Diffusion in countably infinite networks
Michel Grabisch,
Agnieszka Rusinowska and
Xavier Venel ()
Additional contact information
Xavier Venel: Centre d'Economie de la Sorbonne, https://sites.google.com/site/xaviervenelsite/home
Documents de travail du Centre d'Economie de la Sorbonne from Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne
Abstract:
We investigate the phenomenon of diffusion in a countably infinite society of individuals interacting with their neighbors. At a given time, each individual is either active (i.e., has the status or opinion 1) or inactive (i.e., has the status or opinion 0). The configuration of the society describes active and interactive individuals. The diffusion mechanism is based on an aggregation function, which leads to a Markov process with an uncountable set of states, requiring the involvement of s-fields. We focus on two types of aggregation functions - strict, and Boolean. We determine absorbing, transient, and irreducible sets under strict aggregation functions. We shhow that segregation of the society cannot happen, and its state evolves towards a mixture of infinitely many active and infinitely many inactive agents. In our analysis, we mainly focus on the network structure. We distinguish networks with a blinker (periodic class of period 2) and those without. Ø-irreducibility is obtained at the price of a richness assumption of the network, meaning that it should contain infinitely many complex stars and have enough space for storing local configurations. When considering Boolean aggregation functions, the diffusion process becomes deterministic, and the contagion model of Morris (2000) can be seen as a particular case of our framework with aggregation functions. In this case, consensus and non trivial absorbing states as well as cycles can exist
Keywords: diffusion; countable network; aggregation function; absorbing set; transiet set; irreducible set (search for similar items in EconPapers)
JEL-codes: C7 D7 D85 (search for similar items in EconPapers)
Pages: 41 pages
Date: 2019-07
References: Add references at CitEc
Citations: View citations in EconPapers (1)
Downloads: (external link)
ftp://mse.univ-paris1.fr/pub/mse/CES2019/19017.pdf (application/pdf)
Related works:
Working Paper: Diffusion in countably infinite networks (2019) 
Working Paper: Diffusion in countably infinite networks (2019) 
This item may be available elsewhere in EconPapers: Search for items with the same title.
Export reference: BibTeX
RIS (EndNote, ProCite, RefMan)
HTML/Text
Persistent link: https://EconPapers.repec.org/RePEc:mse:cesdoc:19017
Access Statistics for this paper
More papers in Documents de travail du Centre d'Economie de la Sorbonne from Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne Contact information at EDIRC.
Bibliographic data for series maintained by Lucie Label ().