Two‑resource case: does the impossibility extend?

Determine whether, in the multi‑dimensional fees model with exactly two resources, any online algorithm must lose a constant fraction of social welfare under average block size constraints with sublinear slackness/extension, analogous to the impossibility shown for three or more resources.

Background

The paper proves that with three or more resources, any online algorithm must lose a constant fraction of social welfare under the specified average block size constraints. However, the status of the two‑resource case remains unresolved.

Clarifying whether a similar impossibility holds for two resources would complete the lower‑bound landscape for multi‑dimensional settings and guide the design of algorithms in practical systems with a small number of concurrent resource constraints.