Guaranteed shares of benefits and costs

TL;DR

This paper introduces a framework for fair division that guarantees bounds on each agent's share, applicable to various economic scenarios like indivisible goods, commons, and cost sharing, ensuring fairness under all type profiles.

Contribution

It formalizes tight guarantees for fair division, linking them to known and new sharing rules, with broad applicability across economic models.

Findings

Provides a formal definition of tight fairness guarantees.

Connects guarantees to existing and novel fair sharing rules.

Applies framework to diverse economic scenarios.

Abstract

A context-free problem of Fair Division is a function W from a profile of n types to a freely transferable amount of surplus W(x) 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 ony 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.