Marginal Games and Characterizations of the Shapley Value in TU Games

  • Takumi Kongo
  • Yukihiko Funaki
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 758)


Axiomatizations and recursive representations of the Shapley value on the class of all cooperative games with transferable utilities are given. Marginal games, which are closely related to dual games, play central roles in our results. Our axiomatizations are based on axioms that are marginal game variations of the well-known balanced contributions property, so that they are interpreted as fair treatment between two players in games as the balanced contributions property is. Our general recursive representation enables us to represent the Shapley value for n-person games by those for r-person and \((n-r)\)-person games with fixed \(r<n\). The particular case of \(r=1\) has a clear contrasting interpretation to the existing recursive formula.


Shapley value Marginal game Dual game Balanced contribution Recursive representation 



The authors thank Rodica Branzei, Irinel Dragan, and Stef Tijs for their helpful comments. This work was supported by JSPS KAKENHI Grant Number 15K17031 (Kongo), 24220033 (Funaki), 26245026 (Funaki), and 26380247 (Funaki).


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© Springer Nature Singapore Pte Ltd. 2017

Authors and Affiliations

  1. 1.Faculty of EconomicsFukuoka UniversityFukuokaJapan
  2. 2.School of Political Science and EconomicsWaseda UniversityTokyoJapan

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