Naming on a directed graph

  • Authors:

  • Giorgio Gosti;William H. Batchelder

  • Affiliations:

  • Institute for Mathematical Behavioral Sciences, School of Social Sciences, University of California, Irvine, CA;Institute for Mathematical Behavioral Sciences, School of Social Sciences, University of California, Irvine, CA

  • Venue:
  • SBP'11 Proceedings of the 4th international conference on Social computing, behavioral-cultural modeling and prediction
  • Year:
  • 2011

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Abstract

We address how the structure of a social communication system affects language coordination. The naming game is an abstraction of lexical acquisition dynamics, in which N agents try to find an agreement on the names to give to objects. Most results on naming games are specific to certain communication network topologies. We present two important results that are general to any graph topology: the first proves that under certain topologies the system always converges to a name-object agreement; the second proves that if these conditions are not met the system may end up in a state in which sub-networks with different competing object-name associations coexist.