theorem strategic_independence_qualitative (hJ : 2 ≤ J) {ρ : ℝ} (hρ : ρ < 1)
{c : ℝ} (hc : 0 < c)
(δ : Fin J → ℝ) (hδ : orthToOne J δ)
(hδ_ne : ∃ j, δ j ≠ 0) :
-- The second-order approximation of the manipulation payoff is negative
cesHessianQF J ρ c δ < 0 :=
ces_strict_concavity_on_perp hJ hρ hc δ hδ hδ_neStrategic independence of CES (Paper 1, Sections 7-8):