The Agencies make clear that the risk of coordination from a merger does not depend on whether the coordination is explicit or tacit. The 2023 Merger Guidelines state in Guideline 3 that “[c]oordination among rivals lessens competition whether it occurs explicitly—through collusive agreements between competitors not to compete or to compete less—or tacitly, through observation and response to rivals.” Furthermore, the Agencies state that preventing tacit collusion is especially important because it is out of the reach of the Sherman Act. The Agencies’ concern with tacit collusion arising from a merger is summarized succinctly in the 2023 Merger Guidelines:
Tacit coordination can lessen competition even when it does not rise to the level of an agreement and would not itself violate the law. For example, in a concentrated market a firm may forego or soften an aggressive competitive action because it anticipates rivals responding in kind. This harmful behavior is more common the more concentrated markets become, as it is easier to predict the reactions of rivals when there are fewer of them.
Both Guideline 2 and Guideline 3 contain a list of factors the Agencies consider in evaluating whether the merger is likely to substantially lessen competition. The list of factors considered when evaluating unilateral effects contains numerous potential quantitative analyses that may be employed. For example, the 2023 Merger Guidelines discusses in Guideline 2 utilizing event studies—prior mergers, exit, or entry—in the context of unilateral effects, in addition to measuring customer substitution. By contrast, the list of factors the Agencies consider when evaluating Guideline 3 are much more qualitative in nature. For example, the Agencies consider whether they were any prior or actual attempts to coordinate, whether the merger would eliminate a “maverick” firm, the degree of transparency in the market, and other structural factors that inhibit or enhance the potential for coordination.
The price leadership model developed by Mansley et al. (2023) proposes to help fill the gap in quantitative analysis of coordinated effects by giving antitrust authorities and other researchers a methodology for quantifying the potential coordinated effects of a merger.
What are Price Leadership Models?
Price leadership models are a type of structural equilibrium model used by economists in both academic research and competition law investigations to predict the impact of market structure changes on competition. These models are especially valuable for assessing potential coordinated effects of mergers, specifically how a merger might facilitate tacit collusion, where firms coordinate their strategies without explicit agreements.
Structural Equilibrium Models
To understand price leadership models fully, it is crucial to first understand structural equilibrium models in general. These models analyze how competing firms interact within a market equilibrium, based on specific assumptions about their strategic behavior. There are two main forms of competitive behavior typically assumed in these models:
- Price Competition (known as “Bertrand Competition”): In this type of structural equilibrium model, firms independently set their prices to maximize own profits while treating their competitors’ prices as given. The model predicts equilibrium prices based on these pricing decisions, with the total output determined by market demand, reflecting the quantities consumers choose to purchase at those price levels.
- Quantity Competition (known as “Cournot Competition”): Here, firms independently decide their production levels to maximize profits, taking their competitors’ output levels as given. The model forecasts equilibrium quantities based on these production decisions, with the market price determined by the total supply relative to market demand.
In practice, structural equilibrium models operate as follows.
- Gathering Market Data: Economists start by analyzing observable market data to calibrate the model. Direct data on costs and demand parameters are often unavailable, so economists usually rely on prices and quantities, which are more easily obtainable.
- Inferring Costs and Demand: Economists use assumptions about firms’ strategic behavior to estimate the underlying costs and demand parameters that would explain the observed market prices or quantities. This involves reverse-engineering the model to determine the costs and demand parameters consistent with the observed outcome. The observed outcome is assumed to represent an equilibrium.
- Simulating Structural Changes: Economists then introduce changes into the model, such as a merger between two firms, to predict the new market equilibrium. By applying the previously estimated costs and demand parameters, they forecast how prices and production levels would adjust in response to the merger.
Traditional structural equilibrium models generally assume that firms act independently, making them suitable for analyzing unilateral effects, but less effective for understanding coordinated effects. Price leadership models, on the other hand, are a subcategory of structural equilibrium models that address this limitation by focusing on a specific type of coordinated interaction known as “follow-the-leader.” Price leadership models are designed to analyze how firms may implicitly coordinate their pricing strategies without direct communication or formal agreements.
How Price Leadership Models Work
In a price leadership model, one firm, known as the “leader,” sets a price above the competitive level, establishing a benchmark for other firms in the market, called “followers.” The followers then adjust their prices to match the leader’s pricing decision hoping that other firms will follow suit, rather than undercutting to maximize individual profits. This pricing strategy by the leader thus influences the pricing behavior of the follower firms, leading to tacit collusion, where firms indirectly coordinate their pricing strategies without an explicit agreement.
The core principle of price leadership models is that, under typical market conditions, the leader can generally induce followers to raise prices slightly above the competitive level, even in markets with a significant number of firms. As long as the price increase is modest, followers have little incentive to deviate from the leader’s price, as a small price cut is unlikely to capture significant market share. However, as the number of firms decreases, the market becomes more concentrated and coordinating larger price increases becomes easier to sustain. With fewer firms, the benefits of collusion are distributed among a smaller group, enhancing the incentives to follow the leader.
For instance, in a market with ten firms where one firm is the leader, a minor price increase by the leader (e.g. 1%) is likely to be followed by the nine other firms, as undercutting the leader would not significantly raise their market share. However, a 20% price increase by the leader might lead followers to deviate and keep their prices low to capture business from the leader. In contrast, in a market with only three firms, a 20% price increase by the leader may be more sustainable, as the increased market profits from collusion are shared among only three firms, making the incentive to follow the leader stronger.
Thus, price leadership models allow economists to assess not only the risk of collusion resulting from a merger, but also the magnitude of collusion. By focusing on a form of collusion where competitors follow a market leader, these models can predict price dynamics in the market equilibrium both before and after a merger. They might show that if, pre-merger, the leader can maintain a market-wide price increase of 5% above the competitive level, then post-merger, it might be feasible to sustain a 15% or 20% coordinated price increase through a follow-the-leader strategy. This information is crucial for authorities to evaluate mergers in markets where there is a risk of this type of collusion.
Price Leadership Models in the Academic Literature
A notable application of price leadership models is the 2021 study by Miller, Sheu and Weinberg on the US beer industry. This research introduces one of the first methodologies for assessing the coordinated effects of mergers in markets characterized by price leadership. By analyzing market data on prices and quantities to estimate marginal costs and collusion markups, the study shows that price leadership can significantly enhance profits. Specifically, it finds that price leadership led to profit increases of 17% in 2006-2007 and 22% in 2010-2011, with the greater gains in the latter period attributed largely to market consolidation in 2008. The study also confirms that mergers can raise prices through coordinated effects—even when efficiency gains might otherwise offset unilateral effects.
Building on this foundational work, the same authors, with co-author Mansley, published another paper in 2023, with more practical guidance, that simplifies their earlier framework for use in merger reviews. This recent article simplifies their earlier model by focusing on a single market and using a less data intensive “logit demand” function. The authors demonstrate how their streamlined approach can be calibrated using data typically available to antitrust authorities during merger investigations, such as market shares, diversion ratios and markups. Their paper also provides guidance on when and how to apply their revised modeling approach.
Brief overview of the Price Leadership Model in Mansley et al
(2023). In the model proposed by Mansley et al. (2023), the market consists of firms selling differentiated products, with a subset of firms, termed the “coalition,” coordinating their pricing decisions. Firms in the coalition raise their prices by a fixed increment (a so-called “super markup”), which is announced by the coalition leader. The identity of coalition firms is known to both market participants and researchers. Firms outside the coalition set their prices independently. Products are produced with constant marginal costs, and there are no capacity constraints.
The model is dynamic in the sense that firms interact repeatedly over time. In each period, the leader announces the super markup, which influences firm beliefs and guides pricing decisions. Then, all firms, including the leader, set prices simultaneously, and profits are determined by these prices. If price leadership is successful, every period coalition firms apply the super markup as long as there are no deviations in past periods. Fringe firms set their prices independently, considering the super markup applied by coalition firms. Deviations from the super markup by a coalition firm result in a punishment, where all coalition firms revert to independent pricing forever.
When setting the super markup, the leader aims to maximize their own profit while ensuring that all coalition firms have a sufficient incentive to follow. This incentive, similar to traditional collusion models, arises when the long-term benefits of maintaining a super markup outweigh the short-term gains from undercutting prices to capture market share. The authors assert that “under mild regularity conditions, there is always some positive super markup that increases the profit of the leader” and provides followers with an incentive to comply.
Using a numerical example, the authors demonstrate that firms have an incentive to follow the market leader when the super markup is relatively small. As the super markup increases, there comes a point where the incentives to follow the leader decline and eventually turn negative. At this stage, firms prefer to cut prices to capture market share rather than adhere to the super markup. Coalition firms, which are larger and benefit more from higher profits under collusion, have a stronger incentive to follow the leader compared to smaller firms, which are more inclined to undercut prices to attract business from the larger players.
An important element of the Mansley et al practical framework is its method for calibrating model parameters using readily available market data typically collected during merger investigations. This approach is advantageous in antitrust analysis due to the accessibility of such data. Once calibrated, the model allows competition authorities to simulate the potential impact of a merger and predict post-merger price effects. In contrast, the 2021 study by Miller, Sheu, and Weinberg used more complex regression techniques to estimate the model’s structural parameters. While these regression methods are standard in academic literature, they are less practical for authorities constrained by limited resources and time during merger investigations.
Potential Benefits of Price Leadership Models as a Tool for Merger Review
The main advantage of the price leadership model proposed by Mansley et al. is that it provides economists with a practical method for quantifying the coordinated effects of a merger. Traditionally, while unilateral effects are frequently measured during a merger investigation, coordinated effects are often assessed qualitatively and are rarely quantified, likely due to a lack of simple, established tools—like the UPP and GUPPI tests for for unilateral effects—that can be routinely applied by authorities. As a result, even though economists sometimes assess the risk of coordinated effects by analyzing market characteristics that facilitate collusion—such as product homogeneity, market transparency and cost symmetry—they typically do so without actually quantifying the merger’s impact on prices or output.
Price leadership models thus offer a valuable tool for quantifying the coordinated effects of a merger ex-ante. By making assumptions about strategic interactions between firms, these models simulate how firms would coordinate post-merger, enabling authorities to assess potential impact on prices, output and other market variables. In the absence of structural models, quantification of coordinated effects would need to rely on comparisons with similar industries or geographic markets where analogous mergers have occurred. While this benchmarking approach can be useful, finding relevant benchmarks in newer, concentrated markets with historical data on similar mergers can be challenging.
Additionally, the price leadership model proposed by Mansley et al. allows authorities to make predictions using data typically available during a merger investigation. Metrics such as market shares, diversion ratios and markups—already collected for assessing unilateral effects of mergers—can also be used to quantify coordinated effects. Their model is therefore simpler and less data-intensive than more complex regression-based methods, which can be challenging and time consuming to implement. Consequently, price leadership models are more practical and feasible for real world ex-ante merger assessments.
Price leadership models ultimately enable authorities to address a crucial question: absent efficiencies, what is the likely impact of a specific merger on prices, given the potential for tacit collusion post-merger? The answer to this question can vary significantly from an analysis focusing solely on unilateral effects. In relatively unconcentrated markets, mergers generally lead to modest unilateral price effects, but accounting for coordinated effects might suggest a larger price increase due to the potential for collusion. Conversely, in highly concentrated markets involving major competitors, a unilateral effects analysis might predict a substantial price increase. However, when coordinated effects are considered, the expected price increase might be smaller, especially if the merging parties were already coordinating prices near the monopoly level before the merger.
Mansley et al. provide two examples where assessing coordinated effects may reveal a significantly higher risk of price increases compared to an analysis based solely on unilateral effects. First, consider the acquisition of a high-cost or low-quality firm. While such a firm may not exert sufficient competitive pressure to prevent unilateral price increases by competitors, it can still act as a constraint on collusion. Specifically, the price leader may need to announce a lower markup to ensure that the cost-inefficient or low-quality firm has an economic incentive to follow. Post-merger, this constraint is removed, allowing the leader to announce a higher markup. Similarly, the acquisition of a small fringe firm by a coalition firm can enhance the leader’s ability to sustain higher markups after the merger. The fringe firm’s presence may previously have limited the leader’s ability to implement significant price increases. With its removal, the leader can more effectively coordinate and maintain higher prices.
When a merger raises competitive concerns, price leadership models can help determine the magnitude of efficiencies needed to offset both unilateral and coordinated effects. The benefits of efficiencies to consumers can vary depending on whether coordinated effects are considered alongside unilateral effects. For example, if two efficient firms merge, a reduction in marginal costs might lead to a lower coordinated price post-merger. However, if a high-cost firm is acquired and its costs are substantially reduced to align with other competitors, the merger could enable a higher markup. This is because the merger removes a high-cost firm that previously constrained collusion, allowing for more effective coordination among the remaining competitors post-merger. In such scenarios, efficiencies might not only fail to benefit consumers but could also enhance coordinated effects post-merger, potentially leading to higher prices.
Finally, price leadership models can assist in determining appropriate remedies when the coordinated effects of a merger are not mitigated, or are even worsened, by potential cost efficiencies. Again, the analysis of coordinated effects may lead to different conclusions about remedies compared to an analysis focused solely on unilateral effects. For instance, in a merger between two efficient firms, divesting assets to a less efficient or low-quality firm that previously constrained collusion might be counterproductive. Such a divestiture could enhance the efficiency of the divested firm, increasing its incentives to follow the leader. Conversely, divesting to a new firm entering the market could introduce a new constraint on collusion, thereby restoring competition. These insights demonstrate that price leadership models can help competition authorities not only decide whether to clear or block a merger, but also design effective remedies to address the risk of collusion.
Challenges of Price Leadership Models
Despite their potential to effectively predict the coordinated effects of mergers, price leadership models have a fundamental limitation: they rely on the assumption that competitors will follow a leader. If this assumption does not reflect actual competitive behavior, the model’s results could be inaccurate. This limitation is common to all structural equilibrium models, which are based on specific assumptions about competitive behavior in equilibrium. When these assumptions do not align with reality, the model’s predictions lose validity. For example, if an economist uses a price leadership model that assumes firms set a substantial markup above marginal cost based on following a leader, but in reality, firms are engaged in price competition, the model may significantly underestimate the true marginal cost derived from observed prices, leading to inaccurate predictions.
This problem persists even in industries prone to collusion, but where the specific collusive behavior differs from price leadership. As recognized by Mansley et al., predicting coordinated effects is challenging due to the existence of multiple collusive equilibria. In industries where collusion is viable, firms can coordinate prices in various ways and at different pricing levels. Although price leadership assumes that a market leader maximizes profits while ensuring that competitors have an incentive to follow, other collusive strategies are possible. For example, firms might coordinate asymmetric prices to maximize joint profits—though this scenario is more typical of formal cartels than tacit collusion. Alternatively, firms could set a suboptimal price that increases profits compared to competitive pricing but remains low enough to deter entry. If the actual collusive dynamics in the industry diverge significantly from those assumed by the price leadership model, predictions may become less accurate.
Aside from the price leadership assumption, there are other relevant but relatively less consequential assumptions, such as the use of logit or nested logit demand functions. This assumption helps keep the model simple and reduces the amount of data needed for calibration, as logit demand functions offer favorable statistical properties that enhance analytical tractability and simplify estimation procedures. However, logit demand functions impose restrictions, such as limited substitution patterns between alternative products due to the “Independence from Irrelevant Alternatives” (IIA) property. If this does not accurately reflect real-world consumer preferences, it may impact the model’s results. Nonetheless, in their application to the US beer markets, Mansley et al. found that “despite the simplifications we have made to the demand side, we can obtain merger simulation results comparable to those [without a logit demand].”
Another relevant assumption in the price leadership model by Mansley et al. is the need to distinguish between coalition firms and fringe firms, along with the requirement for the economist to clearly identify which firms belong to each group. This distinction is critical because, as noted in their paper, “if one does not observe a marginal cost for a fringe product, calibration can perform poorly, particularly in separately identifying the super markup and consumers’ price sensitivity.” While smaller fringe firms not involved in price-fixing conspiracies are common in real-world markets, accurately determining which firms are part of the coalition versus the fringe can be challenging. This uncertainty may affect the model’s accuracy.
A more general problem with price leadership models, as with other structural equilibrium models, is their lack of a rigorous method for testing the realism and reasonableness of their assumptions. Without a robust way to validate these assumptions, assessing whether the model’s predictions are reliable for a specific market is challenging. Using a price leadership methodology blindly could lead to predictions about coordinated effects without a clear means of verifying their likelihood in practice. Therefore, before applying these models to ex-ante merger investigations, it is crucial to test them under real-world conditions to determine when they provide accurate predictions, as discussed next.
The Way Forward for Price Leadership Models
Given the potential of price leadership models to estimate the coordinated effects of mergers, but considering their reliance on relatively strong assumptions about firm behavior in equilibrium, it is crucial to combine these models with empirical methods that test the validity of those assumptions. The most critical assumption to test is whether collusion is likely to occur in the market and, specifically, if it could take the form of follow-the-leader behavior. Fortunately, methods to test these assumptions, known as “screens” for collusion, are available in the literature. Some of these methods are frequently used in mergers and antitrust investigations, while others are emerging and gaining importance.
One such test is the analysis of structural factors for collusion (also known as “structural screens”), which helps determine whether collusion is likely in a given market. Economists commonly use this analysis to assess collusion risk based on characteristics such as homogeneous products, barriers to entry, market transparency, cost symmetry, inelastic and growing demand, and market concentration. If a market exhibits many of these characteristics, it is likely prone to collusion, and the use of a price leadership model to measure the magnitude of coordinated effects post-merger could more easily be justified.
Behavioral screens can complement structural screens by verifying whether follow-the-leader behavior is present. One such method involves assessing “Granger causality,” which examines whether changes in the prices of firms are statistically caused by changes in the prices of other firms. In markets with price leadership, we expect to see a market leader consistently causing price changes in competitors, while the reverse should not be true. Conversely, if behavioral screens reveal mutual dependence among competitors, where all firms influence each other’s prices, this would be inconsistent with follow-the-leader behavior.
Structural and behavioral screens for collusion are therefore valuable tools that can complement and enhance the application of price leadership models. They enable economists to assess whether a market has pre-existing structural characteristics and behaviors consistent with price-leadership collusion. If these conditions are met, the assumption of price leadership is validated, and the model can then be used to predict whether the merger will enable the leader to coordinate prices closer to monopoly levels. In other words, combining collusion screens with price leadership models allows economists first to test for the existence of collusion resulting from price leadership and then measure the potential increase in coordination due to the merger.
Even if price leadership accurately reflects competitive behavior in a market, this alone does not guarantee that the predictions of a price leadership model are always reliable. As noted earlier, price leadership models, like other structural equilibrium models, depend on various assumptions that can influence the results, including assumptions related to logit demand and the identification of firms not involved in the coalition. Ideally, all model assumptions should be tested to evaluate their relevance to the market under analysis. However, this approach would complicate the analysis, making it time-consuming and potentially counterproductive to the model’s purpose of providing a straightforward tool for authorities and economists during real-world merger investigations.
A more practical approach than testing every assumption of price leadership models is to assess their performance in predicting actual effects from past mergers. A common challenge in merger investigations is the difficulty of evaluating post-merger effects until the merger takes place. If a merger is blocked based on predictions, its true effect remains unknown. By conducting ex-post assessments of completed mergers, we can apply the price leadership model to historical cases and compare its predictions with actual outcomes. This will enable us to evaluate the model’s effectiveness in estimating coordinated effects by comparing its price forecasts with real-world data. Ultimately, this approach will help determine whether the model’s simplified assumptions offer a reliable approximation for generating accurate results, even if those assumptions are not entirely realistic.
In conclusion, price leadership models are a valuable tool for understanding the coordinated effects of mergers, offering economists a structured framework to assess potential price increases resulting from market consolidation. While challenges exist—such as reliance on assumptions about competitive behavior—these can be addressed by integrating price leadership models with other methodologies available in the literature, such as cartel screens. Additionally, empirical testing, particularly through ex-post assessments of past mergers, might help determine and even improve the predictive accuracy and reliability of these models. Applying price leadership models to historical mergers not only validates their underlying assumptions but also builds greater confidence in their application by competition authorities, potentially allowing them to use these models as part of a systematic analysis toolkit for merger investigations.
