Abstract We consider a cooperative game based on a network in which nodes represent players and the characteristic function is defined using a maximal covering by the pairs of connected nodes. Problems of this form arise in many applications such as mobile communications, patrolling, logistics and sociology. The Owen value, which describes the significance of each node in the network, is derived. We show that the method of generating functions can be useful for calculating this Owen value and illustrate this approach based on examples of network structures.

中文翻译：

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合作网络覆盖博弈中的生成函数和欧文值

摘要 我们考虑一个基于网络的合作博弈，其中节点代表玩家，特征函数是使用连接节点对的最大覆盖来定义的。这种形式的问题出现在许多应用中，例如移动通信、巡逻、物流和社会学。导出描述网络中每个节点重要性的 Owen 值。我们展示了生成函数的方法可用于计算此 Owen 值，并基于网络结构示例说明这种方法。