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On the Construction of High Dimensional Simple Games

Title data

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

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Official URL: Volltext

Abstract in another language

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, working paper, discussion paper
Keywords: simple games; weighted games; dimension; coding theory; Hamming distance
Subject classification: Mathematics Subject Classification Code: 91B12 (91A12 68P30)
Institutions of the University: Faculties > Faculty of Mathematics, Physics und Computer Science
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics in Economy
Profile Fields > Emerging Fields > Governance and Responsibility
Faculties
Profile Fields
Profile Fields > Emerging Fields
Result of work at the UBT: Yes
DDC Subjects: 000 Computer Science, information, general works > 004 Computer science
300 Social sciences > 320 Political science
500 Science > 510 Mathematics
Date Deposited: 06 Feb 2016 22:00
Last Modified: 06 Feb 2016 22:00
URI: https://eref.uni-bayreuth.de/id/eprint/30589

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