In this research, we address the problem of computing the Shapley value in minimum-cost spanning tree (MCST) games. We introduce the saving game as a key framework for approximating the Shapley value. By reformulating MCST games into their saving-game counterparts, we obtain structural properties that enable multiplicative (relative-error) approximation. Building on this reformulation, we develop a Monte Carlo based Fully Polynomial-time Randomized Approximation Scheme (FPRAS) for the Shapley value.

翻译：本研究探讨了最小成本生成树（MCST）博弈中沙普利值的计算问题。我们引入节省博弈作为近似沙普利值的关键框架。通过将MCST博弈重新表述为其对应的节省博弈形式，我们获得了支持乘性（相对误差）近似的结构性质。基于这一重新表述，我们开发了一种基于蒙特卡洛的全多项式时间随机近似方案（FPRAS）用于计算沙普利值。