Language evolution in finite populations

Michael J. Fox, Jeff S. Shamma

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

We study a simple game-theoretical model of language evolution in finite populations. This model is of particular interest due to a surprising recent result for the infinite population case: under replicator dynamics, the population game converges to socially inefficient outcomes from a set of initial conditions with non-zero Lesbegue measure. If finite population models do not exhibit this feature then support is lent to the idea that small population sizes are a key ingredient in the emergence of linguistic coherence. It has been argued elsewhere that evolution supports efficient languages in finite populations using the method of comparing fixation probabilities of single mutant invaders to the inverse of the population size. We instead analyze an alternative generalization of replicator dynamics to finite populations that leads to the emergence of linguistic coherence in an absolute sense. After a long enough period of time, linguistic coherence is observed with arbitrarily high probability as a mutation rate parameter is taken to zero. We also discuss several variations on our model.

Original languageEnglish (US)
Title of host publication2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011
Pages4473-4478
Number of pages6
DOIs
StatePublished - 2011
Externally publishedYes
Event2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011 - Orlando, FL, United States
Duration: Dec 12 2011Dec 15 2011

Publication series

NameProceedings of the IEEE Conference on Decision and Control
ISSN (Print)0191-2216

Other

Other2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011
Country/TerritoryUnited States
CityOrlando, FL
Period12/12/1112/15/11

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Modeling and Simulation
  • Control and Optimization

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