Abstract
The Naming Game has proven to be an important model of opinion dynamics in complex networks. It is significantly enriched by the introduction of nodes committed to a single opinion. The resulting model is still simple but captures core concepts of opinion dynamics in networks. This model limitation is rigid commitment which never changes. Here we study the effect that making commitment variable has on the dynamics of the system. Committed nodes are assigned a commitment strength, w, defining their willingness to lose (in waning), gain (for increasing) or both (in variable) commitment to an opinion. Such model has committed nodes that can stick to a single opinion for some time without losing their flexibility to change it in the long run. The traditional Naming Game corresponds to setting w at infinity. A change in commitment strength impacts the critical fraction of population necessary for a minority consensus. Increasing w lowers critical fraction for waning commitment but increases this fraction for increasing commitment. Further, we show that if different nodes have different values of w, higher standard deviation of w increases the critical fraction for waning commitment and decrease this fraction for increasing commitment.
Highlights
Attempts to understand social interactions on networks has led to many diverse models, each balancing the needs for capturing the essence of network dynamics while keeping the model simple and efficiently computable
Further extensions of the committed binary agreement (BA) models have become rather popular[11,12,13,14], but most of them retain the infinite commitment of individuals
This property causes an increase in pc which becomes a function of w: pc(w) −pc(∞)∼wd, where pc(∞) represents a critical value with infinite commitment strength, d ≈−1.73
Summary
Attempts to understand social interactions on networks has led to many diverse models, each balancing the needs for capturing the essence of network dynamics while keeping the model simple and efficiently computable. The listener adds the new opinion to its list Allowed to evolve this way, the system will eventually reach a stable consensus state in which every node holds the same opinion. A simulation using these rules can be used to observe the effects of two competing opinions in a society, eventually converging to a consensus on one opinion The simplicity of this model allows for studying with it how spreading is affected by such phenomena as the addition of committed agents (nodes that will never change opinion regardless of interaction)[9]. An extension of this work allows for the existence of two competing committed groups[10], creating three distinct regions in parameter space designated as generalizing a region of the absorbing regime into a beak with respect to the committed populations for each opinion. When waining commitment is applied to competing committed groups, the beak widens in parameter space
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