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Authoritative: http://dx.doi.org/10.1103/PhysRevE.75.027101   (Publisher's PDF... likely be available here.)

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Abstract

We present a modified naming game by introducing weights of words in the evolution process. We assign the weight of a word spoken by an agent according to its connectivity, which is a natural reflection of the agent's influence in population. A tunable parameter is introduced, governing the word weight based on the connectivity of agents. We consider the scale-free topology and concentrate on the efficiency of reaching the final consensus, which is of high importance in the self-organized system. Interestingly, it is found that there exists an optimal parameter value, leading to the fastest convergence. This indicates appropriate hub's effects favor the achievement of consensus. The evolution of distinct words helps to give a qualitative explanation of this phenomena. Similar nontrivial phenomena are observed in the total memory of agents with a peak in the middle range of parameter values. Other relevant characters are provided as well, including the time evolution of total memory and success rate for different parameter values as well as the average degree of the network, which are helpful for understanding the dynamics of the modified naming game in detail.

@article{tang07languageGame,
  author={Chuan-Long Tang and Bo-Yu Lin and Wen-Xu Wang and Mao-Bin Hu and Bing-Hong Wang},
  title={Role of connectivity-induced weighted words in language games.},
  journal={Physical Review E},
  year={2007},
  month={Feb},
  volume={75},
  pages={027101},
  doi={10.1103/PhysRevE.75.027101},
  url={http://www.isrl.uiuc.edu/~amag/langev/paper/tang07languageGame.html}
}