SD-EF1 for agents together with EF1 for market values

Establish whether, for every instance of fair division with additive subjective utilities u_i over indivisible goods and a single additive market valuation v, there exists an allocation that is stochastically-dominant envy-free up to one good (SD-EF1) with respect to the subjective utilities (u_i) and envy-free up to one good (EF1) with respect to the market valuation v.

Background

The paper studies allocations of indivisible goods that must be fair with respect to both heterogeneous, additive subjective utilities and a common additive market valuation. It shows that SD-EF1 for both sides is not always achievable, but EF1 w.r.t. subjective utilities together with SD-EF1 w.r.t. market values is always achievable via a reduction to Biswas–Barman (2018).

The complementary guarantee—SD-EF1 on the agents’ side and EF1 on the market side—remains unresolved. This question sits directly at the heart of simultaneous fairness under two evaluation criteria and asks whether a slightly weaker market-side requirement enables existence in general.