On the characterization of weighted simple games

Titelangaben

Freixas, Josep ; Freixas, Marc ; Kurz, Sascha:
On the characterization of weighted simple games.
In: Theory and Decision. Bd. 83 (2017) Heft 4 . - S. 469-498.
ISSN 1573-7187
DOI: https://doi.org/10.1007/s11238-017-9606-z

Volltext

Link zum Volltext (externe URL):

Abstract

This paper has a twofold scope. The first one is to clarify and put in evidence the isomorphic character of two theories developed in quite different fields: on one side, threshold logic, on the other side, simple games. One of the main purposes in both theories is to determine when a simple game is representable as a weighted game, which allows a very compact and easily comprehensible representation. Deep results were found in
threshold logic in the sixties and seventies for this problem. However, game theory has taken the lead
and some new results have been obtained for the problem in the last two decades. The second and main goal of this paper is to provide some new results on this problem and propose several open questions and conjectures
for future research.The results we obtain depend on two significant parameters of the game: the number of types of equivalent players and the number of types of shift-minimal
winning coalitions.