Theory and Decision

, Volume 71, Issue 2, pp 163–174 | Cite as

Differential marginality, van den Brink fairness, and the Shapley value

Article

Abstract

We revisit the characterization of the Shapley value by van den Brink (Int J Game Theory, 2001, 30:309–319) via efficiency, the Null player axiom, and some fairness axiom. In particular, we show that this characterization also works within certain classes of TU games, including the classes of superadditive and of convex games. Further, we advocate some differential version of the marginality axiom (Young, Int J Game Theory, 1985, 14: 65–72), which turns out to be equivalent to the van den Brink fairness axiom on large classes of games.

Keywords

TU game Superadditive game Additivity Solidarity Convex cone 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Aumann R. J. (1989) Lectures on game theory. Westview Press, BoulderGoogle Scholar
  2. Casajus, A. (2009). Another characterization of the Owen value without the additivity axiom. Theory and Decision (forthcoming). doi: 10.1007/s11238-009-9148-0.
  3. Chun Y. (1989) A new axiomatization of the Shapley value. Games and Economic Behavior 1: 119–130CrossRefGoogle Scholar
  4. Harsanyi, J. C. (1959). A bargaining model for cooperative n-person games. In A. W. Tucker & R. D. Luce (Eds.), Contributions to the theory of games IV (Vol. 2, pp. 325–355). Princeton, NJ: Princeton University Press.Google Scholar
  5. Huettner, F. (2007). Axiomatizations of the Shapley value. Master’s thesis, Wirtschaftswissenschaftliche Fakultät. Germany: Universität Leipzig.Google Scholar
  6. Nowak A. S., Radzik T. (1994) A solidarity value for n-person transferable utility games. International Journal of Game Theory 23: 43–48CrossRefGoogle Scholar
  7. Owen, G. (1977). Values of games with a priori unions. In R. Henn & O. Moeschlin, Essays in mathematical economics & game theory (pp. 76–88). Berlin: Springer.Google Scholar
  8. Shapley, L. S. (1953). A value for n-person games. In H. Kuhn & A. Tucker, Contributions to the theory of games (Vol. II, pp. 307–317). Princeton: Princeton University Press.Google Scholar
  9. van den Brink R. (2001) An axiomatization of the Shapley value using a fairness property. International Journal of Game Theory 30: 309–319CrossRefGoogle Scholar
  10. van den Brink R. (2007) Null or nullifying players: The difference between the Shapley value and equal division solutions. Journal of Economic Theory 136: 767–775CrossRefGoogle Scholar
  11. Young H. P. (1985) Monotonic solutions of cooperative games. International Journal of Game Theory 14: 65–72CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC. 2009

Authors and Affiliations

  1. 1.IMW Institute of Mathematical EconomicsBielefeld UniversityBielefeldGermany
  2. 2.Chair of Economics and Information SystemsHHL Leipzig Graduate School of ManagementLeipzigGermany
  3. 3.Wirtschaftswissenschaftliche FakultätUniversität LeipzigLeipzigGermany

Personalised recommendations