Journal :: Journal of Mathematical Biology
2003
Bifurcation Analysis of the Fully Symmetric Language Dynamical EquationPDF
Journal of Mathematical Biology 46(3):265-285, 2003
Abstract In this paper, I study a continuous dynamical system that describes language acquisition and communication in a group of individuals. Children inherit from their parents a mechanism to learn their language. This mechanism is constrained by a universal ...
2000
Journal of Mathematical Biology 41(2):172-188, 2000
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 ...MORE ⇓
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).