Cooperative Games With Bounded Dependency Degree


  • Ayumi Igarashi University of Oxford
  • Rani Izsak Weizmann Institute of Science
  • Edith Elkind University of Oxford



Cooperative games provide a framework to study cooperation among self-interested agents. They offer a number of solution concepts describing how the outcome of the cooperation should be shared among the players. Unfortunately, computational problems associated with many of these solution concepts tend to be intractable---NP-hard or worse. In this paper, we incorporate complexity measures recently proposed by Feige and Izsak (2013), called dependency degree and supermodular degree, into the complexity analysis of coopera- tive games. We show that many computational problems for cooperative games become tractable for games whose dependency degree or supermodular degree are bounded. In particular, we prove that simple games admit efficient algorithms for various solution concepts when the supermodular degree is small; further, we show that computing the Shapley value is always in FPT with respect to the dependency degree. Finally, we observe that, while determining the dependency among players is computationally hard, there are efficient algorithms for special classes of games.




How to Cite

Igarashi, A., Izsak, R., & Elkind, E. (2018). Cooperative Games With Bounded Dependency Degree. Proceedings of the AAAI Conference on Artificial Intelligence, 32(1).



AAAI Technical Track: Game Theory and Economic Paradigms