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We study the problem of fairly allocating a set of indivisible goods amongagents with {\em bivalued submodular valuations} -- each good provides amarginal gain of either $a$ or $b$ ($a < b$) and goods have decreasing marginalgains. This is a natural generalization of two well-studied valuation classes-- bivalued additive valuations and binary submodular valuations. We present asimple sequential algorithmic framework, based on the recently introducedYankee Swap mechanism, that can be adapted to compute a variety of solutionconcepts, including max Nash welfare (MNW), leximin and $p$-mean welfaremaximizing allocations when $a$ divides $b$. This result is complemented by anexisting result on the computational intractability of MNW and leximinallocations when $a$ does not divide $b$. We show that MNW and leximinallocations guarantee each agent at least $\frac25$ and $\frac{a}{b+2a}$ oftheir maximin share, respectively, when $a$ divides $b$. We also show thatneither the leximin nor the MNW allocation is guaranteed to be envy free up toone good (EF1). This is surprising since for the simpler classes of bivaluedadditive valuations and binary submodular valuations, MNW allocations are knownto be envy free up to any good (EFX).

Dividing Good and Better Items Among Agents with Bivalued Submodular Valuations