Deterministic DSIC Mechanism Beating a 1/2-Approximation for Weighted Matroid Rank Valuations

Construct a polynomial-communication deterministic DSIC mechanism beating a 1/2-approximation for two weighted matroid rank valuations.

Background

Weighted matroid rank valuations are a subclass of gross substitutes valuations. The paper proves that achieving a 0.9999-approximation for two weighted matroid rank valuations requires exponential communication for universally DSIC mechanisms, while its positive mechanism results concern submodular valuations. The authors leave unresolved whether deterministic DSIC mechanisms can achieve any approximation strictly better than 1/2 with polynomial communication for this valuation class.

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”