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On minimum integer representations of weighted games

Title data

Freixas, Josep ; Kurz, Sascha:
On minimum integer representations of weighted games.
In: Mathematical Social Sciences. Vol. 67 (January 2014) . - 9 - 22.
ISSN 0165-4896
DOI: https://doi.org/10.1016/j.mathsocsci.2013.10.005

Official URL: Volltext

Abstract in another language

We study minimum integer representations of weighted games, i.e. representations where the weights are integers and every other integer representation is at least as large in each component. Those minimum integer representations, if they exist at all, are linked with some solution concepts in game theory. Closing existing gaps in the literature, we prove that each weighted game with two types of voters admits a (unique) minimum integer representation, and give new examples for more than two types of voters without a minimum integer representation. We characterize the possible weights in minimum integer representations and give examples for t ≥ 4 types of voters without a minimum integer representation preserving types, i.e. where we additionally require that the weights are equal within equivalence classes of voters.

Further data

Item Type: Article in a journal
Refereed: Yes
Institutions of the University: Faculties
Faculties > Faculty of Mathematics, Physics und Computer Science
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics in Economy
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics in Economy > Chair Mathematics in Economy - Univ.-Prof. Dr. Jörg Rambau
Profile Fields
Profile Fields > Emerging Fields
Profile Fields > Emerging Fields > Governance and Responsibility
Research Institutions
Research Institutions > Research Centres
Research Institutions > Research Centres > Forschungszentrum für Modellbildung und Simulation (MODUS)
Result of work at the UBT: Yes
DDC Subjects: 500 Science > 510 Mathematics
Date Deposited: 04 Jun 2014 06:48
Last Modified: 03 Nov 2016 07:41
URI: https://eref.uni-bayreuth.de/id/eprint/741