Optimal Pricing with Generalized Run-Out Rate Policies

We consider the single-item dynamic pricing problem when the initial inventory level is fixed and the market size grows large. Previous results were obtained for this regime assuming that the customer item valuation distribution lies in the Gumbel domain attraction of extreme value theory. In the present paper, we extend these results to include the Weibull and Frechet domains of attraction too. Our main results provide the asymptotics of the optimal expected revenue, pricing policy and purchasing probability policy in the large market regime for both the Weibull and Frechet domains of attraction. These results imply that asymptotically the optimal pricing policy of the firm is not a classical run-out rate policy as was shown to be the case in the Gumbel domain of attraction. We therefore introduce the family of generalized run-out rate policies, specific instances of which are shown to be asymptotically optimal. We then proceed to characterize the regret of any asymptotically optimal policy relative to a fluid-derived upper bound. Finally, we conduct several numerical experiments to test the accuracy and performance of our results.