Regulating Algorithmic Pricing Part 3

5 Equilibrium Calibrations Having derived best responses for A and W given all four scenarios, I analyze Perfect Bayesian Nash Equilibrium (PBNE) results for the pricing subgame given the algorithm investments. All pricing strategies are formulated in terms of p∗A , p̃A , p∗W , p̃W , which are functions of v, γA , γW , σA , σW . Note that σA and σW varies with algorithm investment decisions, so σi for firm i depends on whether i invests in the algorithm. For reference, I summarize the best-response prices for A and W in each of the four scenarios. (Alg, Alg): • A charges p∗A1 for first-searchers and conjectured first price pW for second-searchers. • W charges p∗W 1 for first-searchers and conjectured first price pA for second-searchers. (Alg, Non): • If conjectured pW > p∗A1 θ̃θAk ∗ , A charges pW − η for first-searchers and pW for secondk searchers. W charges p∗W for all consumers. ∗ • If conjectured pW ≤ p∗A1 θ̃θAk ∗ , A charges pA1 for first-searchers and pW for secondk searchers. W charges max{p∗W , p∗W 2 + σA (1−θ̃Ak ) } 2 if p∗W ≤ pW or p∗A1 if p∗W > pW for all consumers. (Non, Alg): • If conjectured pA > p∗W 1 , A charges p∗A for all consumers. W charges pA − η for firstsearchers and pA for the second-searchers. • If conjectured pA ≤ p∗W 1 , A charges max{p∗A , p∗A +σW θ̃W k } 2 if p∗A ≤ pA or p∗W 1 if p∗A > pA for all consumers, W charges p∗W 1 for first-searchers and pA for second-searchers. (Non, Non): Many cases exist. 33 5.1 Market Calibrations Solving for PBNE results analytically is complicated by many edge cases. To illustrate the main takeaways of my model, in lieu of analytical results, I calibrate PBNE with judiciously chosen values for each variable. I analyze five related markets. • Market 1 is the symmetric base case. It highlights the difference in σi with and without an algorithm for firm i. The algorithm proportionally lowers σi for every consumer. • In Market 2, there exists asymmetry in σi with algorithm across the two firms. It captures the case that, even when both firms may have algorithms, one’s algorithm is more sophisticated and effective than the other. • In Market 3, there exists a greater difference between algorithmic σi and non-algorithmic σi symmetric for each firm. Due to even more reduced search cost, market overlap expands even more, leading to even more potential second-searchers. • Market 4 considers asymmetry in consumers’ belief structure. If consumers expect firm i to have lower prices than its rival, γi > γ−i . Different γ across A and W introduces vertical differentiation: the firm with higher γi benefits from a “low price” reputation. • Market 5 captures how a decrease in consumer value v may narrow the demand overlap, which might result in disjoint markets for some scenarios. Comparing Markets 2 to 5 with Market 1’s results yields insights on how the use of algorithm provides pro-consumer effects, and how much the effects differ in various market conditions. Market 1: Base Case I consider a market where the product is sufficiently valued such that all consumers will search at least once regardless of the algorithms. Moreover, v is large enough such that market overlap exists across all four scenarios. But algorithms can lower search cost significantly such that they can induce a much larger degree of market overlap. To focus on this particular 34 dynamic, I make the two firms, with the possible exception of their algorithm investment, symmetric. I let v = 5, γA = γW = 0.4. For σi , • With algorithm, σA = σW = 0.8 • Without algorithm, σA = σW = 2 Given these parameters, market overlap exists for all four scenarios, as the consumer expects to receive high enough of a surplus from searching and purchasing the good. Table 1 shows PBNE prices for A and W. If firm i is able charge two prices, its pricing profile is shown as an ordered pair (pi1 , pi2 ). Table 1: PBNE Prices: Base Case Scenario (Alg,Alg) (Alg,Non) (Non,Alg) (Non,Non) A W (3.4, 3.4) (3.4, 3.4) (3.57, 3.57 − ϵ) 3.57 3.57 (3.57, 3.57 − ϵ) 4 4 The prices in Market 1 depict pro-consumer effects of the adoption of algorithms. In the (Non, Non) case, each firm charges pi = p−i = 4 for all consumers. Even without algorithms, the price is still below monopolistic pricing due to the market overlap. If only one firm has an algorithm, the price drops to 3.57 or 3.57 − ϵ for all consumers regardless of their search sequence or number of searches. The drop in the price for a firm with an algorithm is a result of all three effects of algorithm. Recommendation effect reduces the search cost and expands the overlapped market, which the second-searched firm with algorithm can capture by matching its rival’s first price offering. The sequence tracking and rival price monitoring effects drive the price down in the overlapped markets due a variation of Bertrand’s competition. What appears surprising is that the price offering by the firm without an algorithm also drops. This can be explained by the theory of credible threat: any firm with an algorithm can credibly threaten its rival that it matches the first price for any 35 second-searchers. The firm without an algorithm is incentivized to deter its first-searchers from second search via a discount. Prices drop more when both retailers use an algorithm, as the market overlap is the most extensive and both firms face credible threat of price matches from their rival. Market 2: Greater difference in Alg σi and Non σi for A Similar to Market 1 except that I let: • With algorithm, σA = 0.7 < σW = 0.8 • Without algorithm, σA = σW = 2 Intuitively, these parameters reflect scenario where some firms can adopt more sophisticated algorithms than others. The more sophisticated the algorithm, the greater reduction in search cost, and the greater expansion of market overlap. Table 2: PBNE Prices with Asymmetric Algorithmic σi Scenario (Alg,Alg) (Alg,Non) (Non,Alg) (Non,Non) A W (3.34, 3.34) (3.34, 3.34) (3.46, 3.46 − ϵ) 3.46 3.57 (3.57, 3.57 − ϵ) 4 4 Asymmetry in algorithmic σi creates different sizes of the market overlap when only one firm has the algorithm. When A has an algorithm and W does not, the greater expansion of overlap as a result of lower σA leads to more second-searchers, which requires A to lower the price for first-searchers to discourage them from searching twice. In the (Non, Alg) case, W’s algorithm reduces search cost less and causes less market overlap. The equilibrium price in (Alg, Non) is lower than in (Non, Alg). Ceteris peribus, consumers benefit more from adoption of more sophisticated algorithms which lower the search cost. 36 Market 3: Symmetric σi with Smaller Difference Similar to Market 1 except that I let: • With algorithm, σA = σW = 1 • Without algorithm, σA = σW = 2 In this market, there exists a smaller difference in σi for with and without algorithm. Table 3: PBNE Prices: Symmetric σi with Smaller Difference Scenario (Alg,Alg) (Alg,Non) (Non,Alg) (Non,Non) A W (3.5, 3.5) (3.5, 3.5) (3.67, 3.67 − ϵ) 3.67 3.67 (3.67, 3.67 − ϵ) 4 4 Smaller algorithmic effect to reduce search cost leads to a smaller overlap in the market, hence less threat of second search from consumers. A smaller recommendation effect results in higher prices than the base case. Market 4: Asymmetry in γi Similar to Market 1 except that I let: • γA = 0.5 > γW = 0.4. Asymmetry in consumers’ belief structure introduces difference in expected price, p̄A and p̄W . This asymmetry implies that, ceteris peribus, all consumers expect A’s price to be lower than W’s: p̄A = (1 − γA )v < p̄W = (1 − γW )v. Ceteris peribus, this leads consumers to favor A over W, a vertical differentiation. But the difference in consumer’s search cost with respect to their location on the Hotelling line incentivizes some consumers to search at W. The indifferent consumer of first search should be located to the right of the indifferent consumer in Market 1 across all scenarios. 37 Table 4: PBNE for Prices with Asymmetry in γi Scenario (Alg,Alg) (Alg,Non) (Non,Alg) (Non,Non) A W (3.15, 3.15) (3.15, 3.15) (3.21, 3.21 − ϵ) 3.21 3.42 (3.42, 3.42 − ϵ) 3.75 3.75 When consumers expect A’s price to be cheaper than W’s before initiating the search, all prices– including the equilibrium price where neither firm has algorithm– drop relative to the prices in Market 1. The increase in the expected surplus a consumer gains from purchasing the good induces more consumers to search at A than in Market 1. With large enough of an AO demand, A can still gain significant sales even if W gains all second-searchers. When A has an algorithm, the marginal benefit of first-searching and second-searching at A increases, and the marginal cost of search decreases. Ceteris peribus, it costs W more to deter W’s first-searchers to second-search A. Therefore, W offers a lower price than in Market 1 for each scenario, regardless of whether A has an algorithm or not. Market 5: Decrease in Value, Disjoint Markets The market is similar to Market 1 except for a smaller v. Algorithmic effect in reducing search cost and tracking search sequence is less pronounced when consumers do not necessarily commit to searching. That is, if the value they could gain from the good is small, search cost appears relatively high. Even if some consumers would search twice and incur search costs for both firms, the additional surplus they obtain from consuming the good at a lower price is small. To demonstrate how a smaller v may lead to disjoint markets for different scenarios, I calculate the equilibrium prices for two vs: v = 2 and v = 1.3. When v = 2, (Non, Non) scenario forms a disjoint market, and all other scenarios form overlapped markets. In contrast, when v = 1.3, only (Alg, Alg) scenario has an overlapped market. 38 Table 5: PBNE for Prices with v = 2 and v = 1.3 v Scenario (Alg,Alg) (Alg,Non) (Non,Alg) (Non,Non) v=2 v = 1.3 A W A W (1.6, 1.6) (1.6, 1.6) (1.18, 1.18) (1.18, 1.18) (1.77, 1.77 − ϵ) 1.77 (1.3 − ϵ, 1.3 − ϵ) 1.3 − ϵ 1.77 (1.77, 1.77 − ϵ) 1.3 − ϵ (1.3 − ϵ, 1.3 − ϵ) 2−ϵ 2−ϵ 1.3 − ϵ 1.3 − ϵ In scenarios without market overlap, the indifferent consumer does not obtain a positive payoff for searching at either A or W. There exist consumers who do not search at all. A and W each act as a monopoly among their searchers without the need to worry about poaching, leading them to a price right below v. The only “escape” from monopolistic pricing is for algorithms to reduce the search costs for some consumers enough to induce searching twice. Given a low value of consuming the good, the effect of the algorithm is small due to the small marginal benefit of second search for most consumers. Ceteris peribus, the lower v, the less likely overlap, and the less algorithmic effect on improving consumer welfare to escape monopolistic pricing. 5.2 Algorithmic Investment PBNE prices I just calibrated are good indicators for consumer welfare, as consumers are generally better off with lower prices.18 It remains to show, however, that algorithms confer any competitive advantage to the firm. If the adoption of algorithm improved consumer surplus but decreased producer surplus, no firm would be incentivized to offer the service in the first place (Stage 0). To demonstrate the margin of algorithmic advantage to the firms, I calculate firm’s expected payoff given the PBNE pricing strategy in Market 1. Let K be the upfront fixed cost to investment to have an algorithm for both firms. 18. In overlapped markets, all consumers end up buying the good in PBNE. 39 Table 6: Payoffs for Algorithmic Investment Game in Market 1 W A N on Alg N on (2, 2) (1.02, 2.55 − K) Alg (2.55 − K, 1.02) (1.7 − K, 1.7 − K) The algorithm investment game has a payoff structure similar to Prisoner’s Dilemma with investment in algorithm a dominant strategy as long as K is sufficiently small (K < 0.55). The firm gains the most profit when it invests in an algorithm but its rival does not (2.55−K). The firm gains the least profit when its rival adopts an algorithm but it does not (1.02). When both firms invest in an algorithm, they may get lower profits (1.7−K) than in the case where neither firm invests in an algorithm (2.2). Therefore, consumers are the main beneficiary of mutual adoption of algorithms. However, if either firm is willing to invest more to create asymmetry in σi values between the two firms, their algorithmic advantage expands, leading to an increase in the (Alg, Alg) profit that asymptotically approaches (Non, Non) profit. As in Prisoner’s Dilemma, what drives investment is less the advantage of having an algorithm but more the disadvantage of not having one when its rival does. 40 6 Discussion and Conclusion My sequential search duopoly model demonstrates the under-discussed pro-competitive potential of algorithmic pricing from the joint effect of the three features: search cost reduction through recommendation, search sequence tracking, and rival price monitoring. When either or both firms develop pricing strategy with algorithms, the resulting competitive equilibrium may increase consumer welfare for all consumers. That second-searchers can enjoy the benefit of algorithmic pricing due to search-sequence-based price discrimination is intuitive. Perhaps surprising is that the first-searchers may obtain a similar magnitude of benefit merely from the possibility that some of them may be poached by a rival. The size of the pro-consumer effect largely depends on the extent of market overlap. By stating that firms charge a price approximate to consumer’s value v in the disjoint market, we assume that firms already have some technology that enables them to do near first degree price discrimination in a monopoly. Empirical evidence supports this assumption. Calvano et al. (2018) showed the ability of algorithms to identify each consumer’s reservation price, enabling them to sell at each consumer’s willingness to pay. But in overlapped market, my model shows how strategic price discrimination can lead to price discounts for all consumers, depending on the extent of overlap. The greater the overlap, the more consumers considering searching twice, and the greater the price discount has to be offered to deter second searches. As my calibrations have shown, a greater difference in algorithmic and non-algorithmic σi may lead to a greater reduction of search cost and greater improvement of consumer welfare. A higher γi and a lower expected price may lead to greater marginal benefit of second search, which also improves consumer welfare. A lower consumer value of consuming the good, however, may cause narrower market overlap or disjoint market conditions, hence smaller algorithmic effect on reducing equilibrium prices. The model does not predict that algorithms are universally pro-competitive, nor will all firms adopt them solely for their competitive advantage. The cost of search versus the value of purchasing the good determines the extent to which consumers can benefit from strategic 41 algorithmic competition. The model is most applicable to consumers who highly value the good but lack a concrete idea of its prices. Algorithms encourage firms to offer lower prices to consumers inclined to purchase the good from that firm. Even with the recommendation effect, consumers who derive limited value from the good receive a relatively small algorithmic benefit. When consumers expect high prices and face high search costs, they may choose not to search twice and receive quasi-monopolistic pricing. The algorithmic effect would be limited for consumers who already have sufficient knowledge of the good’s price before conducting a search, as they would not expect significant welfare gain from second search. Regulatory Insights Combined with existing research on algorithmic facilitation of tacit collusion, my thesis may inform regulatory authorities to adopt a more nuanced approach to assessing the competitive implications of algorithmic pricing. Most economic analyses on the anti-competitiveness of algorithms implicitly assumes market overlap. They conclude that algorithms’ tracking technologies provide greater convenience for the firms to monitor each other’s pricing behaviors and punish deviations from price coordination. However, monitoring rival prices only makes sense if the firms face contested demand. With market overlap, there is a tension between the pro-competitive benefit and tacit collusion concern. The U.S. antitrust law’s “consumer welfare standard” doctrine dictates that antitrust law is only violated if the conduct’s anti-consumer effect outweighs its proconsumer effect.19 Although overt collusion is illegal, tacit collusion is evaluated based on its impact on consumer welfare. When market characteristics make collusion difficult to sustain, such as low discount factor, high product differentiation, or high cross-group externalities, regulators should avoid blanket outlawing of algorithms as the net effect may be pro-competitive. The legal implications of strategic algorithmic price discrimination depend on legal insti19. “Pricing Algorithms: The Antitrust Implications — Advisories,” Arnold & Porter. 42 tutions and different doctrinal focuses. The EU antitrust regulatory framework, in particular, does not view unilateral improvements in consumer welfare as a compelling justification for collusion.20 While recommendation and tracking technologies improve consumer welfare, they also raise privacy concerns that regulatory authorities are aware of. Some consumers who are skeptical of tracking may turn off Cookies, clear browsing history, or prefer shopping in person, which renders the algorithmic pro-consumer effect almost negligible in the model. In such cases, the authorities may have stronger grounds for corporate scrutiny as the reduction in search cost comes at the expense of personal privacy. Possible Extensions My model builds upon three key sets of assumptions. The first set of assumptions concerns my particular characterization of pricing algorithms, focusing on recommendation, search sequence tracking, and rival price monitoring. The second set of assumptions involves consumers behaving as expected price-takers, which is supported by some behavioral studies. The third set of assumptions involve abstracting away the prospect of collusion and other coordination among firms, as the model is one-shot. I consider possible extensions and relaxations of each assumption. Additional Algorithmic Characterizations Apart from the investment decision, algorithms are static in my model. The characterization is innocuous in a one-shot game. But in a repeated game framework, it may be desirable to model algorithms as evolving, motivated by the observation that algorithms can get more sophisticated with continual use. This suggests an even stronger incentive for firms to adopt algorithms due to the cumulative advantage they may enjoy. Firms that invest in algorithms earlier than their rivals may gain a “first-mover advantage,” as their algorithms may improve inference precision by collecting more data compared to algorithms created later. As a result, 20. “Sector inquiry into e-commerce.” 43 the algorithmic overlap expansion may become more pronounced over time. Alternatively, regulatory authorities in some economies have restricted some of the features considered in my thesis. For example, regulators in Australia have preemptively limited algorithms from actively collecting certain information about consumers, including demographic characterizations that could result in algorithmic discrimination on race and gender.21 Similarly, Malaysian regulators are considering outlawing the tracking of consumers’ browsing history, which could make it difficult for the second-searched firm to undercut its rival’s first price offering precisely.22 A valuable avenue for future research could be to develop a version of my model with a subset of the considered algorithmic effects and examine how the distinction affects my pro-competitive results. Sophisticated Consumers The model assumes that consumers form their price expectations exogenously and invariant of their location on the Hotelling line. The expected price for a consumer depends solely on their value of consuming the good, and not on their position on the demand line or σi . However, consumers may form more sophisticated price expectations. They may be fully rational economic agents who consider both firms’ strategies to develop an optimal strategy for themselves. For instance, a fully rational consumer may intentionally click on multiple websites before making a purchase to take advantage of heavier discounts offered to multiple searchers. Thus, how consumers position themselves in the algorithmic game can affect their consumer welfare. However, empirical surveys reviewed earlier suggest that such full rationality may be unrealistic. Alternatively, consumer sophistication could be framed as a partition of the consumer group into attentive and inattentive learners. In a one-shot game, consumer attention is 21. “AI, Machine Learning & Big Data Laws and Regulations — Australia — GLI,” GLI - Global Legal Insights - International legal business solutions. 22. “Antitrust and Competition Laws in Malaysia,” Global Compliance News,. 44 captured in the relative search costs they need to pay to access a retailer’s product. In a repeated game, an attentive consumer may update their belief about a firm’s price offering by observing their previous interactions with the firm. This memory becomes important when a consumer “guesses” the pattern of algorithmic pricing and becomes increasingly skeptical about the pricing of the recommended products. In this case, price discrimination becomes more severe, as inattentive consumers may turn into more attentive consumers over time. Therefore, the firm needs to devise a strategy that not only pays the second-searchers to switch but also compensates the first-searchers to stay. Collusion An obvious direction for future research is to extend the current model to a repeated game framework that allows for possible collusion. Firms could renew their commitment to collusion and their investments in algorithms in each period, resulting in repeated investment and pricing strategy subgames. To ensure that collusion is incentive-compatible, the firms could re-negotiate the surplus transfer required for both to stay in the collusive scheme. If both firms have algorithms, monitoring deviation is not costly, which would provide the firms with greater incentive to remain in the collusive game. However, if one firm has an algorithm and the other does not, one-way monitoring can potentially destabilize the firm with the algorithm, as its deviation cannot be easily detected, and thus it would be difficult to enforce punishment for deviation. Moreover, firms’ temptation to deviate from the collusive scheme may increase by possible strategic algorithmic price discrimination. This temptation could be especially strong if the gains from such price discrimination by poaching most consumers in the market are greater than the expected punishment from the colluding partner(s). Future research could delve deeper into how a possible strategic algorithmic price discrimination may affect incentive compatibility of tacit collusion, as well as the ways in which the terms of collusion might, in turn, impact algorithm investments. Following these re- 45 search topics, it is crucial to show how collusion could potentially undermine the benefits that algorithmic pricing brings to consumers. A more comprehensive understanding of these issues can inform policymakers and firms alike in designing effective strategies to regulate algorithmic pricing and prevent anti-competitive behavior. 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