Arieli, Itai, Ashkenazi-Golan, Galit 
ORCID: 0000-0003-3896-4131, Peretz, Ron and Tsodikovich, Yevgeny
(2025)
Minimal contagious sets: degree distributional bounds.
Journal of Economic Theory.
ISSN 0022-0531
(In Press)
Abstract
Agents in a network adopt an innovation if a certain fraction of their neighbors has already done so. We study the minimal contagious set size required for a successful innovation adoption by the entire population, and provide upper and lower bounds on it. Since detailed information about the network structure is often unavailable, we study bounds that depend only on the degree distribution of the network – a simple statistic of the network topology. Moreover, as our bounds are robust to small changes in the degree distribution, they also apply to large networks for which the degree distribution can only be approximated. Applying our bounds to growing networks shows that the minimal contagious set size is linear in the number of nodes. Consequently, for outside of knife-edge cases (such as the star-shaped network), contagion cannot be achieved without seeding a significant fraction of the population. This finding highlights the resilience of networks and demonstrates a high penetration cost in the corresponding markets.
| Item Type: | Article |
|---|---|
| Additional Information: | © 2025 The Author(s) |
| Divisions: | Mathematics |
| Subjects: | H Social Sciences > HB Economic Theory |
| JEL classification: | O - Economic Development, Technological Change, and Growth > O3 - Technological Change; Research and Development > O33 - Technological Change: Choices and Consequences; Diffusion Processes M - Business Administration and Business Economics; Marketing; Accounting > M3 - Marketing and Advertising > M30 - General |
| Date Deposited: | 16 Apr 2025 09:30 |
| Last Modified: | 16 Apr 2025 09:30 |
| URI: | http://eprints.lse.ac.uk/id/eprint/127953 |
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