Global optimality of the minimax monitoring set

Establish whether the monitoring set that minimizes maximum regret under the fixed half-budget Japanese disclosure release is globally minimax-optimal, rather than merely the best set found by the finite-scenario search.

Background

For the Japanese application, the authors fix the 1,606-statistic half-budget release and search for a set of twenty buyers that minimizes maximum regret across all networks compatible with that release. The computational procedure iteratively adds worst-case allocations and produces a candidate set with maximum regret of 3.285 percentage points.

However, the search terminates at a prespecified computational limit and leaves a substantial gap between a lower bound of 2.615 points and an upper bound of 3.286 points for the minimax value. Consequently, the reported set is not certified to be globally optimal, and the optimal disclosure policy is likewise not established.

References

The bounds on $R*(y)$, rounded outward, are [2.615, 3.286] points. The gap calculated before rounding is 0.669 points. This gap concerns the choice of monitoring set, whereas the numerical gap for evaluating each reported set is below $10{-5}$ points. The saved worst-case allocations attain the unrounded upper bounds within that tolerance.

— Decision-Relevant Information in Partially Observed Production Networks  (2609.29905 - Luo et al., 24 Sep 2026) in Appendix, Section “Choosing a monitoring set at a fixed release” (subsection of Appendix [?]—Release Design and Monitoring Guarantees); see also Section 5.2