Pricing Problems in Adoption of New Technologies

TL;DR

This paper introduces a new discrete-time diffusion model incorporating price effects, analyzes optimal pricing strategies for monopolists, and examines policy-maker and monopolist interactions in a Stackelberg game to maximize adoption and profits.

Contribution

It presents a novel price-sensitive diffusion model and characterizes optimal pricing and strategic interactions in a unified framework.

Findings

New discrete-time diffusion model with explicit price effects

Characterization of optimal pricing strategies for monopolists

Analysis of Stackelberg game between policy-maker and monopolist

Abstract

We propose a generalization of the Bass diffusion model in discrete-time that explicitly models the effect of price in adoption. Our model is different from earlier price-incorporated models and fits well to adoption data for various products. We then utilize this model to study two decision-making problems. First, we provide a series of structural results on optimal pricing strategies to maximize profits from product sales by a monopolist over a finite horizon. We fully characterize the optimal pricing strategy in the single-period problem, and establish several structural properties of the same for the multi-period counterpart. Second, we study a Stackelberg game between a policy-maker and a monopolist, where the former seeks to maximize adoption through rebates, while the latter focuses on profits. For this problem, we analytically characterize crucial properties of the equilibrium path of the single-period game, and demonstrate how they carry over to the multi-period variant.