  We revisit the classic Cournot model and extend it to a two-echelon supply
chain with an upstream supplier who operates under demand uncertainty and
multiple downstream retailers who compete over quantity. The supplier's belief
about retail demand is modeled via a continuous probability distribution
function F. If F has the decreasing generalized mean residual life (DGMRL)
property, then the supplier's optimal pricing policy exists and is the unique
fixed point of the mean residual life (MRL) function. This closed form
representation of the supplier's equilibrium strategy facilitates a transparent
comparative statics and sensitivity analysis. We utilize the theory of
stochastic orderings to study the response of the equilibrium fundamentals -
wholesale price, retail price and quantity - to different demand distribution
parameters. We examine supply chain performance, in terms of the distribution
of profits, supply chain efficiency, in terms of the Price of Anarchy, and
complement our findings with numerical results.
