Achieving Equitability with Subsidy

TL;DR

This paper investigates the minimum subsidy needed to achieve equitable and envy-free allocations of indivisible items, providing bounds, characterizations, and polynomial-time algorithms for fair and efficient solutions.

Contribution

It offers new bounds and characterizations for subsidies needed to attain equitability and envy-freeness, along with algorithms for fair and efficient allocations.

Findings

Derived upper and lower bounds for subsidies to achieve EQ.

Characterized allocations that satisfy both EQ and EF.

Designed polynomial-time algorithms for fair and efficient allocations.

Abstract

We study the fair allocation problem of indivisible items with subsidy. In this paper, we focus on the notion of fairness - equitability (EQ), which requires that items be allocated such that all agents value the bundle they receive equally. First, we study the upper bounds of the minimum required subsidy to achieve EQ in different item settings and provide the corresponding lower bounds. Second, we consider the bounded subsidy for achieving EQ and another popular notion of fairness - envy-freeness (EF), and give a characterization of allocations that can achieve both EQ and EF. Finally, we analyze the bounds of subsidy of allocations achieving fairness and efficiency (utilitarian social welfare or Nash welfare) and design several polynomial-time algorithms to compute the desired allocation.