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Journal of Mathematical Biology

, Volume 41, Issue 2, pp 172–188 | Cite as

Nash equilibria for an evolutionary language game

  • Peter E. Trapa
  • Martin A. Nowak

Abstract.

We study an evolutionary language game that describes how signals become associated with meaning. In our context, a language, L, is described by two matrices: the P matrix contains the probabilities that for a speaker certain objects are associated with certain signals, while the Q matrix contains the probabilities that for a listener certain signals are associated with certain objects. We define the payoff in our evolutionary language game as the total amount of information exchanged between two individuals. We give a formal classification of all languages, L(P, Q), describing the conditions for Nash equilibria and evolutionarily stable strategies (ESS). We describe an algorithm for generating all languages that are Nash equilibria. Finally, we show that starting from any random language, there exists an evolutionary trajectory using selection and neutral drift that ends up with a strategy that is a strict Nash equilibrium (or very close to a strict Nash equilibrium).

Keywords

Nash Equilibrium Evolutionary Language Stable Strategy Evolutionary Trajectory Evolutionarily Stable Strategy 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Peter E. Trapa
    • 1
  • Martin A. Nowak
    • 2
  1. 1.School of Mathematics, Institute for Advanced Study, Princeton, NJ 08540, USA. e-mail: ptrapa@math.ias.eduUS
  2. 2.Program in Theoretical Biology, Institute for Advanced Study, Princeton, NJ 08540, USA. e-mail: nowak@ias.eduUS

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