Polynomial-time computation of competitive equilibrium for divisible chores

Determine whether a competitive equilibrium in Fisher markets with divisible chores under additive valuations can be computed in polynomial time; equivalently, establish or refute the existence of a polynomial-time algorithm that computes such a competitive equilibrium.

Background

For divisible goods with additive valuations, competitive equilibrium can be computed in polynomial time and yields strong fairness and efficiency properties. In contrast, for divisible chores, while an FPTAS exists, the status of an exact polynomial-time algorithm is unresolved.

The quoted sentence explicitly identifies the complexity of computing competitive equilibria for divisible chores with additive valuations as an open question.