SMU SOE Seminar Series (September 4, 2025): Tight Guarantees for Fair Division: A General Model

TOPIC:

ABSTRACT

A context-free problem of Fair Division is a function W from n-profiles of "types" x_{i} to a freely transferable amount of "surplus" W(x₁,⋯,x_{n}) they must share in the common property regime. A pair of tight guarantees assigns to each type an upper and a lower bound on its share under any profile of types of the other agents, and these bounds cannot be improved. The choice of a particular pair of such guarantees when the types and W have an economic interpretation vindicates only some familiar "fair" sharing rules and suggests many new ones. Our examples include the allocation of an indivisible good or bad, the classic model of a "commons" where types enter additively in the function W, and sharing the cost of a capacity or of the transportation costs to a location on a line.

Keywords: Fair Division, Unanimity, Upper and Lower Guarantees, Modular Surplus Functions.

JEL: D6, D63.

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