Summary
Kholina A.G., Gizatulin A.M. Problems of applying genetic algorithms to economic models. In the article the problem of applying genetic algorithms to economic models is handled. Some reasons connected with its features, as a biological model, are given.
In computer science, the genetic algorithm (GA) is known as a very useful optimization technique. It belongs to the larger class of evolutionary algorithms, which generate solutions to optimization problems using techniques inspired by natural evolution, such as inheritance, mutation, selection, and crossover.
Genetic Algorithms, originally developed by John Holland (1975) as a simple model of genetic evolution, have swiftly evolved to be used in lots of different areas, including some economic models as well. Up to now, there have been quite a number of publications in this area (e.g. Marks 1992, Birchenhall 1995, Miller 1996, Axelrod 1997, Curzon Price 1997). In the majority of the papers GA are applied to well known standard economic models, such as cobweb-type models, the prisoner's dilemma, or industrial organization problems.
One reason for GA being an attractive tool for economic research has to do with the assumption of a normative behavioral foundation of individual action. In economics this is a very common assumption, and it makes models analytically tractable. The downside of this procedure is that it demands other strong assumptions like homogeneity, unbounded rationality and convexity. However, in reality one will hardly find economic agents perfectly behaving like economic models want them to behave. Therefore, instead of a normative behavioral foundation, it appears to be a promising alternative among others to derive individual behavior from artificial intelligence methods, of which GA are one. Because they always involve a number of strategies competing against each other GA-based economic models can be interpreted particularly well in a game theoretic context.
GA have been developed in analogy to the concepts of biological evolution and even the terminology is quite similar. Even though there is no standard GA but many variations of GA, there are some basic elements common to all GA (pic.1).
Pic. 1. The flow chart of the genetic algorithm
A GA consists in a number of strings containing information about how to behave in their environment and some operators, changing the strings. After “behaving“, the strings are evaluated by a fitness function, representing their environment, and the better adapted strings get higher scores. These in turn are important for the probability to be chosen by a selection operator, that determines which strings are allowed to reproduce. The chosen strings then undergo a procedure of crossing-over and mutation, and the so built “offspring” forms next periods generation that undergoes the same operations.
Because of their notable power to improve and find good solutions even in confusing or changing environments, the GA, initially developed as a descriptive tool, were often used as an optimization procedure for complex technical or logistic problems as well.
When using GA in an economic context, the operators of the algorithm are interpreted as steps of a learning process. A string is an idea or a market strategy of an agent. Selection and the related fitness function are the economic environment of the agents and the success they have. The designer of the model has to decide however, in what variable this success expresses itself: profits, market share, average profits of the last n periods or other. New ideas are then developed by recombining or copying successful old ones (crossing-over), including some mistakes or “unmotivated” experiments (mutation). The interpretation of the operators of a GA in an economic sense is more or less straightforward. When having a closer look at the procedure, there are however important differences between the GA and human learning or strategy choice.
First of all, this originally biological model is restricted by the features of biological reproduction. The problem therefore is, to decide what kind of information transmission seems the right one for the specific phenomenon to be modeled. But even more important seems to be the fact, that the influence of information exchange isn’t very likely to be mutual most times. This biological transmission pattern isn’t valid in social sciences, but it’s easy to remedy.
A second difference between biological and human information transmission not to be neglected is related to the genotype/phenotype-distinction. In biology no individual is able to “guess” what genes are responsible for a visible physical appearance or behavior of another individual, but it doesn’t need to find out, because the genetic information is exchanged directly.
The third and maybe most important limitation, is the explicit and sometimes even implicit lack of several cognitive aspects human learning exhibits:
- memory;
- internal selection;
- motivation and satisfaction level.
The most undisputed point may be the lack of memory in GA, which is closely related to the one of internal selection. If the agents would have a memory, they could compare new strategies with old ones or have a look, whether those “new” strategies haven’t already been tried and didn’t work. Even without a memory, after generating a new strategy, an agent could have a break and think about its potential, given last periods information, instead of just executing it blindly. This amounts to internal selection, not yet included in GA. In some economic applications of GA this is solved by the creation of an election operator.
The least convincing point, concerning missing cognitive elements in GA, seems to be the sometimes criticized lack of a motivation for change or of satisfysing behavior. A motivation to improve is implicitly existent, because less well performing strings disappear and fitter ones reproduce or ameliorate. Even if all strings are identical, the occurrence of mutations can be interpreted as a still prevailing motivation to look for better solutions.
Besides the just discussed problems because of the biological origin of the GA there are some technical questions as well: encoding and parameter setting. The results of a simulation with GA can strongly depend on the parameter setting. Differing from analytical models, simulations require an explicit definition of each parameter. We can’t derive general results, such as the resource economics insight that marginal regeneration ability has to equal the discount rate, without having to know the absolute figures of either. The only way to test the effect of different values is to vary the parameters, which is sort of time consuming and can be difficult or again time consuming to evaluate.
We also have to think about the plausibility of the chosen en- or decoding of the string. Holland’s GA uses binary strings which are decoded to the corresponding decimal numbers. This signifies, that the farther to the left a 1 or 0 is situated in the string, the more important it is for the final value. A mutation of the leftmost location in the string causes a doubling or cutting in half of the former value. Mutations of different locations however all have the same probability. It might be worth to think about either a subsequently rising probability of mutations from the left to the right end of the string or some sort of Grey-code, equalizing the contributions of different locations to the final value.
Since GA are still a rather young field of study and therefore not entirely analytically explored, there is a particular danger to generate artifacts. Due to the general difficulties to validate complex models, it is often difficult to attribute certain results to characteristics of the GA, to the specification of the model, or to the research question. Helpful for a better understanding of the behavior of GA is evolutionary game theory.
Existing theoretical studies concentrate rather on topics that deal with the technicalities of GA rather than on the practical problems with applications of GA to economical questions. Moreover, a multiplicity of interacting GA is very complex in itself. Its exact behavior is very difficult to study and understand since it is determined by a large number of parameters whose impact on the quality of the results is not well understood, yet.
Therefore, if GA are to be applied to complex, analytically intractable problems, model development and analysis resemble much more a (time-consuming) trial and error process than a systematic procedure. Hence, the success of their applications depends on experience and reason as well as on opportunities to generate similar results by other means. The evolution in a GA-based model should also not be confused with economic evolution. Even though the evolution of a GA can be understood as a kind of learning process GA learning is substantially different from the patterns of human and economic learning.
Last but not least, the agents' rationality in GA models is not only limited by the abilities of the GA itself, but also by the model concept.
Altogether the genetic algorithm is clearly a very useful technique in many fields, including Economics. And different economic models taking bounded rationality and uncertainty into account, by using GA or a further developed similar procedure, are a promising direction of economic research.
Literature
1. Balmann A., Happe K. Applying parallel genetic algorithms to economic problems: the case of agricultural land markets. Microbehavior and Macroresults, Proceedings, International Institute of Fisheries Economics and Trade, 2000.
2. Geisendorf S. Genetic Algorithms in Resource Economic Models. Santa-Fe-Institute Working, 1999.
3. Reddinger J. L. The Genetic Algorithm in Economics. Department of Agricultural Economics and Economics, Montana State University, 2007.