2024/07/16 by Julián Chitiva, Chitiva, Julián, Xavier Venel +1 · 1 citation
Computer Science · Physics and Astronomy · #Complex Network Analysis Techniques #Computer Science and Game Theory (cs.GT) #FOS: Computer and information sciences #FOS: Economics and business #Peer-to-Peer Network Technologies #Theoretical Economics (econ.TH)
paper · pdf · doi:10.48550/arxiv.2407.11710
openalex publication_date 2024/07/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.