In 1950, Nash's seminal paper introduced the axiomatic approach to the analysis of bargaining situations. Since then, many bargaining solutions have appeared and been axiomatically analyzed. The fact that agents, when face a bargaining problem, can come up with different solution concepts (that...

This paper explores the introduction of a variable critical-level in a variable population context. We focus the attention on the "Critical- Level Egalitarian Ruleî, a social evaluation procedure which compares two social states as follows: (i) It reproduces the leximin criterion when applied...

Consider a two-person bargaining problem, where both agents have a particular notion of what would be a just solution outcome. In case their opinions differ, a procedure which leads to a compromise between t,he two different views is needed. In this paper we propose a mechanism to solve this...

This paper follows the interpretation of the bankruptcy problems in terms of TU games given in O'Neill (1982). In this context we propose the analysis of the Transition Game associated to each bankruptcy problem. We explore an old solution described by Ibn Ezra in the XII century. Firstly, we...

The solution for the "Contested Garment Problem" proposed in the BabylonicTalmud, one of the most important sources of inspiration for solving situations where demand overcomes supply of some resources, suggests that each agent should receive at least some part of the available amount when...

In a bankruptcy situation individuals are not equally affected since each one has its own specific characteristics. These aspects cannot be ignored and may justify an allocation bias in favor of or against some individuals. This paper develops a theory of differentiation in claims problems that...

Agents involved in a conflicting claims problem may be concerned with the proportion of their claims that is satisfied, or with the total amount they get. In order to relate both perspectives, we associate to each conflicting claims problem a bargaining-in-proportions set. Then, we obtain a...

A minimum cost spanning tree (mcst) problem analyzes the way to effciently connect individuals to a source when they are located at different places. Once the effcient tree is obtained, the question on how allocating the total cost among the involved agents defines, in a natural way, a...

Is it important to negotiate on proportions rather than on numbers? To answer this question, we analyze the behavior of well-known bargaining solutions and the claims rules they induce when they are applied to a "proportionally transformed" bargaining set SP so-called bargaining-in-proportions...

In distribution problems, and specifically in bankruptcy issues, the Proportional (P) and the Egalitarian (EA) divisions are two of the most popular ways to resolve the conflict. Nonetheless, when using the egalitarian division, agents may receive more than her claim. We propose a compromise...