Theory and Decision

, Volume 71, Issue 3, pp 365–372

Marginality, differential marginality, and the Banzhaf value

Article

DOI: 10.1007/s11238-010-9224-5

Cite this article as:
Casajus, A. Theory Decis (2011) 71: 365. doi:10.1007/s11238-010-9224-5

Abstract

We revisit the Nowak (Int J Game Theory 26:137–141, 1997) characterization of the Banzhaf value via 2-efficiency, the Dummy player axiom, symmetry, and marginality. In particular, we provide a brief proof that also works within the classes of superadditive games and of simple games. Within the intersection of these classes, one even can drop marginality. Further, we show that marginality and symmetry can be replaced by van den Brink fairness/differential marginality. For this axiomatization, 2-efficiency can be relaxed into superadditivity on the full domain of games.

Keywords

Banzhaf valueAdditivityMarginalityDifferential marginality

JEL Classification

C71

Copyright information

© Springer Science+Business Media, LLC. 2010

Authors and Affiliations

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