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Continuous Social Networks

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  • Juli'an Chitiva
  • Xavier Venel

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 $W$. 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.

Suggested Citation

  • Juli'an Chitiva & Xavier Venel, 2024. "Continuous Social Networks," Papers 2407.11710, arXiv.org.
    • Handle: RePEc:arx:papers:2407.11710
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    References listed on IDEAS

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