Data-Driven Pricing for a New Product
80 Pages Posted: 24 Mar 2020 Last revised: 14 Jul 2021
Date Written: April 8, 2021
Decisions regarding new products are often difficult to make, and mistakes can have grave consequences for a firm's bottom line. Often, firms lack important information about a new product such as its potential market size and the speed of its adoption by consumers. One of the most popular frameworks that have been used for modeling new product adoption is the Bass model (Bass 1969). While the Bass model and its many variants have been used to study dynamic pricing of new products, the vast majority of these models require a priori knowledge of parameters that can only be estimated from historical data or guessed using institutional knowledge.
In this paper, we study the interplay between pricing and learning for a monopolist whose objective is to maximize the expected revenue of a new product over a finite selling horizon. We extend the generalized Bass model to a stochastic setting by modeling adoption through a continuous-time Markov chain where the adoption rate depends on the selling price and on the number of past sales. We study a pricing problem where the parameters of this demand model are unknown, but the seller can utilize real-time demand data for learning the parameters. Specifically, we formulate the problem as a stochastic optimal control problem where the demand parameters are updated by maximum likelihood estimators, then we derive the optimal pricing-and-learning policy. Since the exact optimal policy is difficult to implement, we propose two simple and computationally tractable pricing policies that are provably near-optimal.
Keywords: Bass adoption model, Data-driven pricing, Demand learning
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