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Abstract

We investigate a model of language evolution, based on population game dynamics with learning. Specifically, we examine the case of two genetic variants of universal grammar (UG), the heart of the human language faculty, assuming each admits two possible grammars. The dynamics are driven by a communication game. We prove using dynamical systems techniques that if the payoff matrix obeys certain constraints, then the two UGs are stable against invasion by each other, that is, they are evolutionarily stable. These constraints are independent of the learning process. Intuitively, if a mutation in UG results in grammars that are incompatible with the established languages, then it will die out because individuals with the mutation will be unable to communicate and therefore unable to realize any potential benefit of the mutation. An example for which the proofs do not apply shows that compatible mutations may or may not be able to invade, depending on the population's history and the learning process. These results suggest that the genetic history of language is constrained by the need for compatibility and that mutations in the language faculty may have died out or taken over depending more on historical accident than on any simple notion of relative fitness.

Keywords: population game dynamics; replicator equation; language dynamical equation; learning; evolution; evolutionary stability; universal grammar; metastrategy

@article{mitchener07universalGrammar,
  author={W. Garrett Mitchener},
  title={Game Dynamics with Learning and Evolution of Universal Grammar},
  journal={Bulletin of Mathematical Biology},
  year={2007},
  month={Apr},
  volume={69},
  number={3},
  pages={1093-1118},
  doi={10.1007/s11538-006-9165-x},
  url={http://www.isrl.uiuc.edu/~amag/langev/paper/mitchener07universalGrammar.html},
  keywords={population game dynamics; replicator equation; language dynamical equation; learning; evolution; evolutionary stability; universal grammar; metastrategy}
}

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