2 research outputs found
Computational Aspects of Extending the Shapley Value to Coalitional Games with Externalities
Until recently, computational aspects of the Shapley value were only studied under the assumption that there are no externalities from coalition formation, i.e., that the value of any coalition is independent of other coalitions in the system. However, externalities play a key role in many real-life situations and have been extensively studied in the game-theoretic and economic literature. In this paper, we consider the issue of computing extensions of the Shapley value to coalitional games with externalities proposed by Myerson [21], Pham Do and Norde [23], and McQuillin [17]. To facilitate efficient computation of these extensions, we propose a new representation for coalitional games with externalities, which is based on weighted logical expressions. We demonstrate that this representation is fully expressive and, sometimes, exponentially more concise than the conventional partition function game model. Furthermore, it allows us to compute the aforementioned extensions of the Shapley value in time linear in the size of the input
Complexity of Computing the Shapley Value in Games with Externalities
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