Complexity of Computing the Shapley Value in Games with Externalities
Oskar Skibski
TL;DR
This paper investigates the computational complexity of calculating the Shapley value in games with externalities, comparing two representations and highlighting their differences in conciseness and computational difficulty.
Contribution
It provides a complexity analysis of Shapley value computation in externality games using embedded and weighted MC-nets, revealing trade-offs between representation conciseness and computational efficiency.
Findings
Weighted MC-nets are more concise than embedded MC-nets.
Weighted MC-nets have slightly worse computational properties for Shapley value calculation.
The study clarifies the complexity landscape for externality games with different representations.
Abstract
We study the complexity of computing the Shapley value in games with externalities. We focus on two representations based on marginal contribution nets (embedded MC-nets and weighted MC-nets). Our results show that while weighted MC-nets are more concise than embedded MC-nets, they have slightly worse computational properties when it comes to computing the Shapley value.
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