Modeling Product Ecosystems
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909817860259840 |
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| author | Banerjee, Tridib |
| author_facet | Banerjee, Tridib |
| contents | This paper develops a dynamical-systems framework for modeling influence propagation in product adoption networks, formulated as a positive linear system with Metzler interaction matrices and utility-based decay. Exact solutions are derived for constant, piecewise-constant, and fully time-varying interaction structures using matrix exponentials and the Peano--Baker series. It establishes five results: (i) positive interactions guarantee nonnegative amplification, (ii) perceived utility saturates after $\approx\!3$ complementary additions (Weber--Fechner), (iii) frequency of comparable introductions dominates incremental quality improvements, (iv) reinforcing interactions yields monotone gains while decay control gives ambiguous effects, and (v) long-run retention under SIS-type dynamics is bounded by the inverse spectral radius of the adoption graph. These results extend epidemic-threshold theory and positive-systems analysis to networked adoption, yielding explicit, calibratable expressions for influence dynamics on networks. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2510_00036 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Modeling Product Ecosystems Banerjee, Tridib Social and Information Networks This paper develops a dynamical-systems framework for modeling influence propagation in product adoption networks, formulated as a positive linear system with Metzler interaction matrices and utility-based decay. Exact solutions are derived for constant, piecewise-constant, and fully time-varying interaction structures using matrix exponentials and the Peano--Baker series. It establishes five results: (i) positive interactions guarantee nonnegative amplification, (ii) perceived utility saturates after $\approx\!3$ complementary additions (Weber--Fechner), (iii) frequency of comparable introductions dominates incremental quality improvements, (iv) reinforcing interactions yields monotone gains while decay control gives ambiguous effects, and (v) long-run retention under SIS-type dynamics is bounded by the inverse spectral radius of the adoption graph. These results extend epidemic-threshold theory and positive-systems analysis to networked adoption, yielding explicit, calibratable expressions for influence dynamics on networks. |
| title | Modeling Product Ecosystems |
| topic | Social and Information Networks |
| url | https://arxiv.org/abs/2510.00036 |