Two-agent cake division achieving EF+PO for agents and EF for market values

Determine whether, for every two-agent cake-cutting instance with strictly positive subjective utility measures and a market value measure, there exists a division that is envy-free (EF) and Pareto optimal (PO) with respect to the subjective utilities and simultaneously EF with respect to the market valuation.

Background

In general, EF+PO for agents and EF for market values cannot be guaranteed for three or more agents, even under strict positivity, as shown via an adaptation of Brams–Jones–Klamler. However, EF+PO w.r.t. agents is attainable for two agents in standard cake cutting.

This open question asks whether, in the two-agent case under the paper’s market-value framework, EF+PO for subjective utilities together with EF for market values is always achievable.