The Consensus Formation in the Naming Game on Spatial Networks

The NG model is a model for the dissemination of opinions, focusing on the dissemination of mainstream opinions and how individuals move towards consensus in the adoption of a single opinion through discussion. This is a multi-individual model that uses exchange and negotiation between neighbors to share ideas, performing naming games without any central control on spatial networks. we consider the geometric structure in the two dimensions. In a L*L spatial grids, every grid represents an agent which owns his vocabulary, and every agent updates his vocabulary in terms of the word received from his neighbor. Finally all agents through the process of reaching an agreement. The agreement process can be divided into 3 stages. Firstly, the total number of words drop quickly and about 10 words left, and the remain words form several clusters, and the area of the clusters are almost the same. The adjacent agents in the same cluster have the same word. Secondly, the clusters mutually annex with the number of words slow decreasing. Because the word with the biggest area cannot gain momentum in the competition with other words with the similar area, the word with biggest area will be varying all the time. Thirdly, one area of word surpasses 50 percent and this area will be expanding continuously until reaching an agreement.