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Nash equilibria for an evolutionary language game.

P E Trapa1, M A Nowak

  • 1School of Mathematics, Institute for Advanced Study, Princeton, NJ 08540, USA. ptrapa@math.ias.edu

Journal of Mathematical Biology
|October 20, 2000
PubMed
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This study models language evolution using an evolutionary game theory framework. It shows that random languages evolve towards stable communication strategies through natural selection and drift.

Area of Science:

  • Evolutionary Game Theory
  • Computational Linguistics
  • Information Theory

Background:

  • Understanding how arbitrary signals acquire meaning is fundamental to linguistics and cognitive science.
  • Previous models often simplified the complexities of bidirectional communication and learning.
  • The evolutionary game theory approach offers a robust framework for analyzing emergent communication systems.

Purpose of the Study:

  • To formally classify languages within an evolutionary game theory model.
  • To identify conditions for stable communication equilibria, specifically Nash equilibria and evolutionarily stable strategies (ESS).
  • To demonstrate the evolutionary pathway from random languages to stable communication.

Main Methods:

  • Defining a language L using speaker (P matrix) and listener (Q matrix) association probabilities.

Related Experiment Videos

  • Quantifying communication success via the total information exchanged as payoff.
  • Developing an algorithm to generate Nash equilibrium languages.
  • Simulating evolutionary trajectories involving selection and neutral drift.

    • Main Results:

    • A formal classification of languages L(P, Q) based on communication payoff.
    • Characterization of conditions leading to Nash equilibria and ESS.
    • An algorithm capable of generating all Nash equilibrium languages.
    • Empirical demonstration that random languages converge to strict Nash equilibria.

    Conclusions:

    • Evolutionary dynamics, including selection and neutral drift, drive languages towards stable communication states.
    • The model provides a theoretical foundation for understanding the emergence and stability of meaning in communication systems.
    • The findings have implications for artificial intelligence, animal communication, and the study of language origins.