  We revisit the linear Cournot model with uncertain demand that is studied in
Lagerl\"of (2006)* and provide sufficient conditions for equilibrium uniqueness
that complement the existing results. We show that if the distribution of the
demand intercept has the decreasing mean residual demand (DMRD) or the
increasing generalized failure rate (IGFR) property, then uniqueness of
equilibrium is guaranteed. The DMRD condition implies log-concavity of the
expected profits per unit of output without additional assumptions on the
existence or the shape of the density of the demand intercept and, hence,
answers in the affirmative the conjecture of Lagerl\"of (2006)* that such
conditions may not be necessary.
  *Johan Lagerl\"of, Equilibrium uniqueness in a Cournot model with demand
uncertainty. The B.E. Journal in Theoretical Economics, Vol. 6: Iss 1.
(Topics), Article 19:1--6, 2006.
