with payments. Second we show that the nucleolus of an n-player matching game with a nonempty core can be computed in O(n4 …. First 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 …

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. …

This paper analyzes the 1-nucleolus and, in particular, its relation to the nucleolus and compromise value. It is seen … that the 1-nucleolus of a cooperative game can be characterized using a combination of standard bankruptcy rules for … associated bankruptcy problems. In particular, for any zero-normalized balanced game, the 1-nucleolus coincides with the Aumann …

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. …

theoretical knowledge we present and compare seven properties of fair profit sharing. Findings: We show that the nucleolus is a … core-solution, which does not fulfil aggregate monotonicity. In contrast the Shapley value is an aggregate monotonic … solution but does not belong to the core of every cooperative game. Moreover, we present the Lorenz dominance as an additional …

nucleolus. This paper is an update on the nucleolus and its two related supersolutions, i.e., the kernel and the bargaining set. …

games. Liability games are superadditive, constant sum, partially convex, and partially concave. The core of a liability … game is empty if and only if the firm is insolvent and has multiple positive liabilities. We analyze the nucleolus of the … game and show that allocating the asset value of the firm using the nucleolus satisfies efficiency, non-negativity, and …