that although the game is not convex its core is always non-empty. Furthermore we provide a painting algorithm for large … families of directed acyclic graph games that finds the nucleolus in polynomial time. …

with payments. Second we show that the nucleolus of an n-player matching game with a nonempty core can be computed in O(n4 … we present an O(nm+n2 log n) algorithm that tests if the core of a matching game defined on a weighted graph with n … vertices and m edges is nonempty and that computes a core member if the core is nonempty. This algorithm improves previous work …

rationing we give a proof to Aumann and Maschlers theorem i.e. the consistent solution of a bankruptcy problem is the nucleolus … proof is not just simple and demonstrative but also provides an insight how the nucleolus is constructed in such games. …

coalitions determine both the core and the nucleolus in monotonic games whenever the core is non-empty. We show how these two …We provide a new modus operandi for the computation of the nucleolus in cooperative games with transferable utility … sample computation of the nucleolus of bankruptcy games - the shortest of its kind. …

, hence agreements must be stable against both types of deviations. The appropriate extension of the classicakl core concept …, the Sustainable Core, is defined for this new setup to test the stability of allocations in such a complex environment. A … achieved by choosing an element in the Sustainable Core. …

In this paper we investigate some new applications of Scarf's Lemma. First, we introduce the notion of fractional core …

between the methods. There are some properties that an allocation method should satisfy: full allocation, core compatibility … methods from the point of view if they are satisfying core compatibility. We test this with simulation where we add to the … existing literature that we test core compatibility with different assumptions on returns: on normal and t-distributed returns …

axiomatization of the Shapley value that the requirements of Core Compatibility, Equal Treatment Property and Strong Monotonicity are …

-based cost games. We demonstrate that in general a DAG-game is not concave, even its core might be empty, but we provide an … associated DAG-game. We introduce a network canonization process and prove various structural results for the core of canonized … DAG-games. In particular, we characterize classes of coalitions that have a constant payoff in the core. In addition, we …

games with non-empty cores this means that the core can be reached via a bounded sequence of blocks. …