We review the theory of fairness as it pertains to concretely specified problems of resource allocations. We present punctual notions designed to evaluate how well individuals, or groups, are treated in relation to one another: no-envy, egalitarian-equivalence, individual and collective lower or...

We identify a natural counterpart of the standard GARP for demand data in which goods are all indivisible. We show that the new axiom (DARP, for “discrete axiom of revealed preference”) is necessary and sufficient for the rationalization of the data by a well-behaved utility function. Our...

I consider the problem of assigning agents to indivisible objects, in which each agent pays a price for his object and all prices sum to a given constant. The objective is to select an assignment-price pair that is envy-free with respect to the agents' true preferences. I propose a simple...

We study problems of allocating objects among people. Some objects may be initially owned and the rest are unowned. Each person needs exactly one object and initially owns at most one object. We drop the common assumption of strict preferences. Without this assumption, it suffices to study...

We study the allocation problem of an indivisible object to one of several agents on the full preference domain when monetary transfers are not allowed. Our main requirement is strategy-proofness. The other properties we seek are Pareto optimality, non-dictatorship, and non-bossiness. We provide...

An Equivalence Theorem between geometric structures and utility functions allows new methods for understanding preferences. Our classification of valuations into "Demand Types" incorporates existing definitions (substitutes, complements, "strong substitutes", etc.) and permits new ones. Our...