Minimum cost and the emergence of the Zipf-Mandelbrot law

Abstract

This paper illustrates how the Zipf-Mandelbrot law can emerge in language as a result of minimising the cost of categorising sensory images. The categorisation is based on the discrimination game in which sensory stimuli are categorised at different hierarchical layers of increasing density. The discrimination game is embedded in a variant of the language game model, called the selfish game, which in turn is embedded in the framework of iterated learning. The results indicate that a tendency to communicate in general tenns, which is less costly, can contribute to the emergence of the Zipf- Mandelbrot law.

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