The second-best bilateral trade mechanism captures at least 1/2 of first-best gains from trade, and the bound is tight.
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Existence of EF1 and constant-ρ MMS allocations proven for submodular valuations.
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Second-Best Bilateral Trade is $1/2$ Efficient
The second-best bilateral trade mechanism captures at least 1/2 of first-best gains from trade, and the bound is tight.
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Simultaneous EF1 and approximate MMS allocations for submodular valuations
Existence of EF1 and constant-ρ MMS allocations proven for submodular valuations.