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2018 The naming game on the complete graph
Eric Foxall
Electron. J. Probab. 23: 1-42 (2018). DOI: 10.1214/18-EJP250

Abstract

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 some useful estimates for semimartingales with bounded jumps.

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Eric Foxall. "The naming game on the complete graph." Electron. J. Probab. 23 1 - 42, 2018. https://doi.org/10.1214/18-EJP250

Information

Received: 1 March 2017; Accepted: 23 November 2018; Published: 2018
First available in Project Euclid: 19 December 2018

zbMATH: 07021682
MathSciNet: MR3896863
Digital Object Identifier: 10.1214/18-EJP250

Subjects:
Primary: 60K35

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Vol.23 • 2018
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