Determine the optimal dependence for i.i.d. Bernoulli values

Determine the optimal competitive-ratio dependence on q for prophet inequalities under intersections of q unit-capacity partition matroids when all element values are identically distributed Bernoulli random variables.

Background

The lower-bound construction in the paper uses independent two-point distributions whose positive values vary across buyers, so it does not resolve the more restrictive i.i.d. Bernoulli setting. Earlier lower bounds for this setting are weaker than the paper's Omega(q/log q) bound, and the paper states that the optimal dependence on q remains unresolved.

References

Our instance uses independent, nonidentically distributed values; the corresponding question for i.i.d. Bernoulli values remains open.

— A Nearly Tight Lower Bound for Matroid Intersection Prophet Inequalities  (2609.20696 - Fotakis et al., 17 Sep 2026) in Section 1, Introduction; reiterated in Section Conclusion