An optimal bound to access the core in TU-games

For any transferable utility game in coalitional form with a nonempty core, we show that that the number of blocks required to switch from an imputation out of the core to an imputation in the core is at most n-1, where n is the number of players. This bound exploits the geometry of the core and is optimal. It considerably improves the upper bounds found so far by Koczy (2006), Yang (2010, 2011) and a previous result by ourselves (2012) in which the bound was n(n-1)/2

An optimal bound to access the core in TU-games

For any transferable utility game in coalitional form with a nonempty core, we show that that the number of blocks required to switch from an imputation out of the core to an imputation in the core is at most n-1, where n is the number of players. This bound exploits the geometry of the core and is optimal. It considerably improves the upper bounds found so far by Koczy (2006), Yang (2010, 2011) and a previous result by ourselves (2012) in which the bound was n(n-1)/2

The Equivalence of the Minimal Dominant Set and the Myopic Stable Set for Coalition Function Form Games

In cooperative games, the coalition structure core is, despite its potential emptiness, one of the most popular solutions. While it is a fundamentally static concept, the consideration of a sequential extension of the underlying dominance correspondence gave rise to a selection of non-empty generalizations. Among these, the payoff-equivalence minimal dominant set and the myopic stable set are defined by a similar set of conditions. We identify some problems with the payoff-equivalence minimal dominant set and propose an appropriate reformulation called the minimal dominant set. We show that replacing asymptotic external stability by sequential weak dominance leaves the myopic stable set unaffected. The myopic stable set is therefore equivalent to the minimal dominant set

An Optimal Bound to Access the Core in TU-Games

International audienceWe show that the core of any n-player TU-game with a non-empty core can be accessed with at most n−1n−1 blocks. It turns out that this bound is optimal in the sense there are TU-games for which the number of blocks required to access the core is exactly n−1n−1

An optimal bound to access the core in TU-games

International audienceWe show that the core of any n-player TU-game with a non-empty core can be accessed with at most n−1n−1 blocks. It turns out that this bound is optimal in the sense there are TU-games for which the number of blocks required to access the core is exactly n−1n−1