For a two-opinion preferential-attachment network with multiple sampling and general reinforcement, the normalized opinion count, influence capital and activity converge almost surely to invariant sets of a mean-field ODE, provided a fixed-point root is unique.
Continuous Social Networks
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
We develop an extension of the classical model of DeGroot (1974) to a continuum of agents when they interact among them according to a DiKernel. We show that, under some regularity assumptions, the continuous model is the limit case of the discrete one. Additionally, we establish sufficient conditions for the emergence of consensus. We provide some applications of these results. First, we establish a canonical way to reduce the dimensionality of matrices by comparing matrices of different dimensions in the space of DiKernels. Then, we develop a model of Lobby Competition where two lobbies compete to bias the opinion of a continuum of agents. We give sufficient conditions for the existence of a Nash Equilibrium and study their relation with the equilibria of discretizations of the game. Finally, we characterize the equilibrium for a particular case of DiKernels.
citation-role summary
background 1
citation-polarity summary
fields
math.PR 1years
2026 1verdicts
CONDITIONAL 1roles
background 1polarities
unclear 1representative citing papers
citing papers explorer
-
A model of opinion dynamics evolving via a preferential attachment mechanism involving multiple extractions
For a two-opinion preferential-attachment network with multiple sampling and general reinforcement, the normalized opinion count, influence capital and activity converge almost surely to invariant sets of a mean-field ODE, provided a fixed-point root is unique.