Increasingly, retailers have access to better pricing technology, especially in online markets. Using hourly data from five major online retailers, the authors show that retailers set prices at regular intervals that differ across firms. Faster firms appear to use automated pricing rules that are functions of rivals’ prices.

These observations are inconsistent with the standard assumptions about pricing technology used in the empirical literature. Motivated by this, the present paper – available here – considers a model of competition in which firms can differ in pricing frequency, and can choose pricing algorithms rather than prices. Relative to the standard simultaneous price-setting model, pricing technology with these features can increase prices. A simple counterfactual simulation implies that pricing algorithms can lead to meaningful increases in mark-ups, especially for firms with the fastest pricing technology.

Section 2 highlights key features of pricing algorithms used by online retailers.

The authors identify three characteristics of the use of high-frequency price data for over-the-counter allergy medications by the five largest online retailers. The first is heterogeneity in pricing technology. Two firms have within-the-hour (“hourly”) pricing technology, one firm has daily pricing technology, and the remaining two have weekly pricing technology, and update their prices early every Sunday morning. Second, the fastest firms quickly react to price changes by slower rivals, consistent with the use of automated pricing algorithms that monitor rivals’ prices and follow a pre-specified pricing strategy. Third, asymmetric pricing technology is associated with asymmetric prices – and firms with faster pricing technology have persistently lower prices for identical products. Relative to the firm with the fastest pricing technology, the firm with daily pricing technology sells the same products at prices that are 10% higher, whereas the firms with weekly pricing technology sell those products at prices that are approximately 30% higher.

These facts are inconsistent with standard models that assume symmetric price-setting technology. This is an issue, since the literature has focused on the price effects of learning algorithms or prediction algorithms in the context of a standard simultaneous price (or quantity) game. Given this, the authors consider it necessary to develop a model to understand how the use of asymmetric price-setting technology may influence competition and prices.

Section 3 introduces a game in which firms differ in pricing frequency.

The model generates prices that lie between simultaneous (Bertrand) and sequential (Stackelberg) equilibria, and nests both as special cases. When prices are strategic complements, as is typical in empirical models of demand, the faster firms have lower prices and higher profits than the slower firms do. Thus, this model provides a supply-side explanation for the price dispersion observed in the data. Moreover, this model show that, when firms can choose their pricing frequency, each firm has a unilateral profit incentive to choose either more or less frequent pricing than their rivals. Therefore, simultaneous price-setting is not an equilibrium outcome when pricing frequency is endogenous.

  • Section 4 develops a more general model for algorithmic pricing with commitments.

According to the model, algorithms enable firms to differ in their pricing frequency and to commit to a pricing strategy for future price updates. With asymmetric commitment—i.e., when only one firm can condition its algorithm on its rival’s price—the equilibrium closely parallels the equilibrium with asymmetric frequency. If one derives a one shot competitive game where all firms can condition on rivals’ prices, it is found that short-run commitments, in the form of automated pricing, can also generate higher prices. Further, algorithms that depend on rivals’ prices do not generate Bertrand prices in equilibrium.

Intuitively, this may be the result of the owner of superior-technology committing to best respond to whatever price is offered by its rivals, and its investments in frequency or automation making this commitment credible. The rivals take this into account, softening price competition.

Section 5 compares observed prices to a counterfactual equilibrium in which firms have simultaneous price-setting technology.

This counterfactual tries to reflect the fact that empirical literature on price competition and firm mark-ups has almost exclusively assumed that firms play a simultaneous pricing game. The authors introduce a model of demand that allows for flexible substitution patterns among retailers and provides a tractable empirical approach to modelling supply-side competition with algorithms.

Using the observed pricing technology of the retailers as an input, they then fit the model to average prices and market shares in their data. This calibrated model predicts that algorithmic competition increases average prices by 5.2 percent across the five firms. This corresponds to a 9.6 percent increase in profits and a 4.1 percent decrease in consumer surplus.

Section 6 briefly discusses the implications for policy makers.

Online markets were initially expected to usher in “frictionless commerce” and intensify competition among firms. This paper’s results demonstrate how advances in pricing technology can have the opposite effect, generating higher prices and exacerbating price dispersion. By employing high-frequency pricing algorithms, firms can soften competition and increase profits in equilibrium, even if the firms are otherwise identical. The model further suggests that pricing algorithms can have an economically meaningful effect on mark-ups.

Thus, if policymakers are concerned that algorithms will raise prices, their focus must go beyond collusion. Simple pricing algorithms can increase prices in a competitive equilibrium, and may even achieve fully collusive outcomes. To prevent such price increases, policymakers would have to limit the ability of firms to react to rivals’ prices. Enforcement measures along these lines raise conceptual and legal challenges, as they do not fit neatly into existing regulatory and antitrust frameworks.


This paper is a good example of the type of research mentioned in the paper reviewed above. I am not competent to analyse the model, but I found it refreshing that the authors admitted that their model seeks to explain the data they collected– instead of, as usual, arguing that they developed the model in abstract and it just so happened that the data thankfully confirmed the model’s assumptions and conclusions. My only comment is that I would have liked a bit more discussion of the possible policy implications and reactions to these developments, but I suppose that is my job…

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