The ignorant monopolist redux - Roger Koenker (Centre for Microdata Methods and Practice (cemmap), 2019)
The classical problem of the monopolist faced with an unknown demand curve is considered in a simple stochastic setting. Sequential pricing strategies designed to maximize discounted profits are shown to converge sufficiently rapidly that they leave the monopolist ignorant about all but the most local features of demand. The failure of the monopolist to "learn" his demand curve would seem to call into question some standard assumptions about agents' grasp of their economic environment.
Keywords: 330; Stochastic approximation; Statistical learning; Demand analysis