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原文摘要

Every complete allocation that is envy-free up to one good (EF1) guarantees each of the $n$ agents her $1$-out-of-$(2n-1)$ maximin share. Can we construct allocations that satisfy EF1 together with stronger ordinal maximin share guarantees? For additive valuations, we prove that there always exists a complete allocation that is simultaneously EF1 and ($1$-out-of-$\lfloor\varphi n\rfloor$)-MMS, where $\varphi=(1+\sqrt{5})/2$ is the golden ratio. For bivalued valuations, where each agent may have her own two non-negative values for the goods, we obtain a complete allocation that is simultaneously envy-free up to any good (EFX) and ($1$-out-of-$\lceil(7n-1)/6\rceil$)-MMS.