Topological Aspects of the Multi-Language Phases of the Naming Game on Community-Based Networks

Filippo Palombi and Simona Toti
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Filippo Palombi: ENEA—Italian Agency for New Technologies, Energy and Sustainable Economic Development, Via E. Fermi 45, 00044 Frascati, Italy
Simona Toti: ISTAT—Italian National Institute of Statistics, Via C. Balbo 16, 00184 Rome, Italy

Games, 2017, vol. 8, issue 1, 1-35

Abstract: The Naming Game is an agent-based model where individuals communicate to name an initially unnamed object. On a large class of networks continual pairwise interactions lead the system to an ultimate consensus state, in which agents onverge on a globally shared name. Soon after the introduction of the model, it was observed in literature that on community-based networks the path to consensus passes through metastable multi-language states. Subsequently, it was proposed to use this feature as a mean to discover communities in a given network. In this paper we show that metastable states correspond to genuine multi-language phases, emerging in the thermodynamic limit when the fraction of links connecting communities drops below critical thresholds. In particular, we study the transition to multi-language states in the stochastic block model and on networks with community overlap. We also xamine the scaling of critical thresholds under variations of topological properties of the network, such as the number and relative size of communities and the structure of intra-/inter-community links. Our results provide a theoretical justification for the proposed use of the model as a community-detection algorithm.

Keywords: Naming Game; community-based networks; mean ?eld theory; phase diagram; stochastic simulations (search for similar items in EconPapers)
JEL-codes: C C7 C70 C71 C72 C73 (search for similar items in EconPapers)
Date: 2017
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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