2 research outputs found
Weighted nucleoli and dually essential coalitions
We consider linearly weighted versions of the least core and the (pre)nuceolus and
investigate the reduction possibilities in their computation. We slightly extend some
well-known related results and establish their counterparts by using the dual game.
Our main results imply, for example, that if the core of the game is not empty, all
dually inessential coalitions (which can be weakly minorized by a partition in the dual
game) can be ignored when we compute the per-capita least core and the per-capita
(pre)nucleolus from the dual game. This could lead to the design of polynomial time
algorithms for the per-capita (and other monotone nondecreasingly weighted versions
of the) least core and the (pre)nucleolus in specific classes of balanced games with
polynomial many dually essential coalitions
A polynomial time algorithm for computing the nucleolus for a class of disjunctive games with a permission structure
TU-game, Nucleolus, Game with permission structure, Peer group game, Information market game, Algorithm, Complexity, C71,