at Google ScholarTitle data
Hof, Frits ; Kern, Walter ; Kurz, Sascha ; Paulusma, Daniël:
Simple Games versus Weighted Voting Games.
2018
Event: 11th International Symposium on Algorithmic Game Theory, SAGT 2018
, 11.-13.09.2018
, Beijing, China.
(Conference item: Conference
,
Speech
)
Abstract in another language
A simple game (N,v) is given by a set N of n players and a partition of 2^N into a set L of losing coalitions L' with value v(L')=0 that is closed under taking subsets and a set W of winning coalitions W' with v(W')=1. Simple games with alpha= \min_{p>=0}\max_{W' in W,L' in L} p(L')/p(W') <1 are known as weighted voting games. Freixas and Kurz (IJGT, 2014) conjectured that alpha<=n/4 for every simple game (N,v). We confirm this conjecture for two complementary cases, namely when all minimal winning coalitions have size 3 and when no minimal winning coalition has size 3. As a general bound we prove that alpha<=2n/7 for every simple game (N,v). For complete simple games, Freixas and Kurz conjectured that alpha=O(sqrt(n)). We prove this conjecture up to a ln n factor. We also prove that for graphic simple games, that is, simple games in which every minimal winning coalition has size 2, computing alpha is NP-hard, but polynomial-time solvable if the underlying graph is bipartite. Moreover, we show that for every graphic simple game, deciding if alpha<a is polynomial-time solvable for every fixed a>0.
Further data
| Item Type: | Conference item (Speech) |
|---|---|
| Refereed: | Yes |
| Additional notes: | Speaker: Walter Kern |
| Keywords: | simple game; weighted voting game; graphic simple game; complete simple game |
| Subject classification: | Mathematics Subject Classification Code: 91B12 94C10 |
| 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 Mathematical Economics Profile Fields > Emerging Fields Profile Fields > Emerging Fields > Governance and Responsibility Faculties Profile Fields |
| Result of work at the UBT: | Yes |
| DDC Subjects: | 000 Computer Science, information, general works > 004 Computer science 500 Science > 510 Mathematics |
| Date Deposited: | 27 Sep 2018 09:09 |
| Last Modified: | 27 Sep 2018 09:09 |
| URI: | https://eref.uni-bayreuth.de/id/eprint/45891 |