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We revisit the classic Cournot model and extend it to a two-echelon supplychain with an upstream supplier who operates under demand uncertainty andmultiple downstream retailers who compete over quantity. The supplier's beliefabout retail demand is modeled via a continuous probability distributionfunction F. If F has the decreasing generalized mean residual life (DGMRL)property, then the supplier's optimal pricing policy exists and is the uniquefixed point of the mean residual life (MRL) function. This closed formrepresentation of the supplier's equilibrium strategy facilitates a transparentcomparative statics and sensitivity analysis. We utilize the theory ofstochastic orderings to study the response of the equilibrium fundamentals -wholesale price, retail price and quantity - to different demand distributionparameters. We examine supply chain performance, in terms of the distributionof profits, supply chain efficiency, in terms of the Price of Anarchy, andcomplement our findings with numerical results.

Comparative Statics via Stochastic Orderings in a Two-Echelon Market with Upstream Demand Uncertainty