Propensity and stickiness in the naming game: tipping fractions of minorities.
Agent-based models of the binary naming game are generalized here to represent a family of models parameterized by the introduction of two continuous parameters. These parameters define varying listener-speaker interactions on the individual level with one parameter controlling the speaker and the other controlling the listener of each interaction. The major finding presented here is that the generalized naming game preserves the existence of critical thresholds for the size of committed minorities. Above such threshold, a committed minority causes a fast (in time logarithmic in size of the network) convergence to consensus, even when there are other parameters influencing the system. Below such threshold, reaching consensus requires time exponential in the size of the network. Moreover, the two introduced parameters cause bifurcations in the stabilities of the system's fixed points and may lead to changes in the system's consensus.
Network Science and Technology Center, Rensselaer Polytechnic Institute, 110 8th Street, Troy, New York 12180-3590, USA and Department of Mathematics, Rensselaer Polytechnic Institute, 110 8th Street, Troy, New York 12180-3590, USA.
Andrew M
AM
Thompson
Network Science and Technology Center, Rensselaer Polytechnic Institute, 110 8th Street, Troy, New York 12180-3590, USA and Department of Computer Science, Rensselaer Polytechnic Institute, 100 8th Street, Troy, New York 12180-3590, USA and The Faculty of Computer Science and Management, Wroclaw University of Technology, Wyb. Wyspianskiego 27, 50-370 Wroclaw, Poland.
Boleslaw K
BK
Szymanski
Network Science and Technology Center, Rensselaer Polytechnic Institute, 110 8th Street, Troy, New York 12180-3590, USA and Department of Mathematics, Rensselaer Polytechnic Institute, 110 8th Street, Troy, New York 12180-3590, USA.
Chjan C
CC
Lim