Social influencing and associated random walk models: Asymptotic consensus times on the complete graph
Abstract
We investigate consensus formation and the asymptotic consensus times in stylized individual- or agent-based models, in which global agreement is achieved through pairwise negotiations with or without a bias. Considering a class of individual-based models on finite complete graphs, we introduce a coarse-graining approach (lumping microscopic variables into macrostates) to analyze the ordering dynamics in an associated random-walk framework. Within this framework, yielding a linear system, we derive general equations for the expected consensus time and the expected time spent in each macro-state. Further, we present the asymptotic solutions of the 2-word naming game and separately discuss its behavior under the influence of an external field and with the introduction of committed agents.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Jun 01, 2011
- Source ID
- 10.1063/1.3598450
Entities
People
- Boleslaw Szymanski
- C. Lim
- G. Korniss
- Junfei Xie
- S. Sreenivasan
- Wei Zhang
Organizations
- Army Research Office
- Office of Naval Research
- Rensselaer Polytechnic Institute