchian’s ideas were translated into models by Nelson and Winter and others. This section raises systematic difficulties with the status of these models as a preamble to showing how they are solved using Evolutionary Algorithms. The fourth chapter begins by introducing the Artificial Intelligence approach to modelling It also discusses the general treatment of search problems in Artificial Intelligence. This section shows how many search algorithms fail in complex environments. The next few sections provide a detailed discussion of Evolutionary Algorithms and their ability to overcome the search problem. This section also discusses how Evolutionary Algorithms can be used as plausible descriptive models of adaptation. The third section provides a detailed review of all descriptive models using Evolutionary Algorithms to explore firm decision making. It compares the strengths and weaknesses of different Evolutionary Algorithms for this task, concluding that Genetic Programming is the best technique for producing realistic descriptive models and addressing the limitations of the models discussed in the previous chapter. The fifth chapter independently replicates the only other descriptive model of firm decision adaptation under oligopoly. The first half of the chapter describes the model and modifies it to increase its behavioural plausibility and consistency of interpretation. The second part of the chapter presents replicated results for the model, interprets both the replicable and non-replicable results (showing that some of the original findings must be treated with considerable caution) and carries out additional experiments. The sixth and final chapter begins by discussing the applicability and limitations of the Dosi et al. model. It then presents three case studies that extend the model or develop its interpretation. The first introduces a simple tool for interpreting strategies in terms of elasticity and shows how in can be used to sharpen analysis. The second case study allows firms to have multiple goals for evaluating their strategies. It shows that certain goals have profound effects on the strategies evolved and the resulting state of the market. The third case study, for which the thesis was named, allows firms to develop expectations rather than only acting on lagged information. It is shown that this has a dramatic impact on co-ordination. The conclusion sums up the findings of the thesis, suggests some general limitations of the approach and possible directions for further research. The three appendices contain the bibliography and two programmes: one for the main oligopoly simulation and one for the strategy interpretation tool.