离散Bass模型中的边界效应
Boundary Effects in the Discrete Bass Model
摘要：
为了研究边界对新产品扩散的影响，我们引入了两种新的分析工具：无差异原理，它使我们能够明确地计算各种网络上的总扩散，以及优势原理，它使我们能够对不同网络上的扩散进行排名。利用这些原理，我们证明了我们的主要结果，在有限线上，单侧扩散（即，当每个消费者只能受到她的左边邻居的影响时）严格地慢于双侧扩散（即，当每个消费者可以受到她的左右邻居的影响时）。这与圆上扩散的周期性情况不同，其中单侧和双侧扩散相同。我们在更高的维度上观察到数值上类似的结果。
英文摘要：
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.
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