Regulating Algorithmic Pricing Part 1

Regulating Algorithmic Pricing 2023 Submitted to the Department of Economicsin partial fulfillment of the requirements for the degree of Bachelor of Arts with honors Regulating Algorithmic Pricing Haoran Tong April 14, 2023 Abstract Algorithms have led to more sophisticated pricing strategies adopted by firms. They can lower consumers’ search costs through recommendations, track their search sequences, and monitor rival prices. Previous literature has studied the effects of tracking technology in facilitating tacit collusion, which is an anti-competitive concern for antitrust regulators. My thesis presents a countervailing argument that suggests the pro-competitive potential for strategic algorithmic price discrimination. I model sequential consumer search on a Hotelling line with differing search costs in a duopoly market. The model illustrates how the three algorithmic features jointly expand market overlap, create a credible threat of multiple searches, and lower Perfect Bayesian Nash Equilibrium prices for all consumers. It also shows that the payoff structure of firms’ investment in algorithms resembles a Prisoner’s Dilemma. My analysis provides regulatory insights on balancing the pro-competitive features and anti-competitive concerns of algorithmic pricing in antitrust enforcement. Keywords: algorithm, price discrimination, antitrust, search cost JEL Classification: C72, D43, D47, D82, K21, L11, L41, O33 Contents 1 Introduction 1 2 Background on Pricing Algorithms 6 2.1 Search Cost Reduction through Recommendations . . . . . . . . . . . . . . . 6 2.2 Search Sequence Tracking . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.3 Rival Price Monitoring . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.4 Joint Features . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 3 Model 11 3.1 Firms and Consumers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 3.2 Sequential Search Game . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 3.3 Consumer Payoffs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 3.4 Algorithmic Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 4 Analysis 15 4.1 Disjoint Markets or Overlapped Markets . . . . . . . . . . . . . . . . . . . . 15 4.2 (Alg, Alg) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 4.3 (Alg, Non) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 4.4 (Non, Alg) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 4.5 (Non, Non) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 5 Equilibrium Calibrations 33 5.1 Market Calibrations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 5.2 Algorithmic Investment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 6 Discussion and Conclusion 41 References 46 1 Introduction Over the past decade, algorithmic technology, compounded by increasingly available consumer information, has led to more sophisticated pricing strategies adopted by firms. A pricing algorithm automates the retailer’s pricing decision at each instance by dynamically mapping observed inputs about market characteristics to a desired set of price offering outputs. By analyzing vast amounts of processed data, obtained from sources such as cookies and data brokers, these algorithms can provide valuable insights into consumer preferences and the actions of competitors within the online market space. European Commission’s 2020 Final report on the E-commerce Sector Inquiry finds that “a majority of retailers track the online prices of competitors and consumer profiles. Three fourths of them use software programs that autonomously infer the willingness to pay for consumers and observe prices of competitors.”1 Per US Department of Justice, most large online shopping sites in the US, including Amazon, Walmart, eBay, Bookings, Zillow, Walgreens, and Uber collect and process consumers’ purchase data, browsing history, and demographic characteristics either in their own database or through third-party sources.2 Even smaller retailers have been relying on independent algorithm providers such as Intelligence Node, which advertises its algorithm service as “having eyes on competitor movements at all times and . . . automatically update your prices to maximize profit.”3 In this thesis, I identify three salient features of modern pricing algorithms that seem to facilitate strategic pricing the most. Machine learning algorithms analyze consumer preferences and provide customized recommendations that reduce the time and effort required for the consumer to find relevant products or services. By narrowing down the range of choices and presenting options that are more likely to be of interest, algorithms help reduce 1. “Sector inquiry into e-commerce.” 2. “Competition and Antirust Law Enforcement Act Proposes Wholesale Changes to U.S. Antitrust Law,” The National Law Review. 3. Marco Bertini and Oded Koenigsberg,“The Pitfalls of Pricing Algorithms,” Harvard Business Review. 1 consumers search cost. Second, algorithms track the consumers’ sequence of search by using browser cookies or requiring the consumer to create an account and log in to a website or app. As the consumer navigates the website or app, the algorithm records each search query, click, and other actions taken by the user. Importantly, with access to cookies, the firms can detect if a consumer browses a competitor’s website for a similar product and infer the consumer’s search sequence. Third, algorithms monitor rival price offerings from earlier searches. They can do this by crawling rival websites or by subscribing to third-party data providers that collect and analyze pricing information. Through such monitoring, algorithms can arrive at pricing strategies responsive to actual rival prices. My thesis responds to concerns from regulatory authorities and legal scholars over these features of pricing algorithms. In addition to privacy concerns, they worry that real-time tracking of consumers and rival firms’ behavior may facilitate greater tacit collusion among firms, enabling far more effective coordination of prices even without an explicit agreement. Members of the Congress have voiced concern over the lack of regulatory tools to restrict algorithmic consumer harms. Senator Amy Klobuchar, while introducing her bill “Competition and Antitrust Law Enforcement Reform Act of 2021,” stated that algorithms “only gets more common and more dangerous” over time.4 Senator Sherrod Brown, Chair of the Senate Committee on Banking, Housing, and Urban Affairs, directly addressed to Lina Khan, Chair of the Federal Trade Commission (FTC), and urged the experts to review rent-setting optimization software like RealPage’s YieldStar and AI Revenue Management.5 A narrative of “inevitable threat” that an algorithm would surely produce to raise prices, lower outputs, and facilitate collusion corroborates with lawmakers’ deep-seated anxiety on the current antitrust framework which, in their characterization, are “ill-equipped” to tackle technologically complex challenges. 4. S.225 - 117th Congress: Competition and Antitrust Law Enforcement Reform Act of 2021. https://www.congress.gov/bill/117th-congress/senate-bill/225. 5. “Brown Calls on FTC to Review Whether Rental Pricing Algorithms Violate the Law — U.S. Senator Sherrod Brown of Ohio”. 2 Meanwhile, the nascent but growing scholarship in law, computer science, and economics has expended their effort mainly on two aspects of algorithmic competition: documenting empirical evidence for algorithmic interactions and analyzing the technical specificities for which algorithmic collusion could be possible. Chen et al. (2016) documented that a significant fraction of sellers in a large online marketplace (Amazon US), where many different types of goods are traded, adopted algorithmic pricing in 2015. Calvano et al. (2018) recorded large-scale price dispersion when consumers of different demographic profiles accessed the item. Clark et al. (2021) empirically estimated the price changes as a result of algorithm adoption for German gasoline retailers. To analyze how algorithms may facilitate tacit or overt collusion, Asker et al. (2021) investigated how the design of machine learning protocols such as Q-learning could lead to competitive or supracompetitive price outcomes when competing in a simple Bertrand pricing game. Their paper informed Brown and MacKay (forthcoming in 2023) to model oligopolistic competition in which firms differ in pricing frequency and choose pricing algorithms that respond to rivals’ prices. Despite the recent success in detecting the use of algorithms in retail spaces, scholars disagree on whether algorithms make collusion a more likely choice for firms in oligopoly. Analysis of algorithmic effect other than collusion is limited in academic literature. I consider the joint effects of all three features and provide a potentially countervailing argument to the abovementioned concern. I argue that, in the same market environment where pricing algorithms may facilitate tacit collusion, pricing algorithms could also allow the firms to strategically price-discriminate in a manner that generates pro-competitive effects. I formally explore this argument using a duopolistic price competition model with search costs that differ across consumers (à la the Hotelling line). The consumers engage in sequential search, and the decision whether to search further is based on their search costs and observed or expected prices. The model is solved using the equilibrium concept of Perfect Bayesian Nash. The model is used to examine how firms would price given algorithms and why they might choose to invest in pricing algorithms. 3 I show that given certain market conditions, algorithms can fundamentally shift retailers’ equilibrium pricing behavior and result in pro-consumer outcomes. While each feature may improve consumer welfare on their own, their combination magnifies the pro-competitive effect. Product recommendation contributes to expansion of trade, as consumers lower their search cost for either or both retailers. The reduction in search cost increases the demand elasticity, for consumers can switch shopping sites easily to compare prices across platforms. Search sequence detection and rival price monitoring could result in greater credible threat of price-matching: since the second-searched firm could precisely undercut the first price offering, the first-searched firm is incentivized to discourage their first searchers from searching twice by offering them a lower price. The algorithms enable credible threat of switching consumers and undercutting rivals, hence lower prices for both first and second searchers in the market. I further demonstrate that the firms’ algorithmic investment game may resemble a Prisoner’s Dilemma. A firm enjoys the most algorithmic advantage when it invests in the algorithm, but its rival does not. This advantage dissipates when both firms have symmetric algorithm, and their competitive payoff may be lower than when neither has an algorithm. Given reasonable upfront investment cost, the firms treat having algorithms as a dominant strategy primarily because of the disadvantage of not having one when its rival does. Pricing algorithms sometimes benefit the consumers more than the firms. My approach to locate algorithmic effect via search-based price discrimination is related to a rich reservoir of economics literature on strategic price discrimination. Scholarship on the impacts of price discrimination in competitive frameworks include Holmes, 1989, Tirole, 1994, Corts, 1998 and Armstrong and Vickers, 2001. Search costs may generate equilibrium price dispersion (Varian, 1980, Burdett, Judd, 1983, Stahl, 1989, Janssen, Moraga, 2004). Firms must possess some degree of market power and there must be factors limiting the potential for buyers’ arbitrage. The structure of search sequence, combined with the algorithmic effect, allows the firm to price-discriminate. Without price discrimination, a retailer faces 4 an essential tradeoff between quantity and price. A firm can forego second-searched sales in an expectation to gain maximum surplus for those who search for its products only. Alternatively, a firm can retain second-searched sales by offering a discount to all consumers, including those who would take the price at the first search. Price discrimination allows the firm to do both without necessarily decreasing overall consumer welfare. Ceteris peribus, consumers who do not incur the additional cost of searching twice would be charged a higher price, while those who do would be offered a discount given Nash conjectures. The amount of discount depends on the observed first price offering and the search cost at the second site. Rival price monitoring, the very technological feature that allows the firm to monitor each other while colluding according to Calvano (2018) and Asker (2021), may also motivate a firm to undercut each other’s prices and improve consumer welfare. My modeling result substantiates recent qualitative discussions by regulating authorities on possible antitrust mechanisms for algorithms. Although price discrimination is made illegal under the Sherman Antitrust Act. 15 U.S.C. §2, the Clayton Act, 15 U.S.C. §13, and by the Robinson-Patman Act, 15 U.S.C. §§13-13b, 21a, current U.S. antitrust doctrine applies a rule-of-reason, consumer-welfare-based test to determine its legality by weighing its anti-competitive effect against its pro-competitive effects. My model offers a guide by which antitrust authorities can examine such weighing. In some markets where collusion is less likely to be sustainable, some algorithms may operate to benefit consumers. My findings echo the intuition expressed by Terrell McSweeney, an FTC commissioner, who wrote, “As with algorithmic pricing generally, algorithmic price discrimination has the potential to provide consumer benefits, such as enabling companies to identify and offer discounts to targeted consumers who were previously priced out of certain markets.”6 The rest of the paper discusses the three algorithmic effects in Chapter 2, sets up the model in Chapter 3, analyzes the model in Chapter 4, presents Perfect Bayesian Nash Equilibrium calibrations in Chapter 5, and concludes with possible extensions of the model. 6. “The Implications of Algorithmic Pricing for Coordinated Effects Analysis and Price Discrimination Markets in Antitrust Analysis,” Federal Trade Commission, December 5, 2017. 5 2 Background on Pricing Algorithms In this section, I discuss explicitly the above-mentioned three features of algorithms: search cost reduction, search sequence tracking, and rival price monitoring. I offer background information for each feature and elaborate on how their combined effects influence strategic competition among retailers to motivate my model. 2.1 Search Cost Reduction through Recommendations Psychology studies have revealed that consumers are more willing to purchase a good if the product “came to them” at just the time they need it. In a survey covering 19 countries and territories, more than 95% of some 19,000 respondents stated having online shopping experience, more than half of them shopping online at least once a month.7 Many studies have estimated consumers’ online search cost for hotels, books, tablets, and so on (Blake, Nosko, and Tadelis 2016; Chen and Yao 2017; De los Santos 2008; De los Santos, Hortaçsu, and Wildenbeest 2012, 2017; Ghose, Ipeirotis, and Li 2018; Jiang et al. 2017; MoragaGonzález, Sándor, and Wildenbeest 2013; Moraga-González and Wildenbeest 2008). Most studies indicate that consumers’ online per-item search cost is between $1 and $20. Some products require higher search costs. Furniture and bedding products are typical examples of maximally differentiated product with many specifications– they require higher search cost than mass-produced, accessible, daily-use items such as toilet paper. With numerous filters, the consumers are able to locate their desired product without the need to record all product characteristics on their own. For products of higher research cost, online platforms offer the shopping platform as a service to consumers who, within several clicks, can apply the right filter and find the products they prefer. Wayfair designs their site such that consumers can locate their preferred dining table or mattress “within 6 clicks.”8 7. Baojun Jiang and Tianxin Zou, “Consumer Search and Filtering on Online Retail Platforms,” Journal of Marketing Research 57, no. 5 (2020): 900–916. 8. Babur De Los Santos, Ali Hortaçsu, and Matthijs R. Wildenbeest, “Search With Learning for Differentiated Products: Evidence from E-Commerce,” Journal of Business & Economic Statistics 35, no. 4 (2017): 6 But algorithmic search cost reduction is most common when a retailer automates and personalizes product recommendations based on inferred consumer characteristics. Consumers who open the homepage of a shopping app receive an automated list of products based on their previous purchases, key words they search, and so on. Once a consumer visits the homepage of Amazon, she will immediately see a list of recommended products labeled as “Amazon selects.” They may include items she browsed upon last visit, frequently purchased by people of the same ZIP code, or “flash discounts” on products purchased by consumers of similar profile nationally. For example, Townley (2017) found that those who recently purchase cosmetic products were often “recommended” a discount for feminine hygiene products.9 Firms also aim to attract retailer-neutral consumers to their platform by using targeted advertisements. These consumers are more likely to click on ads that align closely with their desired products. By utilizing a sophisticated algorithm, firms can increase the number of retailer-neutral consumers who choose to search on their platform first. 2.2 Search Sequence Tracking Online retailers can access the browsing history of every user who agrees with their Cookie policy. If their algorithm detects a competitor’s domain in the searching history, it knows that a consumer has chosen to shop elsewhere before accessing its website. One of the more (in)famous examples involved Amazon, a case in which a user noticed that the price of a DVD offered to him dropped from $26.24 to $22.74 after he deleted cookies identifying him as a regular customer. Amazon attributed the price difference to random price tests, and eventually refunded all customers who had paid the higher price (Cavallo 2018). An alternative explanation is that the “regular consumer” Cookies helped identify the user as a consumer who likely searches the product primarily at Amazon. Relatedly, a regular user of Travelocity found that, if he browsed other ticket reservation platforms, Travelocity would 626–641, issn: 0735-0015. 9. Christopher Townley, Eric Morrison, and Karen Yeung, Big Data and Personalised Price Discrimination in EU Competition Law, 3048688, Rochester, NY, October 6, 2017. 7 more often offer him a discount on exactly the ticket he browsed (Townley et al., 2017). Subsequently, upon clearing her browsing history, the price rose by $59.99. (Townley et al. 2017). Pricing seems to depend on whether a potential consumer is identified as having searched elsewhere earlier. However, research has revealed that only a small fraction of consumers pay attention to systematic price dispersion by online retailers (Kelley et al., 2022). 78% of surveyed consumers reported that they were not aware that their prices were given by an algorithm. Among those who were aware, almost 40% expressed no concern of being manipulated. Despite growing public discussions on the unfairness of algorithmic pricing, most consumers behave like price takers with idiosyncratic beliefs about the price a shopping site may offer. For example, over 50% of shoppers at Walmart believed that Walmart offered goods at a wholesale price, while market researches have shown otherwise. Researchers attribute this phenomenon as “the online cheap trap,” arguing that consumers are not “skeptical enough” of algorithmic pricing schemes.10 They do concede that while algorithms may not give the consumer the cheapest price in the market, they may save consumer significant search cost. 2.3 Rival Price Monitoring Complementing search sequence tracking, the firm may also access log-in and shopping carts the consumer left behind from earlier searches at rivals. Each firm could observe the prices their rivals charged, enabling the firm to offer a price explicitly responsive to prices offered by rivals. Rival price monitoring is a double-edged sword, as the same technology that may help the retailer undercut its rival may also help sustain collusion. Brown and MacKay (forthcoming, 2023) records sustained supracompetitive prices of firms using algorithm, suggesting the inevitability of algorithmic collusion. They argue that repeated interaction between two so10. Tom Blake, Chris Nosko, and Steven Tadelis, Consumer Heterogeneity and Paid Search Effectiveness: A Large Scale Field Experiment, 2444538, Rochester, NY, May 1, 2014. 8 phisticated algorithms may eventually result in a tacit agreement to not undercut their rival. Their finding does not necessarily contradict the pro-competitive side of price monitoring technology, as they assume consumers may observe all prices simultaneously in their model. In this thesis, sequential search is considered essential and shown to have key implications that differ from Brown and MacKay. An online experiment by Vollero et al. (2022) documents the importance of this distinction. A consumer first searches on Amazon for a fridge, for which Amazon charged $327.79. Five minutes after she put the item into Amazon’s shopping cart, Walmart’s target advertisement on social media platform offered a “seasonal discount” which gave her $325.81.11 Walmart essentially used “seasonal discount” as a cover for undercutting Amazon. In this case, even though Amazon attracts the consumer to their site first, subsequent selective discounting from Walmart poaches the consumer in the end. 2.4 Joint Features To demonstrate how these three algorithmic features jointly influence firm’s pricing strategy, consider a product being sold by two online retailers, Azamon (A) and Wamlart (W). A has invested more in developing a superior algorithm, while W has not. A and W independently decide their pricing strategy before making the product available for consumers. Consumers in the market decide whether to search for the product. Every consumer incurs a distinct search cost for A and for W. Consumers can search at most twice: at both A and W. Loyal consumers of A, who have developed some idiosyncratic preference, incur a smaller search cost from searching at A, as A is better able to infer their preference and make precise personalized recommendations. Similar loyal consumers of W would have a smaller search cost at W. Holding all else equal, the more loyal a consumer is to A (W), the smaller search cost it incurs by searching at A (W), and the larger search cost it incurs by 11. Agostino Vollero, Domenico Sardanelli, and Alfonso Siano, “Exploring the role of the Amazon effect on customer expectations: An analysis of user-generated content in consumer electronics retailing,” Journal of Consumer Behaviour, June 29, 2021, cb.1969, issn: 1472-0817, 1479-1838. 9 searching at W (A). Observing the price A (W) offers, the loyal A (W) consumer chooses among three options: give up buying the good; buy the good at the price A (W) offers; try searching at W (A). In order for the consumer to be willing to incur the additional, higher search cost at W (A), the consumer must expect the price at W (A) to be much lower than A (W)’s offering. A loyal A (W) consumer may be willing to search at A (W) but unlikely W (A) unless the expected price difference is substantial. In contrast, consider those consumers who do not have a strong idiosyncratic preference for A or W. The search cost for both retailers may be sufficiently high, leading the consumer to consider not buying the product at all. With a superior algorithm that advertises for products the consumer may like, A shortens the time it takes for the indifferent consumer to locate her desired product. This is where the algorithm expands trade and benefits both the retailer and the consumer. But the reduction in search cost may also expand the set of consumers, not heavily loyal to A or W, who might consider searching at A and at W. Such twice-searching consumers potentially have multiple price offers to consider. Suppose one such consumer second-searches at W after A. Her three options are: take W’s second price offering; take A’s first price offering with a small cost to return to A; exit the market with no purchase. With a sophisticated algorithm, A knows what this consumer is searching at A after having already searched at W. Moreover, the algorithm may reveal to A the price W offered to this consumer. This can facilitate A offering the consumer a competitive price, one she is likely to favor over W’s. Now assume that W has acquired an algorithm of similar quality. As a second-searched retailer, W can also match A’s price and secure all second-searched sales. For any consumer searching twice, W and A would enter a Bertrand-like price competition. The sheer threat of being undercut from the second-searched firm and losing all second-searched sales would incentivize the first-searched firm to lower its price for first-searchers and deter them from searching twice. This leads to lower prices for all searchers. 10