The reverse self-dual serial cost-sharing rule

In this study we define a cost sharing rule for cost sharing problems. This rule is related to the serial cost-sharing rule defined by Moulin and Shenker (1992). We give some formulas and axiomatic characterizations for the new rule. The axiomatic characterizations are related to some previous ones provided by Moulin and Shenker (1994) and Albizuri (2010).

The von Neumann-Morgenstern stable sets for 2x2 games

We analyze the von Neumann and Morgenstern stable sets for the mixed extension of 2 2 games when only single profitable deviations are allowed. We show that the games without a strict Nash equilibrium have a unique vN&M stable set and otherwise they have infinite sets.

Intermediate serial cost-sharing rules

In this paper we give a generalization of the serial cost-sharing rule defined by Moulin and Shenker (1992) for cost sharing problems. According to the serial cost sharing rule, agents with low demands of a good pay cost increments associated with low quantities in the production process of that good. This fact might not always be desirable for those agents, since those cost increments might be higher than others, for example with concave cost functions. In this paper we give a family of cost sharing rules which allocates cost increments in all the possible places in the production process. And we characterize axiomatically each of them by means of an axiomatic characterization related to the one given for the serial cost-sharing rule by Moulin and Shenker (1994).

A common axiom for classical division rules for claims problems

In this paper we introduce a new axiom, denoted claims separability, that is satisfied by several classical division rules defined for claims problems. We characterize axiomatically the entire family of division rules that satisfy this new axiom. In addition, employing claims separability, we characterize the minimal overlap rule, given by O'Neill (1982), Piniles rule and the rules in the TAL-family, introduced by Moreno-Ternero and Villar (2006), which includes the uniform gains rule, the uniform losses rule and the Talmud rule.

The minimal overlap cost sharing rule

In this paper we introduce a new cost sharing rule-the minimal overlap cost sharing rule-which is associated with the minimal overlap rule for claims problems defined by O'Neill (1982). An axiomatic characterization is given by employing a unique axiom: demand separability. Variations of this axiom enable the serial cost sharing rule (Moulin and Shenker, 1992) and the rules of a family (Albizuri, 2010) that generalize the serial cost sharing rule to be characterized. Finally, a family that includes the minimal overlap cost sharing rule is defined and obtained by means of an axiomatic characterization.

A potential approach to claims problems

Hart and Mas Colell (1989) introduce the potential function for cooperative TU games. In this paper, we extend this approach to claims problems, also known as bankruptcy or rationing problems. We show that for appropriate subproblems, the random arrival rule, the rules in the TAL-family (which include the uniform gains rule, the uniform losses rule and the Talmud rule), the minimal overlap rule, and the proportional rule admit a potential. We also study the balanced contributions property for these rules. By means of a potential, we introduce a generalization of the random arrival rule and mixtures of the minimal overlap rule and the uniform losses rule.