Dimension and codimension of simple games
Sascha Kurz, Xavier Molinero, Martin Olsen, and Maria Serna
TL;DR
This paper investigates the complexity of representing simple games through intersections or unions of weighted majority games, exploring their dimension and codimension, and providing examples with varying complexity.
Contribution
It introduces new insights into the complexity of simple game representations, including examples with linear dimension and exponential codimension.
Findings
Examples with linear dimension and exponential codimension
Analysis of complexity in representing simple games
Insights into the structure of simple games
Abstract
This paper studies the complexity of computing a representation of a simple game as the intersection (union) of weighted majority games, as well as, the dimension or the codimension. We also present some examples with linear dimension and exponential codimension with respect to the number of players.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.