Word diversity can accelerate consensus in naming game

In this paper,we introduce word diversity that reflects the inhomogeneity of words in a communication into the naming game.Diversity is realized by assigning a weight factor to each word.The weight is determined by three different distributions(uniform,exponential,and power-law distributions).During the communication,the probability that a word is selected from speaker’s memory depends on the introduced word diversity.Interestingly,we find that the word diversity following three different distributions can remarkably promote the final convergency,which is of high importance in the self-organized system.In particular,for all the ranges of amplitude of distribution,the powerlaw distribution enables the fastest consensus,while uniform distribution gives the slowest consensus.We provide an explanation of this effect based on both the number of different names and the number of total names,and find that a wide spread of names induced by the segregation of words is the main promotion factor.Other quantities,including the evolution of the averaging success rate of negotiation and the scaling behavior of consensus time,are also studied.These results are helpful for better understanding the dynamics of the naming game with word diversity.