Ronald Dickman, Nicholas R. Moloney, Eduardo G. Altmann
We solve the cost-minimization problem posed by Ferrer i Cancho and Sol\'e in their model of communication that aimed at explaining the origin of Zipf's law [PNAS 100, 788 (2003)]. Direct analysis shows that the minimum cost is min {lambda, 1-lambda}, where lambda determines the relative weights of speaker's and hearer's costs in the total. The nature of the minimizing solution changes discontinuously at lambda=1/2, being qualitatively different for lambda < 1/2, lambda > 1/2, and lambda=1/2. Zipf's law is found only in a vanishing fraction of the minimum-cost solutions at lambda = 1/2 and therefore is not explained by this model. We also investigate the solutions reached by the previously used minimization algorithm and find that they correctly recover global minimum states at the transition.
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http://arxiv.org/abs/1207.0238
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