Dynamic pricing with automated purchase-reservation algorithms

We consider the problem of a firm that sells a perishable product such as airline tickets or hotel rooms with a dynamic pricing scheme in the presence of Internet bots. The bots automatically check for changes in the selling price every few seconds and hold the price for a short period by making a tentative reservation. Since the bots are not willing to buy the product, the bots’ reservation does not generate revenue for the firm. In addition, such a behavior would temporarily increase the price in conjunction with decreasing the inventory level. In this paper, we formulate a dynamic pricing model that accounts for tentative reservations made by bots, and derive an optimal pricing policy so as to maximize the total expected revenue. We show the monotone properties of the optimal price: (1) the optimal price decreases with inventory at any given timestep; (2) the optimal price decreases over time even if there is a temporary inventory decrease due to bot reservations. We demonstrate numerically that the optimal pricing policy is robust against the presence of bots, and further show that, as bot activity increases, the optimal price tends to decrease in the first portion of the sales interval.