A Mathematical Analysis of the Long-run Behavior of Genetic Algorithms for Social Modeling
AbstractWe present a mathematical analysis of the long-run behavior of genetic algorithms that are used for modeling social phenomena. The analysis relies on commonly used mathematical techniques in evolutionary game theory. Assuming a positive but infinitely small mutation rate, we derive results that can be used to calculate the exact long-run behavior of a genetic algorithm. Using these results, the need to rely on computer simulations can be avoided. We also show that if the mutation rate is infinitely small the crossover rate has no effect on the long-run behavior of a genetic algorithm. To demonstrate the usefulness of our mathematical analysis, we replicate a well-known study by Axelrod in which a genetic algorithm is used to model the evolution of strategies in iterated prisonerâ€™s dilemmas. The theoretically predicted long-run behavior of the genetic algorithm turns out to be in perfect agreement with the long-run behavior observed in computer simulations. Also, in line with our theoretically informed expectations, computer simulations indicate that the crossover rate has virtually no long-run effect. Some general new insights into the behavior of genetic algorithms in the prisonerâ€™s dilemma context are provided as well.
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Bibliographic InfoPaper provided by Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam. in its series Research Paper with number ERS-2009-011-LIS.
Date of creation: 09 Mar 2009
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Web page: http://www.erim.eur.nl/
genetic algorithm; economics; evolutionary game theory; long-run behavior; social modeling;
This paper has been announced in the following NEP Reports:
- NEP-ALL-2009-04-13 (All new papers)
- NEP-CBE-2009-04-13 (Cognitive & Behavioural Economics)
- NEP-CMP-2009-04-13 (Computational Economics)
- NEP-EVO-2009-04-13 (Evolutionary Economics)
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