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We consider a model of language development, known as the naming game, in which agents invent, share and then select descriptive words for a single object, in such a way as to promote local consensus. When formulated on a finite and connected graph, a global consensus eventually emerges in which all agents use a common unique word. Previous numerical studies of the model on the complete graph with $n$ agents suggest that when no words initially exist, the time to consensus is of order $n^{1/2}$, assuming each agent speaks at a constant rate. We show rigorously that the time to consensus is at least $n^{1/2-o(1)}$, and that it is at most constant times $log n$ when only two words remain. In order to do so we develop sample path estimates for quasi-left continuous semimartingales with bounded jumps.
We examine a naming game with two agents trying to establish a common vocabulary for n objects. Such efforts lead to the emergence of language that allows for an efficient communication and exhibits some degree of homonymy and synonymy. Although homo
In this paper, we study the role of degree mixing in the naming game. It is found that consensus can be accelerated on disassortative networks. We provide a qualitative explanation of this phenomenon based on clusters statistics. Compared with assort
Red and blue particles are placed in equal proportion through-out either the complete or star graph and iteratively sampled to take simple random walk steps. Mutual annihilation occurs when particles with different colors meet. We compare the time it
Consider the complete graph on $n$ vertices. To each vertex assign an Ising spin that can take the values $-1$ or $+1$. Each spin $i in [n]={1,2,dots, n}$ interacts with a magnetic field $h in [0,infty)$, while each pair of spins $i,j in [n]$ interac
In recent times, the research field of language dynamics has focused on the investigation of language evolution, dividing the work in three evolutive steps, according to the level of complexity: lexicon, categories and grammar. The Naming Game is a s