Approximating the Shapley Value of Minimum Cost Spanning Tree Games: An FPRAS for Saving Games

TL;DR

This paper presents an FPRAS method for efficiently approximating the Shapley value in minimum-cost spanning tree games by leveraging a novel saving game framework.

Contribution

It introduces a new saving game framework and develops an FPRAS for the Shapley value in MCST games, improving computational efficiency.

Findings

FPRAS provides a multiplicative approximation of the Shapley value.

Structural properties of saving games enable efficient computation.

The method is applicable to large MCST instances.

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.