Thomas Riechmann

Genetic algorithm learning and evolutionary games

Abstract This paper links the theory of genetic algorithm (GA) learning to evolutionary game theory. It is shown that economic learning via genetic algorithms can be described as a specific form of an evolutionary game. It will be pointed out that GA learning results in a series of near Nash equilibria which during the learning process build up to finally approach a neighborhood of an evolutionarily stable state. In order to characterize this kind of dynamics, a concept of evolutionary superiority and evolutionary stability of genetic populations is developed, which allows for a comprehensive analysis of the evolutionary dynamics of the standard GA learning processes.

Genetic Algorithm Learning and Economic Evolution

This paper tries to connect the theory of genetic algorithm (GA) learning to evolutionary game theory. It is shown that economic learning via genetic algorithms can be described as a specific form of evolutionary game. It will be pointed out that GA learning results in a series of near Nash equilibria which during the learning process build up to finally reach a neighborhood of an evolutionarily stable state. In order to clarify this point, a concept of evolutionary stability of genetic populations will be developed. Thus, in a second part of the paper, it becomes possible to explain both, the reasons for the specific dynamics of standard GA learning models and the different kind of dynamics of GA learning models which use extensions to the standard GA.

The dynamics of behavior in modified dictator games

We investigate the dynamics of individual pro-social behavior over time. The dynamics are tested by running the same experiment with the same subjects at several points in time. To exclude learning and reputation building, we employ non-strategic decision tasks and a sequential prisoners-dilemma as a control treatment. In the first wave, pro-social concerns explain a high share of individual decisions. Pro-social decisions decrease over time, however. In the final wave, most decisions can be accounted for by assuming pure selfishness. Stable behavior in the sense that subjects stick to their decisions over time is observed predominantly for purely selfish subjects. We offer two explanation for our results: diminishing experimenter demand effects and moral self-licensing.

A Model of Boundedly Rational Consumer Choice

The paper presents an extended version of the standard textbook problem of consumer choice. As usual, agents have to decide about their desired quatities of various consumption goods, at the same time taking into account their limited budget. Prices for the goods are not fixed but arise from a Walrasian interaction of total demand and a stilized supply function for each of the goods. After showing that this type of model cannot be solved analytically, three different types of evolutionary algorithms are set up to answer the question whether agents behaving according to the rules of these algorithms can solve the problem of extended consumer choice. There are two important answers to this question: a) The quality of the learned results crucially depends on the elasticity of supply, which in turn can be shown to be a measure of the degree of state dependency of the economic problem. b) Statistical tests suggest that for the agents in the model it is relatively easy to adhere to the budget constraint, but that it is relatively difficult to reach an optimum with marginal utility per Dollar being equal for each good.

Modifications: Election and Meta-Learning

Up to this point, the main focus of the book was on the behavior of the canonical GA (Goldberg, 1989) used as a metaphor for learning in economic models. Originally, the canonical GA has been developed as a tool for optimization of non economic, static problems. The canonical GA is not a genuine tool for economic, agent based modeling. If a genetic algorithm is to be used as a true metaphor for economic learning, modifications to the canonical form of the algorithm are needed.

Algorithms with Real Valued Coding

This chapter is dedicated to an economic problem with a much more complex structure than all the problems focused before. It is the problem of consumer choice of private households. In the model, a population of households has to divide their income between the consumptions of three different consumption goods. The final goal of their decision is to achieve optimal utility.

Extensions: Variable Time Horizon of Selection

The model of regional monopolies discussed up to now, is too simple in at least one point: It is no satisfactory model of economic learning via GAs, because there is no state dependency. It has been mentioned above that the state dependency of individual economic success is an important characteristic of almost every economic problem. Even more, it is a major characteristic of models of economic GA learning. For example, the profit of a supplier in a market (except of a monopolistic market) does not only depend on the quantity of the good the supplier offers, but also on the market price. The market price, in turn, depends on the aggregate supply on the market, i.e. on the quantities all suppliers offer. This means that the profit of every single supplier is inseparably connected to each action of every member of the market and by that, to the state of the whole economy1.

An Exemplary Introduction to Structure and Application of Genetic Algorithms in Economic Research

The goal of this chapter is to provide a simple introduction into the kind of genetic algorithms applied in economic theory. The main focus will be on technical aspects, the economic example merely serves as an illustration. This means that in this chapter new economic results will hardly be found. The model shown here is very simple and, more than this, it lacks one of the most important characteristics of the models to be presented in the further course of this work: It does not include state dependency of individual economic success1. The large number of simplifications make the model look a little stylized. Nevertheless, the simplifications are intentionally introduced in favor of clarity of the main technical goal, the introduction into the basic techniques of modeling economic problems in form of a genetic algorithm.

Statistical Aspects of the Analysis of Economic Genetic Algorithms

Simulation based on economic genetic algorithms generate a large amount of data informing about the performance of the agents and the results of the model. Every analysis and interpretation of GA models is thus based on statistical examinations of these data.

A Multi Population Algorithm

Like all the chapters in the third part of this book, this one, too, has an economic and a technical topic.