A Mathematical Analysis of the Long-run Behavior of Genetic Algorithms for Social Modeling

Ludo Waltman and Nees Jan van Eck

ERIM Report Series Research in Management from 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

Abstract: We 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 prisoner’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 prisoner’s dilemma context are provided as well.

Keywords: economics; evolutionary game theory; genetic algorithm; long-run behavior; social modeling (search for similar items in EconPapers)
JEL-codes: C02 C52 C71 M M11 R4 (search for similar items in EconPapers)
Date: 2009-03-09
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
https://repub.eur.nl/pub/15181/ERS-2009-011-LIS.pdf (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:ems:eureri:15181

Access Statistics for this paper

More papers in ERIM Report Series Research in Management from 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 Contact information at EDIRC.
Bibliographic data for series maintained by RePub ( this e-mail address is bad, please contact ).