Tying in the age of algorithms

A An Overview

Personalized pricing is defined by the Organisation of Economic Cooperation and Development (“OECD”) as “a form of price discrimination in which individual consumers are charged different prices based on their personal characteristics and conduct. Personalized pricing thus results in consumers paying each a different price, generally as a function of their willingness to pay.” ^[5] Algorithmic personalized pricing requires at least three conditions: (1) the ability to segment consumers based on their maximum willingness to pay; (2) market power on the part of the perpetrating firm; and (3) the ability to limit consumer arbitrage. ^[6]

The prospect of personalized pricing has been discussed for more than a decade. Back in 2013, the Office of Fair Trading, the predecessor of the Competition and Markets Authority in the United Kingdom, published a report on the phenomenon. ^[7] In 2015, the Executive Office of the President of the Obama Administration issued a report titled “Big Data and Differential Pricing.” ^[8] Three years later, the OECD joined the fray with a background note prepared for its meeting on personalized pricing. ^[9] Most of these organizations acknowledged the existence of the phenomenon but concluded that it was likely to be limited in scope. It is generally believed that most businesses are deterred by the potential consumer outcry from pursuing personalized pricing extensively. They also conceded the difficulty with detection. Businesses have every reason to hide the practice from consumers after the outrage directed at Amazon in the early 2000s when it was caught red-handed. ^[10] On that occasion, Amazon was compelled by the public outcry to refund the overcharged customers. ^[11] The overall consensus seems to be that personalized pricing is not yet a matter of serious concern.

Scholars have also attempted to study the prevalence of personalized pricing with varying degrees of success. Some concur with the aforementioned organizations and agree that the phenomenon is not widespread. ^[12] Some sound a note of greater caution and call for more regulatory scrutiny. ^[13] Before delving more deeply into personalized pricing and its feasibility and prevalence, it is important to first clarify what it is not. A number of commentators have already drawn a distinction between personalized pricing and dynamic pricing, arguing that they are in fact completely different phenomena despite superficial similarities. ^[14] Dynamic pricing refers to a pricing practice under which prices are adjusted in real time in accordance with changes in demand and supply. The most well-known example would be surge pricing by Uber. ^[15] We will not dwell on this as the difference between these two phenomena should be apparent to most keen observers.

What is perhaps less appreciated is the potential divergence between personalized pricing and first-degree price discrimination. First-degree price discrimination has been defined since Arthur Cecil Pigou as the ability of the seller to charge all consumers their individual reservation price and hence extract all consumer surplus. ^[16] It has been noted that first-degree price discrimination is economically efficient as it replicates the market output of perfect competition despite its heavy toll on consumers. ^[17] Because of the seller’s ability to individualize prices, it is often presumed that the price offered will be the consumer’s reservation price. This, however, need not be the case. Offering each consumer their own price and calibrating every price exactly at a consumer’s willingness to pay are completely different things. Prices can be individualized for each consumer without the seller being able to extract every bit of consumer surplus.

Personalized pricing need not demand that level of precision. It only means that the seller charges every customer a tailored price based on a combination of their personal characteristics such as location, browsing history, past purchase records, perceived preferences, habits and tastes. ^[18] It does not require the seller to exhaust every consumer’s willingness to pay. There is no reason to assume that these factors or attributes must produce an accurate estimation of each consumer’s willingness to pay. The OECD has astutely observed that estimates of a consumer’s willingness to pay need not be perfect. ^[19] Consumers may only be charged “a proportional share (not necessarily the total value) of their willingness to pay.” ^[20]

One may question whether a consumer’s reservation price or willingness to pay is even a helpful guidepost for a seller’s pricing strategy. The reality is that a consumer’s reservation price is likely to fluctuate over time based on objective circumstances such as the weather and subjective factors such as their state of mind. It is not an immutable quantity. Furthermore, the reservation price is likely to be very difficult to verify in practice. While it may be possible to design experiments to measure a consumer’s willingness to pay, ^[21] replicating the same results in a dynamic, real-world environment is likely to elude most businesses.

Some commentators have analogized personalized pricing to first-degree price discrimination and analyzed it against that benchmark. ^[22] While one cannot categorically reject this approach, it is perhaps more apt to conceptualize personalized pricing as a highly refined version of third-degree price discrimination. ^[23] Ariel Ezrachi and Maurice Stucke best encapsulate this when they assert that “pricing algorithms, while not identifying your reservation price, refine the cruder divisions (such as senior citizens and students) to a more detailed, segmented reality, where people are matched to groups which, because of dispositional and situation factors, have similar price sensitivity and purchase behavior.” ^[24]

The fact that algorithms are yet to accomplish first-degree price discrimination, however, does not mean that personalized pricing should be overlooked. Its impact on consumers can still be substantial. More importantly, for our purpose, the potential of personalized pricing to facilitate abuses of dominance is not predicated on a level of precision commensurate with first-degree price discrimination. Complete personalization is not necessary. What is most crucial is the ability to distinguish between marginal and inframarginal customers. Take tying as an example. Their higher degree of loyalty means that inframarginal customers would be more willing to accept a tie. In contrast, marginal customers may more readily defect when confronted with a tie. Knowledge of the individual customer’s susceptibility to a tie suffices for the purpose of a tying firm, even though the ability to implement personalized pricing would be useful and would augment the anticompetitive potential of a tie. In the context of predatory pricing, this Author has argued elsewhere that the degree of precision that is necessary for algorithms to have an appreciable impact on the practice of predation is the ability to distinguish the marginal customers from the inframarginal. ^[25] Determining a consumer’s likely response to a price change or a tie is considerably less challenging than arriving at a precise estimation of their willingness to pay.

B Prevalence of Personalized Pricing

The most important question about personalized pricing seems to be its prevalence. This question is particularly tricky as firms have every reason to conceal it to avoid consumer backlash. As mentioned earlier, the first known case of personalized pricing that garnered considerable public attention involved Amazon. ^[26] In 2000, a consumer discovered that Amazon was engaging in differential pricing for a variety of products including DVDs and that deleting the cookies on their computer would result in lower prices. A public outcry ensued and Amazon insisted that what had happened was merely an experiment and proceeded to refund the affected customers. ^[27] In 2012, the Wall Street Journal reported that Staples and Home Depot, two major retailers in the U.S., individualized prices based on a customer’s geolocation, income level, browsing history, and proximity to a rival’s store. ^[28] Although these retailers seemed to mostly rely on geographic location, which probably does not constitute genuine instances of personalized pricing and counted more as third-degree price discrimination, ^[29] the price differential in some instances was as large as 166 percent. ^[30] In the same year, the New York Times found that Safeway and Kroger, two major American supermarket chains, practiced price discrimination against their loyal customers by charging them higher prices. ^[31] Across the Atlantic, B&Q was also found to have adjusted its prices based on a customer’s loyalty and spending habits. ^[32] Since then, a number of incidents of personalized pricing have been reported featuring Coupons.com, AirAsia, a budget airline in Asia, and most famously, Uber. ^[33]

Uber has never shied away from price discrimination. Its surge pricing, which has been controversial in some jurisdictions such as India, ^[34] is well known. Surge pricing, however, does not constitute personalized pricing. It is more aptly characterized as second-degree price discrimination. Evidence suggests that Uber engages in more refined targeting against its drivers under what is known as the Hell program. ^[35] Uber offers individualized rebates to its drivers to try to entice them to drive more for itself and less for its competitors such as Lyft in the U.S. ^[36] Targeting drivers, however, is likely to be easier than practicing price discrimination against customers. Uber probably possesses much more information about its drivers and their willingness to drive than about its riders’ willingness to pay. ^[37] It is also arguably easier to discern a consumer’s willingness to pay for ride hailing as compared to other products. There are relatively few product attributes that are of concern to a rider. In most cases, they just want to get to their destination as soon as possible. In contrast, purchasing a smartphone will be a much more complex decision. A recent market study in India strongly indicates that Uber has a remarkable ability to individualize prices. This will be discussed in greater detail below.

Personalized pricing began to attract the attention of academic researchers and competition authorities in the early 2010s. Most of the studies at the time did not find conclusive evidence of widespread personalized pricing, although some evidence of personalized pricing was reported. The Office of Fair Trading in the UK found no evidence of individualized pricing. ^[38] A research report commissioned by the Directorate-General for Justice and Consumers of the European Commission found no evidence of systematic and consistent personalized pricing across eight EU Member States and four markets. ^[39] The aforementioned White House report in 2015 noted that “[s]ellers are now using big data and digital technology to explore consumer demand, to steer consumers toward particular products, to create targeted advertising and marketing offers, and in a more limited and experimental fashion, to set personalized prices.” ^[40]

A number of academic studies yielded different results and found personalized pricing to be more commonplace than suggested by these official reports. Aniko Hannak and her co-authors found “evidence of personalization on four general retailers and five travel sites” out of the sixteen websites surveyed. ^[41] In some instances, the price differential was as substantial as hundreds of U.S. dollars. ^[42] Jakub Mikians and his co-authors reported the steering of customers to different products based on geographic location, browsing history, and purchase history in response to identical search queries. ^[43] Affluent customers are shown products that are up to four times as expensive as those shown to budget-conscious customers. ^[44] While steering can, and most probably will, result in price discrimination, it is not quite the same as personalized pricing. It nonetheless confirms the ability of algorithms to implement individual targeting of customers. An empirical analysis by Le Chen, Alan Mislove, and Christo Wilson details the prevalence of algorithmic pricing in Amazon Marketplace and finds that algorithmic sellers are much more active there. ^[45] Chen and his co-authors also find that algorithmic sellers are more likely to be more successful and win the all-important “Buy Box” on Amazon Marketplace even though they do not necessarily offer the lowest prices. ^[46]

Reports also suggest that personalized pricing is technologically feasible for and attainable by most firms. The technology for personalized pricing is widely available and affordable; with firms such as Google, Microsoft, and Amazon “offering algorithmic pricing solutions out of the box, there are no obstacles for the widespread use of the pricing strategy, even for smaller sized companies.” ^[47] Algorithms featuring personalized pricing capabilities apparently can be obtained for as low as $500 from several software companies, such as HubSpot. ^[48] HubSpot’s product Sales Hub contains a function known as “predictive lead scoring,” which measures the likelihood that a price being offered to a potential customer is attractive enough to secure a sale. ^[49] Yet commentators continue to believe that personalized pricing remains relatively uncommon. ^[50] This is confirmed by a 2018 study in the European Union of 160 websites ^[51] and a 2021 study commissioned by the German Ministry of Justice and Consumer Protection. ^[52]

Two explanations have been offered for this anomalous situation. First, firms are hesitant to practice it for fear of getting caught, especially in light of the backlash faced by Amazon in the early 2000s. ^[53] Second, current evidence may be underestimating the extent of the phenomenon due to the fact that “[p]ersonalized pricing is notoriously difficult to prove conclusively, firms have incentives to disguise it, and technical barriers to its use are dropping by the day.” ^[54] One recent study from India contains highly probative evidence that Uber engages in personalized pricing. The lengths to which the authors had to go to establish personalized pricing attests to the difficulty in proving personalized pricing conclusively. One of the complications is the difficulty in disentangling personalized pricing from dynamic pricing, which is increasingly commonplace.

In 2019, the Competition Commission of India commissioned the University of Delhi to conduct a study of possible personalized pricing by the two leading cab aggregators in India, which were not named in the report but are widely believed to be Uber and Ola. ^[55] A controlled experiment involving sixty-eight respondents was conducted at the University of Delhi campus on November 5, 2019 to try to decipher the pricing patterns of the ride-hailing apps. ^[56] Rides were requested from the location to identical destinations at the same time. Data were collected over successive rounds, with the first round serving as control and erratic exogenous demand shocks being applied every five minutes for six rounds subsequently. It was found that cab aggregators charged different base fares for different riders and that fares varied across rounds for a particular individual as well as across different individuals in the same round. Since different fares were offered for identical rides ordered at the same time, other factors such as personal attributes of the riders must have been responsible for the disparity. The study was supplemented by a survey of 2,000 riders in four Indian cities, which confirmed rider perception that individualized pricing does exist. ^[57] Unsurprisingly, both firms disputed the findings of the study. They do, however, concede that while the base fare is the same for all riders, the final fare may differ as discounts are personalized and may vary across riders.

The foregoing discussion is focused on pricing practices. Tying, of course, need not be directly reflected in prices. It may only concern terms of sale pertaining to the existence of a tie unless mixed bundling is involved. In cases where pricing is not involved, it may be more appropriate to address the phenomenon of using algorithms to tailor individual product offerings as algorithmic targeting instead of personalized pricing. The seller uses algorithms to craft its product offerings for individual consumers based on their susceptibility to a tie. To avoid confusion, however, personalized pricing will continue to be used to refer to the relevant phenomenon given the wider acceptability of the term. When personalized pricing is used in the rest of the Article, it encompasses both algorithmic targeting and personalized pricing.

A Michael Whinston’s Strategic Foreclosure Model

In his seminal 1990 article, Whinston launched the first post-Chicago challenge to the Chicago School orthodoxy on tying. ^[65] One of his main contributions is his debunking of the single monopoly profit theorem, ^[66] which had long served as the bedrock of the Chicago School defense of tying. He observes that the theorem falls apart when the tying and the tied products are not used in fixed proportions and when the tied product has separate uses independent of the tying product. The single monopoly profit theorem only holds if the tying and the tied products are used in fixed proportions and the tied product has no independent use without the tying product, as in the case of nuts and bolts. ^[67]

More importantly for our purpose, Whinston posits an offensive foreclosure scenario under which a tie serves as a pre-commitment device for the tying firm to undercut a potential entrant’s prices. ^[68] A firm with a dominant position in the tying product market would generally prefer a competitive tied product market, which would allow it to extract all the surplus from its tying product. ^[69] The firm would thus have no incentive to tie to deter entry into the tied product market. And once entry has occurred, the firm would prefer independent pricing to bundled sales because tying reduces the firm’s profit for two reasons. First, tying causes the firm to lose sales of the tying product to consumers who have a low valuation of the firm’s tied product. ^[70] Second, tying compels the firm to lower its prices for both products through bundled discounts. ^[71]

Under these circumstances, a tie serves as a pre-commitment device to bind the tying firm to undertake price cuts upon market entry. Such a commitment works because once the two products are bundled, the firm will only make sales of the tying product when it also sells the tied product. ^[72] Once an irreversible tie has been put in place, the firm must offer discounts in order to sell the bundle. ^[73] Such discounts reduce the profit from market entry and serve as an effective deterrent to a potential entrant. Whinston calls this strategic foreclosure, where “tying represents a commitment to foreclose sales in the tied good market, which can drive its rival’s profits below the point where remaining in the market is profitable.” ^[74]

This foreclosure scenario is contingent on the tying firm’s ability to make a credible pre-commitment to tie. ^[75] If the tying firm can reverse the tie upon successful market entry, the potential entrant knows that the threatened bundled discounts by the tying firm are not credible and will proceed to enter the market. ^[76] The tie will fail as an entry deterrent. Therefore, the tying firm must be able to make a credible commitment to tie, such as through product design or adjustments to the production process, for foreclosure to materialize. ^[77] Note that the need for this credible commitment disappears if consumers have heterogeneous valuations for the tying product. ^[78]

The tying firm will only commit to tie if successful entry deterrence is more profitable than accommodation. Because independent pricing is actually more profitable for the tying firm once market entry has taken place, the firm would only commit to a tie if it expects entry deterrence to succeed. ^[79] Whether the tie is ultimately profitable for the tying firm comes down to a tradeoff between the profit generated from the additional sales of the tied product following successful domination of the market and the loss sustained from diverted sales from its tying product. ^[80]

The possibility of personalized pricing has two important implications for this theory of harm. First and foremost, as mentioned earlier, personalized pricing minimizes the downside of tying and significantly improves its profitability, rendering it a more rational and feasible strategy. Whinston’s basic model presumes identical consumer valuation of the tying product. ^[81] Under the more realistic assumption of heterogeneous consumer valuation, where some consumers place a higher valuation for the tying product than others, a tie may actually raise the entrant’s profit if there are enough marginal customers who will defect. ^[82] Or at least the detrimental effect on the entrant’s profits may be smaller than under the assumption of identical valuation. Tying may no longer result in strategic foreclosure by lowering the entrant’s profit and may cease to be a rational strategy for the tying firm. ^[83] With the help of personalized pricing, however, the tie can be selectively offered to inframarginal customers who place a high valuation on the tying firm’s tying product, while marginal customers who may defect can be spared. The prospect of defection by marginal customers is minimized through the selective imposition of a tie. The strategic foreclosure effect of a tie is restored despite heterogeneous consumer valuation. Tying results in a sufficient reduction in the entrant’s profit to achieve entry deterrence and will remain a rational strategy for the tying firm even with the prospect of market entry.

A second implication of personalized pricing for this foreclosure model is that the need for a credible pre-commitment to tie in the event of market entry loses its significance. One of the more stringent conditions for Whinston’s foreclosure model is the requirement of a credible pre-commitment to tie. The lack of a binding commitment would undermine the credibility of the threat to tie and would invite market entry. Once entry occurs, the tying firm will simply switch to independent pricing, which, under the assumption of identical consumer valuation of the tying product, would allow the tying firm to extract all surplus. ^[84] Tying is an inferior strategy to independent pricing because, as mentioned above, tying causes the firm to lose sales of the tying product to low valuation customers and compels the firm to lower its prices by offering bundled discounts. There is hence a need for a credible pre-commitment to tie. In the presence of heterogeneous consumer valuation of the tying product, however, independent linear pricing may no longer allow the tying firm to extract all the surplus from consumers. A variable-proportions tie may be necessary for this purpose. Tying may turn out to be a superior strategy to independent pricing for the tying firm.

Personalized pricing changes the analysis. First, with personalized pricing, a variable-proportions tie is no longer needed to extract surplus. The tying firm can do so directly through personalized pricing. Whether tying or independent pricing is a superior strategy thus no longer depends on the capacity for price discrimination. Other factors matter. Recall that one of the reasons that independent pricing is a superior strategy for the tying firm is because tying causes it to lose sales to low-valuation customers. With selective tying, such lost sales are minimized. Tying is no longer the inferior strategy in the event of market entry. The need for a credible pre-commitment to tie is obviated. Whinston confirms this by illustrating that a credible pre-commitment to tie is redundant if the tying firm is able to offer a tie selectively. ^[85] The optimal strategy for a tying firm that is incapable of making such a pre-commitment is in fact to engage in selective tying, i.e., to impose a tie on high-valuation customers and offer independent pricing to low-valuation customers. Tying would be more attainable under Whinston’s model of strategic foreclosure if a binding commitment to tie is no longer necessary.

This conclusion is bolstered once one considers the second reason that independent pricing is a superior strategy absent personalized pricing. It is said that tying compels the firm to lower its prices by offering bundled discounts. Algorithms not only allow a tying firm to impose a tie selectively, but they also make it possible for the firm to offer individualized prices for those customers subject to a tie. The bundled discount can be tailored to an individual customer’s valuation of the tying product. More targeted discounts help to minimize the loss of revenue resulting from the tie. This further augments the attractiveness of tying as a strategy to the tying firm and obviates the need for a credible pre-commitment.

The foregoing discussion may lead one to question, whether tying is even necessary at all as a signaling device for the tying firm’s commitment to price cutting in the event of market entry. If the tying firm can implement price cutting directly through personalized pricing, why would a commitment device still be needed? Perhaps the best way to conceptualize this commitment in light of the possibility of personalized pricing is in terms of the scope of commitment. As opposed to committing to offer discounts to all customers across the market in the event of market entry, a tie can be thought of as a commitment to cut prices for a particularly relevant or valuable group of customers.

To facilitate the discussion, we adopt a simplifying assumption that there are only two levels of valuation, high and low, for the tying and the tied products. There are high-valuation customers and low-valuation customers. Consumer demand for the two products could be positively correlated or negatively correlated. The correlation can be mild or strong. There are thus four possible valuation combinations for these two products among consumers: High/ High, Low/ Low, High/ Low, and Low/ High.

Tying would be rather redundant for the High/ High and Low/ Low customers, but for different reasons. For the High/ High customers, a tie is unnecessary because these customers will purchase the tying firm’s tying and tied products independently without a tie. They prefer these products regardless. In contrast, a tie imposed on the Low/ Low customers will be futile. Given that these customers have a low preference for the tying firm’s tying and tied products, imposing a tie on them will likely drive them even further away. The Low/ High combination is of little interest to us given that our focus is on a firm that is dominant in the tying product market trying to foreclose an effective entrant in the tied product market. Such a firm is unlikely to be concerned about customers who have high valuation for its tied product. These customers will already purchase the tying firm’s tied product without a tie. Imposing a tie on them would be unnecessary and may risk alienating them by compelling them to also purchase the tying product.

The main target of the tie would hence be the High/Low customers, who place a high valuation on the tying product but a low valuation on the tied product. Aided by algorithms, the tying firm will impose a tie selectively on this group of customers while leaving the rest of the customers alone. This customer group is the likely battleground between the incumbent and the entrant because the tying firm will be concerned with retaining customers whose valuation for its tied product has deteriorated following the emergence of alternatives offered by the entrant. These customers are also likely to be the most important customers for the entrant to attract. A tie can be viewed as a commitment to offer bundled discounts to this group. This commitment still serves an important deterrent purpose. In fact, the ability to individualize discounts will likely strengthen the entry deterrent effect by improving the incumbent’s ability to retain its customers.

In conclusion, by facilitating personalized pricing and improving the capacity for selective tying, algorithms will render Whinston’s model of strategic foreclosure more attainable by improving the profitability of a tie and removing the need for a mechanism for credible commitment.

B Barry Nalebuff’s Defensive Leveraging Model

Whinston’s foreclosure model is of an offensive nature. Barry Nalebuff’s, in contrast, is more of a defensive kind. His model is concerned with a firm with a monopoly in both the tying and the tied product markets resorting to tying to deter potential entry. The incumbent is not endeavoring to extend its market power into a second market through leveraging. Instead, it is trying to use its market power in one market to protect its market position in another market. ^[86] One key distinction between Whinston’s and Nalebuff’s models is that the latter does not require a credible commitment to tie. In Nalebuff’s model, incumbent profits are higher with tying even in the event of market entry. ^[87] He notes that “in the post-entry Nash equilibrium pricing game between a two-product incumbent and a one-product rival, bundled pricing is the subgame perfect equilibrium.” ^[88] Characterizing independent pricing as the nuclear option, he asserts that unbundling is not a credible alternative for the incumbent when tying is available. ^[89]

Contrary to the central premise of the single monopoly profit theorem, Nalebuff argues that “[l]everaging market power from A [tying product] into B [tied product] and accepting some one-product competition against the bundle is better than using the monopoly power in good A all by itself.” ^[90] In Whinston’s model, tying helps an incumbent to deter entry by allowing the incumbent to commit to launching a price war upon entry. ^[91] In Nalebuff’s model, tying puts off a potential entrant through the more conventional means of depriving the entrant of sufficient scale economies by diverting customers away. ^[92]

In Nalebuff’s model, the incumbent firm possesses a monopoly in both the tying product market and the tied product market and faces a potential entrant which can enter one but not both of the markets. ^[93] Tying is a superior defense tactic for the incumbent because it allows the firm to defend both markets by lowering the profit potential of the entrant without resorting to price cutting. ^[94] Tying has two advantages as a defense strategy. First, a single-product entrant faces significant difficulty entering the market against a bundling monopolist offering its products at a discount. ^[95] Profits are doubled if entry is successfully deterred. ^[96] Second, even if entry deterrence fails, the tie will lower the damage done by a single-product entrant by allowing the incumbent to hang on to more customers and to keep prices higher. ^[97] In the presence of a tie, a single-product entrant would only be able to attract customers who do not require both the tying and the tied products. All the customers who require both will remain with the tying firm. Even if entry does materialize, incumbent profits will be fifty percent higher with a tie. ^[98]

According to Nalebuff, tying produces two effects that help the incumbent defend its existing dual monopolies: the pure bundle effect and the bundle discount effect. ^[99] The pure bundle effect refers to the effect of combining two independent products into a bundle without any price adjustments. ^[100] He argues that the pure bundle effect alone reduces the entrant’s profits by fifty percent. ^[101] The bundle discount effect refers to the reduction in the bundle price below the combined original component prices. ^[102] Nalebuff argues that this is a low-cost or even costless deterrent strategy for the incumbent because the incumbent would have offered a bundled discount anyway even without regard to potential entry. ^[103] A discount would be necessary to entice consumers to accept the bundle. The bundled discount allows the incumbent to raise its profit in the event of successful deterrence of entry while making entry even less profitable. ^[104]

Personalized pricing will render tying an even more powerful weapon in Nalebuff’s model. One difference between Nalebuff’s model and the basic model in Whinston’s analysis is that while Whinston presumed identical valuation for the incumbent’s tying product, heterogeneous consumer valuation is built into Nalebuff’s model. ^[105] While Nalebuff recognizes heterogeneous consumer valuation in his model, he does not envision the incumbent’s ability to personalize prices, which he could not have given the state of technology in 2004. Our discussion of the impact of algorithms on the practice of tying and its theories of harm has focused on the capacity of algorithms to permit firms to impose ties selectively. It turns out that algorithms alter the dynamics of tying in another important way. We can visualize the incumbent’s customers along a spectrum according to their valuation of the tying product. At the first level, algorithms allow the firm to dissect its customers with reference to their susceptibility to a tie by distinguishing the marginal customers from the inframarginal customers. At the second level, algorithms permit the incumbent to further differentiate customers based on their individual valuation of the bundle and adjust its prices accordingly. They allow the tying firm to offer individualized bundled discounts among the customers who are subject to a tie.

In Nalebuff’s analysis, he calculates that offering a bundled discount of thirty-two percent across the board will result in a forty-five percent reduction in the entrant’s profits, while a bundled discount of sixty percent pushes the entrant’s profits close to zero. ^[106] These calculations are based on a uniform price being offered across the market, which may fall below the valuations of most customers, who will then purchase the bundle, but which may exceed the valuations of some remaining customers, who may then eschew the bundle. By allowing the incumbent to offer individualized bundled discounts, algorithms will permit the incumbent to maximize its sales of the bundle while extracting the most surplus from each customer. Algorithms will help to avert inadvertent loss of inframarginal customers to the entrant due to excessively high prices. They will also help the tying firm to avoid offering unnecessary discounts to customers. With the assistance of algorithms, an incumbent should be able to inflict a forty-five percent loss of profit on the entrant with a bundled discount significantly smaller than thirty-two percent. ^[107]

The foregoing analysis indicates that even though tying is usually understood as non-price conduct, there is ultimately always a sale involved. This means that personalized pricing will have relevance even for non-price conduct. If the effectiveness of the abusive conduct is enhanced by the ability of algorithms to offer individualized prices, algorithms will render such conduct more potent and will magnify its anticompetitive potential. Given that the main purpose of tying is to increase the tying firm’s sales in the tied product market, whether for an offensive or a defensive purpose, the ability of algorithms to tailor prices to individual consumers, which allows the tying firm to maximize sales, will inevitably enhance the capacity for foreclosure.

A Intra-Product Price Discrimination

Under intra-product price discrimination, otherwise known as variable-proportion ties, what the seller seeks to do is to extract higher consumer surplus from high-valuation customers by way of a tie. The products involved are most often complements. ^[118] One example is printers and replacement ink cartridges, with the former being the tying product. Consumers place different valuations on the tying product, some being high-intensity users and some low-intensity users. High-intensity users naturally value the printer more highly. If the seller wants to maximize sales, it will have to charge a price equal to the valuation attached by the marginal user to the printer, which is the maximum that the user would pay for the printer. This leaves the inframarginal customers, i.e., high-intensity users, considerable surplus which the seller covets.

The problem for the seller is that there is no way for the seller to distinguish between a high-intensity user and a low-intensity user at the point of sale. The seller can make use of a tie to achieve the same outcome without the need for a capacity for direct verification. Because the tied product is a complement to the tying product, their intensity of use increases together. The more someone uses a printer to print, the more frequently they would have to replace the ink cartridge. By imposing a tie on the two products and charging a supra-competitive price for the ink cartridge, the seller can indirectly extract more surplus from the high-intensity users and achieve price discrimination.

Tying is often justified when it is used for intra-product price discrimination. Although the welfare effects of price discrimination usually depend on its impact on output level, Herbert and Erik Hovenkamp analogize intra-product price discrimination to second-degree price discrimination and argue that because variable-proportion ties usually involve a reduction in the price of the tying product, consumer welfare is enhanced in most cases. ^[119] This is so even despite a reduction in output. ^[120] And if output increases as a result of the tie, the consumer welfare effect is most likely to be positive. ^[121] Thus, when a tie is used for the purpose of intra-product price discrimination, the consumer welfare effect is likely to be positive and tying should therefore be presumptively legal. ^[122]

With the help of algorithms, the seller would be able to implement price discrimination directly, obviating the need to resort to tying. The reason that tying is needed is due to the seller’s inability to detect and determine the consumer valuation of the tying product. Algorithms should allow the seller to do that and charge considerably more tailored if not individualized prices directly. In fact, firms may be able to draw finer distinctions than simply high- and low-intensity and tailor their prices accordingly. There should be no loss in the precision of price discrimination when it is practiced directly.

For price discrimination to succeed, the seller must be able to prevent arbitrage. Arbitrage refers to the resale of the product by a buyer who is offered a low price by the seller to a buyer who is offered a higher price. ^[123] For that to happen, consumers must be able to self-identify whether they are offered a higher or lower price. This will be challenging for consumers under personalized pricing, as prices will be highly dispersed and dynamic. When consumers do not even know that they have been overcharged, they will not know to look for cheaper prices from other consumers. Arbitrage is likely to be futile. Therefore, personalized pricing is likely to render variable-proportion ties redundant.

B Inter-Product Price Discrimination

When a tying product and a tied product do not share a complementary relationship, the constellation of consumer valuations of the two products can be conceptualized in terms of the four possible combinations of valuations that were previously discussed. Tying serves different purposes among these four valuation combinations. First, if the valuation combination is Low/Low, tying is likely to be futile. Tying a product that consumers do not much care for with another similar product is not going to generate much additional demand for the two products. Nor will consumers feel compelled to purchase the bundle. The tying firm will be better off forgoing this market segment. Among the remaining three combinations, the role of tying depends on whether the correlation is positive or negative.

When demand correlation is positive, in this instance High/High, inter-product price discrimination is more difficult and thus a firm would only tie for other benefits. ^[124] With positive correlation, the entrant is forced to enter the tied product market at very low prices, hence making entry unprofitable. ^[125] In fact, when correlation is perfectly positive, the entrant’s profit is reduced to zero. ^[126] There are hence significant incentives to use tying as an entry deterrent tool. Even when entry deterrence fails, tying when demand is positively correlated still elevates profit for the tying firm significantly. ^[127] However, it is worth pointing out that positive correlation is also one of the factors that nullify the anticompetitive effects of tying. Einer Elhauge observes that the single monopoly profit theorem propounded by the Chicago School in the 1960s and 1970s, under which tying creates no anticompetitive consequences, would only be valid when the respective demand for the tying and the tied products share a strong positive correlation. ^[128] When the demand for two independent products is negatively correlated, High/Low or Low/High, the main motivation for a tie is to pursue price discrimination, in particular inter-product price discrimination. ^[129] Tying will no longer be a very effective entry deterrent tool. At perfectly negative correlation, tying produces no pure bundle effect at all. ^[130]

Personalized pricing may render tying a redundant means for inter-product price discrimination. If a seller, with the help of algorithms, can come up with a reasonably close estimation of an individual consumer’s valuation of the two products and charge accordingly, the very reason for inter-product price discrimination no longer exists. Recall that tying is necessary to attain inter-product price discrimination precisely because the seller is unable to capture an individual consumer’s surplus from the two products when they are sold separately at market-wide prices. If the seller is now able to do so directly, tying seems redundant.

Personalized pricing may further refine the implementation of inter-product price discrimination. Algorithms will now be able to draw finer distinctions within each group of customers. It will no longer be two monolithic groups of high-valuation and low-valuation customers. The segmentation will be more refined even if it may fall short of genuine individualization. More personalized prices can now be charged whether the two products are sold together or separately. Both the à la carte prices and bundled prices can be individualized.

Whether the seller would still impose a tie would now depend on whether there is anything to be gained by doing so. The seller would only have the incentive to tie if there are advantages from tying. First, it could be because the estimation of consumer surplus would be more accurate when done on a bundled basis. This could well be the case when the negative correlation is strong, in which case the overall valuation of the bundle would tend to converge. Second, it could be because tying allows the seller to pool together its market power in the two markets, thereby enhancing the effectiveness of the price discrimination. Whether there is any incentive to do so would depend on the degree of the seller’s pre-existing market power in the two markets. If that market power is already substantial, the seller may not gain much by pooling together its market power. If that market power is relatively low, however, there may be an incentive to strengthen it through a tie. This, however, will be an unlikely scenario given that algorithms have reduced the market power required for effective price discrimination. Personalized pricing together with dynamic pricing will make it increasingly difficult to undertake price comparisons. Overall, personalized pricing is likely to have rendered tying a redundant tool for implementing inter-product price discrimination, which should no longer be a valid justification for tying.

C Intra-Consumer Price Discrimination

Of the three types of price discrimination, personalized pricing probably has the least impact on intra-consumer price discrimination. Recall that this refers to when a consumer attaches disparate valuations to the multiple units of a product they purchase. In order for a seller to be able to extract the consumer surplus from the inframarginal units to which the consumer attaches a higher valuation, the seller would need to be able to price-discriminate across different units of the same product. Algorithms are indeed powerful, but probably not to that extent. While they may allow the seller to individualize prices across consumers, their capacity does not extend to price discrimination across different units purchased by the same consumer, at least not at the current state of technology. Therefore, a seller keen on implementing intra-consumer price discrimination must continue to rely on tying. Intra-consumer price discrimination will hence continue to offer a valid justification for tying. This kind of price discrimination, however, is likely to be rarer than intra-product and inter-product price discrimination.