# Maximin-Aware Allocations of Indivisible Goods

## TL;DR

This paper introduces the maximin aware (MMA) fairness measure for allocating indivisible goods, ensuring agents recognize at least one other agent they do not envy, with algorithms that approximate MMA and relate to EFX fairness.

## Contribution

It proposes the MMA fairness measure, explores its relaxations, and provides a polynomial-time algorithm that approximates MMA and achieves improved EFX guarantees for subadditive valuations.

## Key findings

- MMA guarantees awareness of non-envy to at least one agent.
- The algorithm computes approximate MMA allocations efficiently.
- Allocations are 1/2 -approximate EFX for subadditive valuations.

## Abstract

We study envy-free allocations of indivisible goods to agents in settings where each agent is unaware of the goods allocated to other agents. In particular, we propose the maximin aware (MMA) fairness measure, which guarantees that every agent, given the bundle allocated to her, is aware that she does not envy at least one other agent, even if she does not know how the other goods are distributed among other agents. We also introduce two of its relaxations and discuss their egalitarian guarantee and existence. Finally, we present a polynomial-time algorithm, which computes an allocation that approximately satisfies MMA or its relaxations. Interestingly, the returned allocation is also 1/2 -approximate EFX when all agents have subadditive valuations, which improves the algorithm in [Plaut and Roughgarden, SODA 2018].