In this paper, we address the problem of fair sharing of the total value of a crowd-sourced network system between major participants (founders) and minor participants (crowd) using cooperative game theory. Shapley allocation is regarded as a fair way for computing the shares of all participants in a cooperative game when the values of all possible coalitions could be quantified. We define a class of value functions for crowd-sourced systems which capture the contributions of the founders and the crowd plausibly and derive closed-form expressions for Shapley allocations to both. These value functions are defined for different scenarios, such as presence of oligopolies or geographic spread of the crowd, taking network effects, including Metcalfe's law, into account. A key result we obtain is that under quite general conditions, the crowd participants are collectively owed a share between $\frac{1}{2}$ to $\frac{2}{3}$ of the total value of the crowd-sourced system. We close with an empirical analysis demonstrating consistency of our results with the compensation offered to the crowd participants in some public internet content sharing companies.

翻译：本文利用合作博弈论，研究了众包网络系统总价值在主要参与者（创始人）与次要参与者（大众）之间的公平分配问题。当所有可能联盟的价值可量化时，Shapley分配被视为计算合作博弈中各参与者份额的公平方式。我们定义了一类适用于众包系统的价值函数，能合理刻画创始人及大众的贡献，并推导出双方Shapley分配的闭式表达式。这些价值函数针对不同场景（如寡头垄断或大众的地理分布）进行定义，同时考虑网络效应（包括梅特卡夫定律）。我们获得的关键结论是：在相当一般的条件下，大众参与者集体应得的份额占众包系统总价值的$\frac{1}{2}$至$\frac{2}{3}$。最后通过实证分析证明，我们的结果与部分公共互联网内容分享公司向大众参与者提供的补偿具有一致性。