Continuous Social Networks
<|reference_start|>Continuous Social Networks: 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 $W$. We show that, under some regularity assumptions, the continuous model is the limit case of the discrete one. We provide some applications of this result. 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. Furthermore, we establish the conditions under which a Nash Equilibrium of the game induce an $\varepsilon$-Nash Equilibrium of the discretization of the game. Finally, we put forward some elements for the characterization of equilibrium strategies.<|reference_end|>
@article{chitiva2024continuous,
    title={Continuous Social Networks},
    author={Juli'an Chitiva and Xavier Venel},
    journal={arXiv preprint arXiv:2407.11710},
    year={2024},
    archivePrefix={arXiv},
    eprint={2407.11710},
    primaryClass={econ.TH cs.GT}
}