Truthful Mechanisms Beating a 1/2-Approximation for Two XOS Valuations

Establish whether a polynomial-communication truthful mechanism can beat a 1/2-approximation for two XOS valuations.

Background

The paper develops a polynomial-communication universally DSIC mechanism achieving an approximation better than 1/2 for two submodular valuations. XOS valuations form a broader class than submodular valuations, so the corresponding guarantee for truthful mechanisms on two XOS bidders remains unresolved. The open problem asks whether any polynomial-communication truthful mechanism can improve strictly over the 1/2-approximation threshold in this broader valuation domain.

References

Although we beat a $1/2$-approximation for submodular valuations with a universally DSIC mechanism, it is still open whether a polynomial-communication truthful mechanism can beat a $1/2$-approximation for XOS valuations.

— The Hardness of Dominant Strategy Mechanism Design, Revisited  (2610.06773 - Qiu, 5 Oct 2026) in Section Conclusion, paragraph “Two-Bidder Settings”