Date of Award
Spring 2023
Document Type
Dissertation
Degree Name
Doctor of Philosophy (PhD)
Department
Management
First Advisor
Kumar, Vineet
Abstract
This thesis provides insights for firms on how to price and design product plans by combining experimentation and machine learning methods. In Chapter 1, we use multi-armed bandits from reinforcement learning to better inform firms on how to price experiment when faced with an unknown demand curve. Chapters 2 and 3 focus on plan design for a subscription based firm. In Chapter 2, we run a field experiment to determine the optimal amount of free offered by a firm, while in Chapter 3 we perform a content-level analysis using machine learning, which helps a firm choose a more appropriate plan based on the kind of content present in its library. The first chapter examines how a firm can learn the most relevant parts of an unknown demand curve more efficiently by conducting adaptive price experimentation. We propose a novel theory-based approach to the reinforcement learning problem of maximizing profits when faced with an unknown demand curve. Our method is based on multi-armed bandits, which are a collection of minimal assumption non-parametric models that balance exploration and exploitation for maximizing rewards while learning across arms. Specifically, we build on Gaussian process bandits, which represent a flexible non-parametric model that unlike other non-parametric alternatives also provide principled estimates of uncertainty. We leverage the informational externality inherent in price experimentation across arms (price levels) in two ways: correlation between demands correspond to closer price levels, and demand curves are weakly monotonically decreasing. Incorporating these informational externalities limits unnecessary exploration of certain prices and performs better (characterized by greater profitability or reduced experimentation) than currently advanced approaches like UCB (with partial identification), or baseline Gaussian process bandits. Additionally, our method can be used in conjunction with methods like partial identification. Across a wide spectrum of true demand distributions our algorithm demonstrated a significant increase in rewards, most notably for right-skewed underlying WTP distributions where current approaches tend to underperform. Our algorithm performed consistently achieving between 96.9\% and 99.1\% of the optimal rewards depending on the simulation setting. In the second chapter, we address the design of free plan and free trial. We conduct a field experiment in collaboration with a company that provides video-based learning in the performing arts space to identify the impact of free content availability on both engagement and monetization outcomes. We find that the generosity of the free plan drives engagement higher, whereas conversion rates are inversely related. However, the revenue impact of generosity demonstrates an inverted-U shaped relationship. Users who have access to less generous free plans tend to convert to lower priced and shorter term premium plans. In contrast, users who are given more generous free plans tend to upgrade to higher priced and longer term premium plans. Therefore, even though the conversion rates for the experimental conditions are similar, the revenue implications are quite different. In the third chapter, we use the same empirical context as the second chapter to undertake content analysis to understand how engagement of different content types varies with plan design. We adapt recent advances in using raw unstructured video data to characterize rich content features to understand how content characteristics explain differential treatment effects. Specifically, we decompose videos into several features corresponding to text, audio, and visual modalities. We find that videos with the following characteristics are those associated with an increase in watch time as more of the video becomes available: longer sentence length, faster speech rate, more collaborative language, lower question rate, more positive speech sentiment, higher quality videos (pre-recorded rather than live-recorded), longer classes, non-neutral visual features, and instructors further away from the camera. This has implications for firms in choosing a more appropriate plan based on the kind of content present in their library.
Recommended Citation
Weaver, Ian Nicholas, "Price Experimentation and Plan Design for Digital Firms" (2023). Yale Graduate School of Arts and Sciences Dissertations. 886.
https://elischolar.library.yale.edu/gsas_dissertations/886
