Nash equilibria for an evolutionary language game |
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Authors: | Peter E Trapa Martin A Nowak |
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Institution: | (1) School of Mathematics, Institute for Advanced Study, Princeton, NJ 08540, USA. e-mail: ptrapa@math.ias.edu, US;(2) Program in Theoretical Biology, Institute for Advanced Study, Princeton, NJ 08540, USA. e-mail: nowak@ias.edu, US |
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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).
Received: 1 March 2000 / Published online: 3 August 2000 |
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