Diffusion in large networks

Michel Grabisch, Agnieszka Rusinowska and Xavier Venel
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Xavier Venel: LUISS - Libera Università Internazionale degli Studi Sociali Guido Carli [Roma], PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École nationale des ponts et chaussées - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement

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Abstract: We investigate the phenomenon of diffusion in a countably infinite society of individuals interacting with their neighbors in a network. At a given time, each individual is either active or inactive. The diffusion is driven by two characteristics: the network structure and the diffusion mechanism represented by an aggregation function. We distinguish between two diffusion mechanisms (probabilistic, deterministic) and focus on two types of aggregation functions (strict, Boolean). Under strict aggregation functions, polarization of the society cannot happen, and its state evolves towards a mixture of infinitely many active and infinitely many inactive agents, or towards a homogeneous society. Under Boolean aggregation functions, the diffusion process becomes deterministic and the contagion model of Morris (2000) becomes a particular case of our framework. Polarization can then happen. Our dynamics also allows for cycles in both cases. The network structure is not relevant for these questions, but is important for establishing irreducibility, at the price of a richness assumption: the network should contain at least one complex star and have enough space for storing local configurations. Our model can be given a game-theoretic interpretation via a local coordination game, where each player would apply a best-response strategy in a random neighborhood.

Keywords: diffusion; countable network; aggregation function; polarization; convergence; bestresponse (search for similar items in EconPapers)
Date: 2022-06
New Economics Papers: this item is included in nep-gth, nep-net, nep-soc and nep-ure
Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-03881455v2
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Published in Journal of Economic Dynamics and Control, 2022, 139, ⟨10.1016/j.jedc.2022.104439⟩

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Journal Article: Diffusion in large networks (2022)
Working Paper: Diffusion in large networks (2022)
Working Paper: Diffusion in large networks (2022)
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Persistent link: https://EconPapers.repec.org/RePEc:hal:cesptp:halshs-03881455

DOI: 10.1016/j.jedc.2022.104439

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