Annals of Operations Research

, Volume 235, Issue 1, pp 665–673 | Cite as

Young’s axiomatization of the Shapley value: a new proof

  • Miklós PintérEmail author


We give a new proof of Young’s characterization of the Shapley value. Moreover, as applications of the new proof, we show that Young’s axiomatization of the Shapley value is valid on various well-known subclasses of \(\textit{TU}\) games.


TU cooperative games Shapley value Axiomatization of the Shapley value 


  1. Csóka, P., & Pintér, M. (2014). On the impossibility of fair risk allocation. Corvinus Economics Working Papers, CEWP 12/2014.Google Scholar
  2. Khmelnitskaya, A. B. (2003). Shapley value for constant-sum games. International Journal of Game Theory, 32, 223–227.CrossRefGoogle Scholar
  3. Mlodak, A. (2003). Some values for constant-sum and bilateral cooperative games. Applicationes Mathematicae, 30, 69–87.CrossRefGoogle Scholar
  4. Moulin, H. (1988). Axioms of cooperative decision making. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
  5. Neyman, A. (1989). Uniqueness of the shapley value. Games and Economic Behavior, 1, 116–118.CrossRefGoogle Scholar
  6. Peleg, B., & Sudhölter, P. (2003). Introduction to the theory of cooperative games. Dordrecht: Kluwer.CrossRefGoogle Scholar
  7. Shapley, L. S. (1953). A value for \(n\)-person games. In H. W. Kuhn & A. W. Tucker (Eds.), Contributions to the theory of games II, annals of mathematics studies (Vol. 28, pp. 307–317). Princeton: Princeton University Press.Google Scholar
  8. von Neumann, J., & Morgenstern, O. (1953). Theory of Games and Economic Behavior. Princeton: Princeton University Press.Google Scholar
  9. Young, H. P. (1985). Monotonic solutions of cooperative games. International Journal of Game Theory, 14, 65–72.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Department of Mathematics, MTA-BCE “Lendület” Strategic Interactions Research GroupCorvinus University of BudapestBudapestHungary

Personalised recommendations