The Shapley-Ichiishi result states that a game is convex if and only if the convex hull of marginal vectors equals the core. In this paper we generalize this result by distinguishing equivalence classes of balanced games that share the same core structure. We then associate a system of linear...

The process of computing the nucleolus of arbitrary transferable utility games is notoriously hard. A number of papers have appeared in which the nucleolus is computed by an algorithm in which either one or a huge number of huge linear programs have to be solved. <p>We show that on the class of...</p>

This paper investigates the use of egalitarian criteria to select allocations in bankruptcy problems. In our work, we characterize the sets of Lorenz maximal elements for these problems. We show that the allocation selected by the Proportional Rule is the only allocation that belongs to all...

In this paper we introduce and study the w-Coalitional Lorenz Solutions to identify the similarities and differences between the prenucleolus and the Shapley value. The similarity is that they both use egalitarian criteria over coalitions. The two main differences are: the prenucleolus and the...

The paper presents a unified framework where claim and cost sharing problems are jointly analyzed. Both problems have the following common characteristic: given a proposal the agents valuate the suitability of the proposal in two ways, checking how much they loss and how much they gain. Taking...

In this paper we define the Lorenz stable set, a subset of the core consisting of the allocations that are not Lorenz dominated by any other allocation of the core. We introduce the leximin stable allocation, which is derived from the application of the Rawlsian criterion on the core. We also...