Genetic algorithms in economics: Difference between revisions

Revision as of 06:21, 9 November 2006

Revision as of 17:49, 25 November 2006

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=== Reproduction ===

The first operator, reproduction, works by attempting to imitate. In general, it selects another agent to observe it'sits fitness value. If it'sits fitness value is greater than it'sits own, then it elects to adopt the other agent's string. Otherwise, it perserves it own. These strings are then placed into an offspring pool to undergo the mutation operators, crossover and mutation. Most functions are [[stochastic]] and designed so that a small proportion of less fit solutions are selected. This helps keep the diversity of the population large, preventing premature convergence on poor solutions. Popular and well-studied selection methods include [[fitness proportionate selection|roulette wheel selection]] and [[tournament selection]].

=== Crossover ===

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The cobweb model is a simple supply and demand model for a good over t periods. Firms (agents) make a production quantity decision in a given period, however their output is not produced until the following period. Thus, the firms are going to have to use some sort of method to forecast what the future price will be. The GA is used as a sort of learning behaviour for the firms. Initially their quantity production decisions are random, however each period they learn a little more. The result is the agents converge within the area of the [[rational expectations]] equilibrium (RATEX) for the stable and unstable case. If the election operator is used, the GA converges exactly to the RATEX equilibrium.

There are two type of learning methods these agents can be deployed with: social learning and individual learning. In social learning, each firm is endowed with a single string (which is used as it'sits quantity production decision). It then compares this string against other firm's strings. In the individual learning case, agents are endowed with a pool strings. These strings are then compared against other strings within the agent's population pool. This can be thought of as mutual competing ideas within a firm whereas in the social case, it can be thought of as firm's learning from more successful firms. Note that in the social case and in the individual learning case with identical cost functions, that this is a homogeneous solution, that is all agent's production decisions are identical. However, if the cost functions are not identical, this will result in a hetrogenous solution, where firms produce different quantities (note that they are still locally homogeneous, that is within the firm's own pool all the strings are identical).

After all agent's have made a quantity production decision, the quantities are aggregated and plugged into a demand function to get a price. Each firm's profit is then calculated. Fitness values are then calculated as a function of profits. After the offspring pool is generated, hypothetical fitness values are calculated. These hypothetical values are based on some sort of estimation of the price level, often just by taking the previous price level.