Structural characterization of nonlinear objectives admitting constant ex-post guarantees

Identify the structural properties of nonlinear welfare objectives that permit constant ex-post prophet inequalities.

Background

The paper develops a broad ex-ante result for every symmetric, concave, positively homogeneous welfare function, but shows that comparable generality fails for ex-post objectives because alpha-fair welfare with alpha>1 has competitive ratio exactly 1/n even under independent values and full distributional knowledge.

This motivates a general characterization problem: determine which structural features of nonlinear welfare objectives are compatible with constant ex-post prophet guarantees. The question goes beyond the alpha-fair family and concerns the broader theory of nonlinear prophet inequalities.