Sequential interactions in online platforms
Keywords: Business.

The conduct of business has been revolutionized by rapid technological progress, including technologies for tracking, bidding, and computing in real-time. To survive and succeed in business today, companies increasingly rely on adaptive algorithms for decision-making, which has created unprecedented opportunities and challenges, especially considering the intricacy of user behavior in this rapidly evolving arena. Users are interacting with platforms in a variety of ways -- some may stay for brief periods, and some may stay for extended periods (e.g., virtual assistants like Alexa or Siri), raising different challenges as to appropriate models and solution methods. Fascinated by problems that emerge in those settings, I leveraged tools from machine learning, optimization, revenue management, and game theory to better understand the effect of modern technology and to develop methods for solving associated problems. Specifically, my research is divided into three streams. The first looks at the case where the user engages with the interface briefly, and the platform customizes the experience for that user by leveraging information from prior users. The second studies the case when the user visits frequently, the platform gathers information from its historical data, and the interactions between the platform and the user become strategic. The third case complicates the situation by considering the user's two psychological systems of perceptions for processing information and making impulsive or reflective decisions. The seller may adapt to those two distinct ways of thinking and respond differently. In what follows, I provide a more detailed description of each chapter. Advertising Media and Target Audience Optimization via High-dimensional Bandits: In the first chapter, coauthored with Michael Harrison and Harikesh Nair, I present an algorithm that advertisers can use to automate their digital ad campaigns at online publishers in a data-driven way. The algorithm enables the advertiser to search across available target audiences and ad media to find the best possible combination for its campaign via online experimentation. The problem of finding the best audience-ad combination is complicated by a number of distinctive challenges, including (a) a need for active exploration to resolve prior uncertainty and to increase the speed of the search for profitable audience-ad combinations, (b) many combinations to choose from, giving rise to high-dimensional search formulations, and (c) very low success probabilities, typically just a fraction of one percent. Our algorithm (designated LRDL, an acronym for Logistic Regression with Debiased Lasso) addresses these challenges by synchronizing three important elements. The first is a multi-arm bandit framework for active exploration, with a Lasso penalty function to handle high dimensionality. The second is an inbuilt debiasing kernel that handles the regularization bias induced by the Lasso. The third is a semi-parametric regression model for outcomes that promotes cross-learning across arms and induces efficient learning. We implement the algorithm as a Thompson Sampler, and to the best of our knowledge, is the first that can practically address the challenges above in a high-dimensional setting. Simulations with real and synthetic data show the method is effective and documents its superior performance against several benchmarks from the recent high-dimensional bandit literature. Sales Policies of a Virtual Assistant: Whereas my first chapter focuses on the sequential interactions of a data-driven decision-maker (multi-armed bandits), this chapter studies a strategic decision-maker in a game-theoretical setting. This setting is suitable when the user interacts with the environment frequently and stays for an extended time. The growing use of virtual assistants (e.g., Alexa, Siri, Cortana, abbreviated as VA) provides an excellent example for us to study this problem. In Chapter two, coauthored with Haim Mendelson and Mingxi Zhu, I study the implications of selling through a voice-based VA. The seller has a set of products available, and the VA decides which product to offer and at what price, seeking to maximize its revenue. The consumer is impatient and rational, seeking to maximize her expected utility given the information available to her. The VA selects products based on the consumer's request and other information available and then presents them sequentially. Once a product is presented and priced, the consumer evaluates it and decides whether to make a purchase. The consumer's valuation of each product comprises a pre-evaluation value, which is common knowledge, and a post-evaluation component which is private to the consumer. We solve for the equilibria and develop efficient algorithms for implementing the solution. We develop the "Greedy pairwise switch" algorithm to calculate the optimal ranking, which saves an exponential amount of time compared to the naive method. We design an approximation "two-rank" algorithm that finds an approximate solution within O(n) computation. Further, we examine the effects of information asymmetry on the outcomes and study how incentive misalignment depends on the distribution of private valuations. We find that monotone rankings are optimal in the cases of a highly patient or impatient consumer and provide a good approximation for other levels of patience. The relationship between products' expected valuations and prices depends on the consumer's patience level and is monotone increasing (decreasing) when the consumer is highly impatient (patient). Also, the seller's share of the total surplus decreases in the amount of private information. We compare the VA to a traditional web interface, where multiple products are presented simultaneously on each page. We find that within a page, the higher-value products are priced lower than the lower-value products when the private valuations are exponentially distributed. We find a similar relationship between the seller's surplus ratio and information asymmetry. Finally, the web interface generally achieves a higher profit share for the seller due to the postponement option available to the consumer with the VA. When Dual Processing Systems Theory Meets Sequential Online Interactions: Modern Psychologists have distinguished how thought can arise in two different ways or processes. The first system is responsible for fast, automatic, and unconscious behaviors, whereas the second system is responsible for slow, controlled, and conscious behaviors. Whether the consumer invokes one system or another is heavily influenced by different interfaces where the interactions take place. As such, it is important for businesses to adjust to different processing systems which may be present across different interfaces. In Chapter three, coauthored with Haim Mendelson, I model an intuitive thinking system for consumer purchasing via a virtual assistant, then model a consumer that operates according to reflective thinking. We develop tools to calculate the optimal strategies under these two systems and study the implications of the dual processing systems on a seller's optimal strategy and revenue. As one may expect, when a consumer behaves impulsively, the seller will exploit its control over product presentation to extract a larger share of the surplus. We also find that when the consumer's private valuations are exponentially distributed, the value-price margin is always increasing in the product value. That is, the product that represents higher revenue to the seller is also more appealing to the consumer even after the seller deducts the price