We discuss asymptotics for large random planar maps under the assumption that the distribution of the degree of a typical face is in the domain of attraction of a stable distribution with index α ∈ (1, 2). When the number n of vertices of the map tends to infinity, the asymptotic behavior of distances from a distinguished vertex is described by a random process called the continuous distance pr...

We provide a survey of recent developments about capacities (or fuzzy measures) and ccoperative games in characteristic form, when they are defined on more general structures than the usual power set of the universal set, namely lattices. In a first part, we give various possible interpretations and applications of these general concepts, and then we elaborate about the possible definitions of ...

Given the restructure of the electric sector in the whole world , they have developed many methods to allocate cost of the transmission system that, independently we established the different characteristics for one country to another they try to pay to the sector, giving signs of technical and economic efficiency. This publication is to emphasize with in the discussion and describe a method to...

We study the asymptotic nucleolus of a smooth and symmetric oligopoly with an atomless sector. We show that under appropriate assumptions, the asymptotic nucleolus of the TU market game coincides with the unique TU competitive payoff distribution x. This equivalence results from nucleolus of a finite game belonging to its core and the Aumann Core Equivalence, which holds for this economy due to...

We discuss the use of the fuzzy measure for representing information about uncertain variables. We describe the relationship between the fuzzy measure and the Dempster-Shafer belief structure. A method for generating the fuzzy measures associated with a D-S belief structure is described. We discuss the use of the Shapley index as a means for providing an entropy for fuzzy measures. We introduce...

A bargaining solution balances fairness and efficiency if each player’s payoff lies between the minimum and maximum of the payoffs assigned to him by the egalitarian and utilitarian solutions. In the 2-person bargaining problem, the Nash solution is the unique scale-invariant solution satisfying this property. Additionally, a similar result, relating the weighted egalitarian and utilitarian sol...

The Shapley value is one of the most important solution concepts in cooperative game theory. In coalitional games without externalities, it allows to compute a unique payoff division that meets certain desirable fairness axioms. However, in many realistic applications where externalities are present, Shapley’s axioms fail to indicate such a unique division. Consequently, there are many extensio...

We give a simple and concise proof that so-called generalized median stable matchings are well-defined for college admissions problems. Furthermore, we discuss the fairness properties of median stable matchings and conclude with two illustrative examples of college admissions markets, the lattices of stable matchings, and the corresponding generalized median stable matchings. JEL classification...

Constructive definitions of discrete random measures, which specify a sampling procedure for the weights and atom locations of the measure, have proven to be of great value in statistics and related fields. We consider the case of completely random measures and obtain a constructive representation for completely random measures on Euclidean space. For random measures on the real line satisfying...