Approximating the Shapley Value of Minimum Cost Spanning Tree Games: An FPRAS for Saving Games
Computer Science and Game Theory
2026-03-25 v1
Abstract
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.
Cite
@article{arxiv.2603.22843,
title = {Approximating the Shapley Value of Minimum Cost Spanning Tree Games: An FPRAS for Saving Games},
author = {Takumi Jimbo and Tomomi Matsui},
journal= {arXiv preprint arXiv:2603.22843},
year = {2026}
}
Comments
20 pages, 2 figures