No-envy and efficient minimal rights: recursive no-envy

In economics the main efficiency criterion is that of Pareto-optimality. For problems of distributing a social endowment a central notion of fairness is no-envy (each agent should receive a bundle at least as good, according to her own preferences, as any of the other agent’s bundle). For most economies there are multiple allocations satisfying these two properties. We provide a procedure, based on distributional implications of these two properties, which selects a single allocation which is Pareto-optimal and satisfies no-envy in two-agent exchange economies. There is no straightforward generalization of our procedure to more than two-agents.