We consider a natural generalization of Jackson and Wolinsky’s (J Econ Theory 71:44–74, 1996) connections model where the quality or strength of a link depends on the amount invested in it and is determined by a non-decreasing function of that amount. The information that the nodes receive through the network is the revenue from investments in links. We prove that in this most general version of the connections model, the only possibly non-empty efficient networks, in the sense of maximizing the aggregate profit, are still the all-encompassing star and the complete network, with the sole and rare exception of a highly particular case where there is a draw between the all-encompassing star, the complete network and a whole range of a particular type of nested split graph structures intermediate between them.

中文翻译：

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具有内在链路强度的广义连接模型中有效网络的特征

我们考虑了Jackson和Wolinsky（J Econ Theory 71：44-74，1996）连接模型的自然概括，其中链接的质量或强度取决于所投资的数量，并由该数量的非递减函数确定。节点通过网络接收的信息是来自链接投资的收入。我们证明，在这种连接模型的最通用版本中，从使总利润最大化的角度来看，唯一可能的非空有效网络仍然是包罗万象的明星和完整的网络，唯一且罕见的例外是在一个非常特殊的情况下，全包围的恒星，完整的网络和介于它们之间的特定类型的嵌套拆分图结构的整个范围之间会产生吸引。