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

  • Authors:

  • Tomasz Michalak;Talal Rahwan;Dorota Marciniak;Marcin Szamotulski;Nicholas R. Jennings

  • Affiliations:

  • School of Electronics and Computer Science, University of Southampton, UK;School of Electronics and Computer Science, University of Southampton, UK;National Institute of Telecommunications, Poland and Universitat Politècnica de Catalunya, Spain;National Institute of Telecommunications, Poland and Instituto Superior Técnico, Universidade Técnica de Lisboa, Portugal;School of Electronics and Computer Science, University of Southampton, UK

  • Venue:
  • Proceedings of the 2010 conference on ECAI 2010: 19th European Conference on Artificial Intelligence
  • Year:
  • 2010

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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 the Shapley value in time linear in the size of the input.