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腾讯和脸书数据验证了梅特卡夫定律

Tencent and Facebook Data Validate Metcalfe's Law

  • 摘要: 1980年,梅特卡夫(以太网的发明者)提出网络的价值V与其用户数量n的平方成正比,即Vn2。该定律作为网络效应的一种最著名的体现,受到了很大的争议,许多学者将其称为"错的"或者"危险的",其他的定律相继提出:萨洛夫定律(Vn)、里德定律(Vnlog(n))、奥德利兹科定律(Vn2)。
    该定律已提出三十多年,但一直缺乏实证数据支持。直到2013年,梅特卡夫本人给出了梅特卡夫定律的第一个证据:脸书公司的收入与其月活跃用户数的平方成正比。
    本文采用腾讯公司(中国最大的互联网综合服务提供商之一)与脸书公司(全球最大的社交网络公司)过去十年的实际数据,拓展梅特卡夫的方法,得出了下列结果:(1)针对网络效应的四种体现给出了腾讯与脸书实际数据的拟合结果,并显示梅特卡夫定律的拟合误差远小于其他三个定律的拟合误差;(2)梅特卡夫定律对腾讯公司数据与脸书公司数据均成立;(3)腾讯和脸书公司的成本与其月活跃用户均非线性关系,而是与其月活跃用户的平方成正比;(4)腾讯与脸书的月活跃用户数的增长趋势符合netoid函数。

     

    Abstract: In 1980s, Robert Metcalfe, the inventor of Ethernet, proposed a formulation of network value in terms of the network size (the number of nodes of the network), which was later named as Metcalfe's law. The law states that the value V of a network is proportional to the square of the size n of the network, i.e., Vn2. Metcalfe's law has been influential and an embodiment of the network effect concept. It also generated many controversies. Some scholars went so far as to state "Metcalfe's law is wrong" and "dangerous". Some other laws have been proposed, including Sarnoff's law (Vn), Odlyzko's law (Vn log(n)), and Reed's law (Vn2). Despite these arguments, for 30 years, no evidence based on real data was available for or against Metcalfe's law. The situation was changed in late 2013, when Metcalfe himself used Facebook's data over the past 10 years to show a good fit for Metcalfe's law. In this paper, we expand Metcalfe's results by utilizing the actual data of Tencent (China's largest social network company) and Facebook (the world's largest social network company). Our results show that: 1) of the four laws of network effect, Metcalfe's law by far fits the actual data the best; 2) both Tencent and Facebook data fit Metcalfe's law quite well; 3) the costs of Tencent and Facebook are proportional to the squares of their network sizes, not linear; and 4) the growth trends of Tencent and Facebook monthly active users fit the netoid function well.

     

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