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# On the Construction of High Dimensional Simple Games

URN to cite this document: urn:nbn:de:bvb:703-epub-2738-9

## Title data

Olsen, Martin ; Kurz, Sascha ; Molinero, Xavier:
On the Construction of High Dimensional Simple Games.
Bayreuth , 2016 . - 9 S.

## Abstract

Every simple game can be written as the intersection of a finite number of weighted games. The smallest possible such number is the dimension of a simple game. Taylor and Zwicker have constructed simple games with $n$ players and dimension at least $2^{\frac{n}{2}-1}$. By using theory on error correcting codes, we construct simple games with dimension $2^{n-o(n)}$. Moreover, we show that there are no simple games with dimension $n$ times higher than our games. Our results hold for all $n$.

## Further data

Item Type: Preprint, postprint simple games; weighted games; dimension; coding theory; Hamming distance Mathematics Subject Classification Code: 91B12 (91A12 68P30) 000 Computer Science, information, general works > 004 Computer science300 Social sciences > 320 Political science500 Science > 510 Mathematics Faculties > Faculty of Mathematics, Physics und Computer ScienceFaculties > Faculty of Mathematics, Physics und Computer Science > Department of MathematicsFaculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematical EconomicsProfile Fields > Emerging Fields > Governance and ResponsibilityFacultiesProfile FieldsProfile Fields > Emerging Fields English Yes urn:nbn:de:bvb:703-epub-2738-9 04 Feb 2016 11:19 04 Feb 2016 11:19 https://epub.uni-bayreuth.de/id/eprint/2738