A two-step shapley value for cooperative games with coalition structures

Yoshio Kamijo*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

47 Citations (Scopus)


In this paper, we study cooperative games with coalition structures. We show that a solution concept that applies the Shapley value to games among and within coalitions and in which the pure surplus that the coalition obtains is allocated among the intra-coalition members in an egalitarian way, is axiomatized by modified axioms on null players and symmetric players and the usual three axioms: efficiency, additivity and coalitional symmetry. In addition to the original definition, we give two expressions of this solution concept. One is an average of modified marginal contributions and the other is the weighted Shapley value of a game with restricted communication.

Original languageEnglish
Pages (from-to)207-214
Number of pages8
JournalInternational Game Theory Review
Issue number2
Publication statusPublished - 2009 Jun


  • Coalition structure
  • Cooperative game
  • Two-step Shapley value

ASJC Scopus subject areas

  • Business and International Management
  • Computer Science(all)
  • Statistics, Probability and Uncertainty


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