International Journal of Game Theory

, Volume 35, Issue 3, pp 395–426 | Cite as

Dissection of solutions in cooperative game theory using representation techniques

  • L. Hernández-Lamoneda
  • R. Juárez
  • F. Sánchez-Sánchez
Original Paper

Abstract

We compute a decomposition for the space of cooperative TU-games under the action of the symmetric group Sn. In particular we identify all irreducible subspaces that are relevant to the study of symmetric linear solutions – namely those that are isomorphic to the irreducible summands of \(\mathbb{R}^n\). We then use such decomposition to derive, in a very economical way, some old and some new results for linear symmetric solutions.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Amer R, Derks AR, Giménez JM, (2003) On cooperative games, inseparable by semivalues. Int J Game Theory 32(2):181–188CrossRefGoogle Scholar
  2. Dubey P, Neyman A, Weber RJ (1981) Value Theory without Efficiency. Math Oper Res 6(1):122–128CrossRefGoogle Scholar
  3. Driessen T, Radzik T (2002) Extensions of Hart and Mas-Collel’s consistency to efficient, linear and symmetric values for TU-games. In: ICM2002 GTA Proceedings volume. Hongwei, Petrosjan, eds, Quingdao Publishing House, 129–146Google Scholar
  4. Fulton W, Harris J (1991) Representation theory; a first course. Graduate texts in mathematics. vol. 129 Springer, Berlin Heidelberg New YorkGoogle Scholar
  5. Kalai E, Samet D (1987) On weighted Shapley values. Int J Game Theory 16:205–222CrossRefGoogle Scholar
  6. Kleinberg NL, Weiss JH (1985) Equivalent N-person games and the null space of Shapley Value. Math Oper Res 10(2):233–243Google Scholar
  7. Kultti K, Salonen H (2005) Minimum norm solutions for cooperative games. preprintGoogle Scholar
  8. Myerson RB (1991) Game theory: analysis of conflict. Harvard University PressGoogle Scholar
  9. Shapley LS (1953) A value for n-person games. In: Kulin H, Tucker AW (eds) Contributions to the theory of games, vol. 2, Annals of Mathematics Studies Vol. 28. Princeton University Press, Princeton, pp. 307–312Google Scholar
  10. Weber RJ (1988) Probabilistic values for games. In: Roth AE (ed) The Shapley value. Essays in honor of Lloyd S. Shapley. pp 101–120Google Scholar

Copyright information

© Springer Verlag 2006

Authors and Affiliations

  • L. Hernández-Lamoneda
    • 1
  • R. Juárez
    • 2
  • F. Sánchez-Sánchez
    • 1
  1. 1.CIMATGuanajuatoMexico
  2. 2.Department of EconomicsRice UniversityHoustonUSA

Personalised recommendations