Logo
Munich Personal RePEc Archive

The Nakamura numbers for computable simple games

Kumabe, Masahiro and Mihara, H. Reiju (2007): The Nakamura numbers for computable simple games.

Warning
There is a more recent version of this item available.
[thumbnail of MPRA_paper_3684.pdf]
Preview
PDF
MPRA_paper_3684.pdf

Download (214kB) | Preview

Abstract

The Nakamura number of a simple game plays a critical role in preference aggregation (or multi-criterion ranking): the number of alternatives that the players can always deal with rationally is less than this number. We comprehensively study the restrictions that various properties for a simple game impose on its Nakamura number. We find that a computable game has a finite Nakamura number greater than three only if it is proper, nonstrong, and nonweak, regardless of whether it is monotonic or whether it has a finite carrier. The lack of strongness often results in alternatives that cannot be strictly ranked.

Available Versions of this Item

Atom RSS 1.0 RSS 2.0

Contact us: mpra@ub.uni-muenchen.de

This repository has been built using EPrints software.

MPRA is a RePEc service hosted by Logo of the University Library LMU Munich.