笛卡尔网络上新产品扩散中的边界效应
Boundary Effects in the Diffusion of New Products on Cartesian Networks
AI总结：
本文分析了D维笛卡尔网络上离散Bass模型的边界效应，证明边界附近节点采纳率较低且随距离指数衰减，总体采纳水平降幅与节点数M呈$\ rac{1}{M^{1/D}}$关系，并以太阳能采纳数据验证。
摘要：
我们分析了D维笛卡尔网络上离散Bass模型中的边界效应。在2D中，该模型描述了主要通过空间同侪效应扩散的新产品传播，如住宅光伏太阳能系统。我们解析地证明，位于边界附近的节点（住宅单元）比中心位置的节点采纳的可能性更低。这种边界效应是局部的，且随距边界的距离呈指数衰减。在总体层面，边界效应降低了整体采纳水平。这种降低的幅度按~$\ rac{1}{M^{1/D}}$缩放，其中~$M$是节点数。我们的分析得到了关于边界对太阳能采纳效应的经验证据支持。
英文摘要：
We analyze the effect of boundaries in the discrete Bass model on D-dimensional Cartesian networks. In 2D, this model describes the diffusion of new products that spread primarily by spatial peer effects, such as residential photovoltaic solar systems. We show analytically that nodes (residential units) that are located near the boundary are less likely to adopt than centrally-located ones. This boundary effect is local, and decays exponentially with the distance from the boundary. At the aggregate level, boundary effects reduce the overall adoption level. The magnitude of this reduction scales as~$\frac{1}{M^{1/D}}$, where~$M$ is the number of nodes. Our analysis is supported by empirical evidence on the effect of boundaries on the adoption of solar.
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