不同消费者的新产品扩散
Diffusion of new products with heterogeneous consumers
摘要：
一种新产品在不同类型的消费者中传播得更快还是在相同类型的消费者中传播得更快？我们分析了这个问题，使用随机离散巴斯模型，其中消费者可能会不同，在他们的个人外部影响率$\{p_j \}$和他们的个人内部影响率$\{ q_j \}$。当网络是完整的并且异质性仅在$\{p_j \}$中或仅在$\{ q_j \}$中表现时，与相应的同质网络相比，它总是减慢扩散。然而，当消费者在$\{p_j\}$和$\{q_{j}\}$中是异质的时，异质性在某些情况下减缓了扩散，但在另一些情况下加速了扩散。此外，在某些情况下，异质和同质采用水平之间的主导地位是全球性的，但在其他情况下，随着时间的推移而变化。也许令人惊讶的是，两个网络之间的全局优势并不总是在“加性变换”下保持，例如向两个网络添加相同的节点。当网络不完全时，异质性的影响还取决于其在网络中的空间分布。
英文摘要：
Does a new product spread faster among heterogeneous or homogeneous consumers? We analyze this question using the stochastic discrete Bass model, in which consumers may differ in their individual external influence rates $\{p_j \}$ and in their individual internal influence rates $\{ q_j \}$. When the network is complete and the heterogeneity is only manifested in $\{p_j \}$ or only in $\{ q_j \}$, it always slows down the diffusion, compared to the corresponding homogeneous network. When, however, consumers are heterogeneous in both $\{p_j\}$ and $\{q_{j}\}$, heterogeneity slows down the diffusion in some cases, but accelerates it in others. Moreover, the dominance between the heterogeneous and homogeneous adoption levels is global in time in some cases, but changes with time in others. Perhaps surprisingly, global dominance between two networks is not always preserved under "additive transformations", such as adding an identical node to both networks. When the network is not complete, the effect of heterogeneity depends also on its spatial distribution within the network.
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