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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.

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 $n$.