Computational Aspects of Extending the Shapley Value to Coalitional Games with Externalities

Abstract. 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 ...

• Type: Conference
• Year: 2010
• Where: ECAI
• Authors: Tomasz P. Michalak, Talal Rahwan, Dorota Marciniak, Marcin Szamotulski, Nicholas R. Jennings
• Keywords: Artificial Intelligence, Coalitional Games, ECAI 2010, Externalities, Shapley Value