Maximin-Aware Allocations of Indivisible Goods

We study envy-free allocations of indivisible goods to agents in settings where each agent is unaware of the bundles (or allocated goods) of other agents. In particular, we propose maximin aware (MMA) fairness measure, which guarantees that every agent, given the bundle allocated to her, is aware that she does not get the worst bundle, even if she does not know how the other goods are distributed. We also introduce two of its relaxations, MMA1 and MMAX. We show that MMA1 and MMAX potentially have stronger egalitarian guarantees than EF1 and are easier to achieve than MMS and EFX. Finally, we present a polynomial-time algorithm, which computes an allocation such that every agent is either 1/2-approximate MMA or exactly MMAX. Interestingly, the returned allocation is also 1/2-approximate EFX when all agents have subadditive valuations, which answers an open question left in [Plaut and Roughgarden, SODA 2018].