On the domain of two-sided assignment markets, the nucleolus is axiomatized as the unique solution that satisfies … characterization of the nucleolus by means of a strong form of the bisection property that characterizes the inter- section between the … core and the kernel of a coalitional game in Maschler et al (1979). …

solution concepts (such as the nucleolus) violate this property are scarce and have no economic interpretation. We provide an …

(Definition 4.4) and completeness (Definition 4.8). For this class we prove that the core, resp., the nucleolus when the core is … complete Eulerian graphs having the 4-cut property, we are able to test core membership in O(n) time, and when the core is not … empty, we show how to calculate the nucleolus in O(n^2) time, n being the number of players. …

The nucleolus offers a desirable payoff-sharing solution in cooperative games, thanks to its attractive properties …. Although computing the nucleolus is very challenging, the Kohlberg criterion offers a method for verifying whether a solution … is the nucleolus in relatively small games (number of players n at most 15). This approach becomes more challenging for …

This paper discusses the core of the game corresponding to the standard fixed tree problem. We introduce the concept of … a weighted constrained egalitarian solution. The core of the standard fixed tree game equals the set of all weighted …

coalitions also their union is feasible. Properties of solutions (the core, the nucleolus, the prekernel and the Shapley value …