Boundary Effects in the Discrete Bass Model
| Autor: | Oren Yakir, Gadi Fibich, Tomer Levin |
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| Rok vydání: | 2018 |
| Předmět: |
010101 applied mathematics
Social and Information Networks (cs.SI) FOS: Computer and information sciences Bass (sound) Boundary effects Applied Mathematics Mathematical analysis Computer Science - Social and Information Networks 0101 mathematics 01 natural sciences Principle of indifference Mathematics |
| DOI: | 10.48550/arxiv.1801.03030 |
| Popis: | 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 neighbor). 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. Comment: 29 pages, 16 figures |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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