International Journal of Game Theory

, Volume 26, Issue 2, pp 235–248 | Cite as

Effectivity functions and simple games

  • Ton Storcken
Article

Abstract

The rather new notion of effectivity function is related to the notion of simple game. Every effectivity function is associated with a simple game. So theory about simple games may be applicable to effectivity functions. E.g. if the effectivity function is additive, then the associated simple game is weighted. Via a characterization of weighted simple games it is possible to characterize maximal additive effectivity functions.

Finally we characterize additive effectivity functions and their associated simple games.

Key words

Effectivity functions simple games additive weighted k-trade robust asummability convex maximal monotonie strongly monotonie power preserving 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Abdou J, Keiding H (1991) Effectivity functions in social choice. Kluwer Academic Publisher Dordrecht The NetherlandsGoogle Scholar
  2. Elgot CC (1960) Truth functions realized by single threshold organs. AIEE Conference Pape 60-1311. Also in Switching Circuit Theory and Logical Design 1961, 341–345Google Scholar
  3. Fishburn P (1972) The theory of social choice. Princeton University Press Princeton New Jersey Gale D (1960) The theory of linear economic models. Me Graw-Hill Book company New YorkGoogle Scholar
  4. Moulin H, Peleg B (1982) Core of effectivity functions and implementation theory. Journal of Mathematical Economics 10: 57–75Google Scholar
  5. Taylor A, Zwicker W (1992) A characterization of weighted voting. Proceedings of the American Mathematical Society 115: 1089–1094Google Scholar

Copyright information

© Physica-Verlag 1997

Authors and Affiliations

  • Ton Storcken
    • 1
  1. 1.Faculty of EconomicsUniversity of LimburgMD MaastrichtThe Netherlands

Personalised recommendations