Disputed Lands

In this paper we consider the classical problem of dividing a land among many agents so that everybody is satisfied with the parcel she receives. In the literature, it is usually assumed that all the agents are endowed with cardinally comparable, additive, and monotone utility functions. In many economic and political situations violations of these assumptions may arise. We show how a family of cardinally comparable utility functions can be obtained starting directly from the agents’ preferences, and how a fair division of the land is feasible, without additivity or monotonicity requirements. Moreover, if the land to be divided can be modelled as a finite dimensional simplex, it is possible to obtain envy-free (and a fortiori fair) divisions of it into subsimplexes. The main tool is an extension of a representation theorem of Gilboa and Schmeidler (1989).Gender Fair Division; Envy-freeness; Preference Representation.

Some properties of the solutions of obstacle problems with measure data

We study some properties of the obstacle reactions associated with the solutions of unilateral obstacle problems with measure data. These results allow us to prove that, under very weak assumptions on the obstacles, the solutions do not depend on the components of the negative parts of the data which are concentrated on sets of capacity zero. The proof is based on a careful analysis of the behaviour of the potentials of two mutually singular measures near the points where both potentials tend to infinity.Comment: 18 page

Allocation rules incorporating interval uncertainty

This paper provides several answers to the question “How to cope with rationing problems with interval data?” Interval allocation rules which are efficient and reasonable are designed, with special attention to interval bankruptcy problems with standard claims and allocation rules incorporating the interval uncertainty of the estate.allocation rules, bankruptcy, interval uncertainty