Boundary effects in the discrete bass model

Gadi Fibich, Tomer Levin, Oren Yakir

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

Abstract

To study the effect of boundaries on diffusion of new products, we introduce two novel analytic tools: The indifference principle, which enables us to explicitly compute the aggregate diffusion on various networks, and the dominance principle, which enables us to rank the diffusion on different networks. Using these principles, we prove our main result that on a finite line, one-sided diffusion (i.e., when each consumer can only be influenced by her left neighbor) is strictly slower than two-sided diffusion (i.e., when each consumer can be influenced by her left and right neighbors). This is different from the periodic case of diffusion on a circle, where one-sided and two-sided diffusion are identical. We observe numerically similar results in higher dimensions.

Original languageEnglish
Pages (from-to)914-937
Number of pages24
JournalSIAM Journal on Applied Mathematics
Volume79
Issue number3
DOIs
StatePublished - 2019

Funding

FundersFunder number
U.S. Department of EnergyDE-EE0007657

    Keywords

    • Agent-based model
    • Boundary
    • Diffusion
    • Indifference principle
    • New products

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