Annals of Operations Research

, Volume 259, Issue 1–2, pp 1–19 | Cite as

The Shapley value in the Knaster gain game

  • Federica Briata
  • Andrea Dall’Aglio
  • Marco Dall’AglioEmail author
  • Vito Fragnelli
Original Paper


In Briata et al. (AUCO Czech Econ Rev 6:199–208, 2012), the authors introduce a cooperative game with transferable utility for allocating the gain of a collusion among completely risk-averse agents involved in the fair division procedure introduced by Knaster (Ann Soc Pol Math 19:228–230, 1946). In this paper we analyze the Shapley value (Shapley, in: Kuhn, Tucker (eds) Contributions to the theory of games II (Annals of Mathematics Studies 28), Princeton University Press, Princeton, 1953) of the game and propose its use as a measure of the players’ attitude towards collusion. Furthermore, we relate the sign of the Shapley value with the ranking order of the players’ evaluation, and show that some players in a given ranking will always deter collusion. Finally, we characterize the coalitions that maximize the gain from collusion, and suggest an ad-hoc coalition formation mechanism.


Shapley value Knaster procedure Collusion 



The authors would like to thank Stefano Moretti for suggesting Eq. (25) in the “Appendix”, and two anonimous referees for their constructive advices.


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Copyright information

© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of GenovaGenoaItaly
  2. 2.Department of MathematicsSapienza University of RomeRomeItaly
  3. 3.Department of Economics and FinanceLUISS UniversityRomeItaly
  4. 4.Department of Sciences and Innovative TechnologiesUniversity of Eastern PiedmontAlessandriaItaly

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