Complexity of Computing the Shapley Value in Games with Externalities

2020-06-02

Proceedings of the AAAI Conference on Artificial Intelligence, 34

Volume

Vol. 34 No. 02: AAAI-20 Technical Tracks 2

AAAI Technical Track: Game Theory and Economic Paradigms

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) and five extensions of the Shapley value to games with externalities. 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: two out of five extensions can be computed in polynomial time for embedded MC-nets and only one for weighted MC-nets.

10.1609/aaai.v34i02.5601