Monopoly pricing with limited demand information

Traditional monopoly pricing models assume that firms have full information about the market demand and consumer preferences. In this article, we study a prototypical monopoly pricing problem for a seller with limited market information and different levels of demand learning capability under relative performance criterion of the competitive ratio (CR). We provide closed-form solutions for the optimal pricing policies for each case and highlight several important structural insights. We note the following: (1) From the firm's viewpoint the worst-case operating conditions are when it faces a homogeneous market where all customers value the product equally, but where the specific valuation is unknown. In cases with partial demand information, the worse case cumulative willingness-to-pay distribution becomes piecewise-uniform as opposed to a point mass. (2) Dynamic (skimming) pricing arises naturally as a hedging mechanism for the firm against the two principal risks that it faces: first, the risk of foregoing revenue from pricing too low, and second, the risk of foregoing sales from pricing too high. And, (3) even limited learning, for example market information at a few price points, leads to significant performance gains.