4 research outputs found
The kernel is in the least core for permutation games
Permutation games are totally balanced transferable utility cooperative
games arising from certain sequencing and re-assignment optimization problems.
It is known that for permutation games the bargaining set and the core coincide, consequently, the kernel is a subset of the core. We prove that for permutation
games the kernel is contained in the least core, even if the latter is a lower dimensional subset of the core. By means of a 5-player permutation game
we demonstrate that, in sense of the lexicographic center procedure leading to the nucleolus, this inclusion result can not be strengthened. Our 5-player permutation
game is also an example (of minimum size) for a game with a non-convex kernel
A Note on the Computation of the Pre-Kernel for Permutation Games
To determine correctly a non-convex pre-kernel for TU games with more than 4 players can be a challenge full of possible pitfalls, even to the experienced researcher. Parts of the pre-kernel can be easily overlooked. In this note we discuss a method to present the full shape
of the pre-kernel for a permutation game as discussed by Solymosi (2014). By using the property in which the pre-kernel is located in the least core for permutation games, the least core can be covered by a small collection of payoff equivalence classes as identified by Meinhardt
(2013d) to finally establish the correct shape of the pre-kernel