We consider a class of cooperative network games with transferable utilities in which players interact through a probabilistic network rather than a regular, deterministic network. In this class of wealth-generating situations we consider probabilistic extensions of the Myerson value and the position value. For the subclass of probabilistic network games in multilinear form, we establish characterizations of these values using an appropriate formulation of component balancedness. We show axiomatizations based on extensions of the well-accepted properties of equal bargaining power, balanced contributions, and balanced link contributions.

中文翻译：

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概率网络值

我们考虑一类具有可转移效用的合作网络游戏，其中玩家通过概率网络而不是常规的确定性网络进行交互。在这类创造财富的情况下，我们考虑迈尔森值和位置值的概率扩展。对于多线性形式的概率网络游戏的子类，我们使用适当的组件平衡公式来建立这些值的特征。我们展示了基于平等议价能力、平衡贡献和平衡链接贡献的广为接受的属性的扩展的公理化。