theorem cesGameCriticalRatio_bounds {ρ : ℝ} (hρ : 0 < ρ) :
0 < cesGameCriticalRatio ρ ∧ cesGameCriticalRatio ρ < 1 := by
rw [cesGameCriticalRatio_eq ρ hρ]
constructor
· positivity
· apply rpow_lt_one_of_one_lt_of_neg (by norm_num : (1:ℝ) < 2)
exact neg_neg_of_pos (div_pos one_pos hρ)Strategic independence of CES (Paper 1, Sections 7-8):