Measuring Market Performance with Stochastic Demand: Price of Anarchy and Price of Uncertainty

Abstract: Globally operating suppliers face the rising challenge of wholesale pricing under scarce data about retail demand, in contrast to better informed, locally operating retailers. At the same time, as local businesses proliferate, markets congest and retail competition increases. To capture these strategic considerations, we employ the classic Cournot model and extend it to a two-stage 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 property, then the supplier's optimal pricing policy exists and is the unique fixed point of the mean residual life function. We evaluate the realized Price of Uncertainty and show that there exist demand levels for which market performs better when the supplier prices under demand uncertainty. In general, performance worsens for lower values of realized demand. We examine the effects of increasing competition on supply chain efficiency via the realized Price of Anarchy and complement our findings with numerical results.