Nash equilibria for an evolutionary language game

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 t...

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Bibliographic Details
Published in:Journal of mathematical biology 2000-08, Vol.41 (2), p.172-188
Main Authors: Trapa, P E, Nowak, M A
Format: Article
Language:English
Subjects:
Algorithms
Biological Evolution
Game Theory
Humans
Language
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Summary: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).
ISSN:0303-6812
1432-1416
DOI:10.1007/s002850070004