For the problem of adjudicating conflicting claims, we offer simple criteria to compare rules on the basis of the Lorenz order. These criteria pertain to three families of rules. The first family contains the constrained equal awards, constrained equal losses, Talmud, and minimal overlap rules...

For the problem of adjudicating conflicting claims, we consider the requirement that each agent should receive at least 1/n his claim truncated at the amount to divide, where n is the number of claimants (Moreno-Ternero and Villar, 2004a). We identify two families of rules satisfying this bound....

We construct "simple" games implementing in Nash equilibria several solutions to the problem of fair division. These solutions are the no-envy solution, which selects the allocations such that no agent would prefer someone else's bundle to his own, and several variants of this solution....

We formulate and study the requirement on an allocation rule that no agent should be able to benefit by augmenting his endowment through borrowing resources from the outside world (alternatively, by simply exaggerating it). We show that the Walrasian rule is not "borrowing-proof" even on...

This essay surveys the literature on the axiomatic model of bargaining formulated by Nash ("The Bargaining Problem," Econometrica 28, 1950, 155-162).

We consider the problem of fairly allocating a bundle of infinitely divisible commodities among a group of agents with "classical" preferences. We propose to measure an agent's "sacrifice" at an allocation by the size of the set of feasible bundles that the agent prefers to her consumption. As a...

We consider the problem of adjudicating conflicting claims in the context of a variable population. A property of rules is "lifted" if whenever a rule satisfies it in the two-claimant case, and the rule is bilaterally consistent, it satisfies it for any number of claimants. We identify a number...

An allocation rule is consistent if the recommendation it makes for each problem “agrees” with the recommendation it makes for each associated reduced problem, obtained by imagining some agents leaving with their assignments. Some authors have described the consistency principle as a...