Deterministic Truthful Mechanism Beating a 1/2-Approximation for Submodular Valuations

Construct a polynomial-communication deterministic truthful mechanism beating a 1/2-approximation for two submodular valuations.

Background

The paper gives a polynomial-communication universally DSIC mechanism achieving an approximation better than 1/2 for two submodular valuations. Universal DSIC is a randomized notion, whereas this open problem asks for a deterministic truthful mechanism. Thus, whether deterministic truthfulness can surpass the 1/2 threshold for two submodular bidders remains unresolved.

References

Additionally, it remains open to design a polynomial-communication deterministic DSIC mechanism beating a $1/2$-approximation for weighted matroid rank valuations, or to design a polynomial-communication deterministic truthful mechanism beating a $1/2$-approximation for submodular valuations.

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