Werden and Froeb (1998) use Bertrand simulations to assess the role of entry in merger cases. By raising prices, an anticompetitive merger increases what an entrant would earn and creates an opportunity for entry. But whether this opportunity leads to entry or not depends on, among other things, the magnitude of the price increase and potential entrant’s cost. For a large number of randomly generated markets, they find even a large merger creates prospects that are conceivably too small to induce entry. But if entry were to occur, it would render the merger unprofitable for the merging parties, assuming no efficiencies.
Werden and Froeb (1998) solely rely on merger simulation models (rather than analytical methods) to reach the above conclusions. The authors explain the reason why they use simulations is that “[a]nalytical methods are of little use with this model because products are differentiated and because predictions vary with demand parameters and market shares.” However, by drawing on the recent developments in the literature, Caradonna, Miller and Sheu (2022) extend the simulation-based findings of Werden and Froeb analytically to a broader class of demand functions. Specifically, they use the aggregative games framework of Nocke and Schutz (2018) under a differentiated Bertrand model. The oligopoly games are complex and multifaceted as each firm’s action depends on the actions of all other competitors. Under certain conditions, the aggregative framework reduces the degree of complexity significantly to a much simpler oligopoly problem in two dimensions: namely, each player’s payoff depends on its own action and an aggregate of the actions of all other players combined. It is this reformulation that enables the authors to obtain the new analytical results presented in the paper. They use this framework to assess the conditions under which entry sufficient to restore pre-merger consumer surplus renders the merger unprofitable or when entry induced by a profitable merger accompanied by efficiencies can restore (or increase) consumer surplus under alternative demand specifications.
The authors start with demand systems that are characterized by fairly restrictive substitution patterns (i.e., Independence of Irrelevant Alternatives (IIA)). IIA implies the diversion ratio (which measures the percentage of unit sales lost by a product when its price rises that are captured by a competing product) is proportional to market share. This means the merging parties and the entrant are neither particularly close nor particularly distant competitors as the closeness of competition between them depends merely on their market shares under proportionality. Here the indirect utility that a consumer receives from a product depends on the quality and price of the product. Under this scenario, the authors prove analytically that there is no subgame perfect equilibrium (SPE). Any merger that does not yield efficiencies is unprofitable if it induces entry sufficient to preserve pre-merger consumer surplus. Consequently, mergers occur in equilibrium only if barriers restrain entry. It is worth noting that these results are consistent with Werden and Froeb’s (1998) conclusion that “rational incumbents would merge only if they believed that their merger would not induce entry, or if they believed that their merger would generate dramatic efficiency gains that would offset the adverse profit effects of entry.”
The authors then examine whether the above results extend to nested demand models that allow for more flexible substitution patterns. Products that are “closer” substitutes for each other than IIA (or proportionality) would suggest are placed together in the same “nest” and products that are more “distant” substitutes are placed into a different nest. Thus, nesting allows for deviation away from the IIA property for substitution patterns between products that are in two different nests. However, IIA still continues to hold for within nest substitution. Specifically, a nesting parameter depicts the preferences for products in the same versus other nests. Larger nesting parameter values correspond to more substitution between products within nests and less substitution between products across nests.
First, they consider a case where the products of the merging parties and the entrant are in the same nest. Consistent with results obtained in the non-nested models, authors analytically show that no SPE exists in which a merger occurs and consumer surplus does not decrease as a consequence of merger-induced entry. In other words, when merging parties and the entrant are in the same nest, entry that restores pre-merger consumer surplus renders the merger unprofitable.
Second, they consider a case of nested demands that do not limit the merging parties’ and entrant’s products to the same nest or different nests. They find analogous analytical results as before: profitable mergers are incompatible with merger-induced entry sufficient to restore consumer surplus if the nesting parameter is in the neighborhood of the value for which the nested demand reduces to its non-nested counterpart. The intuition is that, as long as there is sufficient substitution between products of the merging parties and the entrant (either because the merging parties and the entrant are in the same nest or in different nests with a nesting parameter that is not too large, meaning that the products of the entrant and the merging parties are not too different), no SPE exists in which a merger occurs and consumer surplus does not decrease as a consequence.
Third, the authors undertake a numerical simulation exercise to assess the extent of within-nest versus inter-nest substitution needed for a merger-induced entry to preserve the pre-merger consumer surplus. This exercise assumes that the merging parties’ products are in one nest and the entrant’s products are in the other nest. Since the equilibrium depends on the “firm type” that summarizes each firm’s product quality and marginal cost, they calibrate the “incumbent firm type” using the incumbent shares and a range of nesting parameters that allows for alternative degrees of substitution between the incumbent and entrant products. The “incumbent firm type” based on market shares fully captures both quality and marginal cost in these demand models. Then they calibrate the “entrant firm type” relative to the “incumbent firm type” such that it allows for the entrant type to vary relative to the incumbent type. If the ratio of “entrant firm type” to the “incumbent firm type” is greater than 1 (i.e., when the share of the entrant would be larger than that of the incumbent), then the entrant’s “quality” is better than incumbent’s, and vice versa. Thus, the simulation exercise accounts for variations in the relative “quality” of the entrant vis-à-vis the incumbent for a range of nesting parameters that allows for incumbents and entrants to be either closer or more distant competitors. The authors then simulate a merger between two incumbents for a given “entrant firm type”.
Based on this setup, they identify the overlapping combination of Entrant Type Ratio and nesting parameter for which the entry induced by a profitable merger also eliminates consumer surplus loss in equilibrium. These results suggest for an SPE in which the merger occurs, the entrants must be substantially differentiated from the merging parties for an entry induced by a profitable merger to preserve pre-merger consumer surplus when the merging parties’ products are in one nest and the entrant’s products are in the other nest.
As an additional robustness check, the authors use a random coefficients logit (RCL) demand to assess whether an entry induced by a profitable merger is sufficient to restore consumer surplus requires an entrant with products that are distant substitutes to those of the merging firms. RCL models allow for more flexible patterns of substitution as compared to flat or nested versions of MNL or CES demand functions. For example, the RCL model does not limit the cross-price elasticities between any two products to depend on just market shares. Instead, it allows for substitution patterns to vary with observable characteristics of products—as one would reasonably expect. However, the aggregative framework does not apply to RCL, and therefore, it cannot be used to derive analytical results. As a result, the authors rely on a numerical analysis analogous to the one discussed above. The random coefficient model confirms their initial findings based on a less flexible demand models, i.e., for a merger-induced entry following a profitable merger to restore the pre-merger consumer surplus requires an entrant with products that are substantially differentiated from those of the merging parties.
Up to this point, the authors have shown a merger-induced entry sufficient to restore pre-merger consumer surplus renders the merger unprofitable in equilibrium characterized by many standard settings of the oligopoly Bertrand model. They have also shown for a merger-induced entry following a profitable merger to restore the pre-merger consumer surplus requires an entrant with products that are substantially differentiated from the merging parties. Next, they consider what impact merger-related efficiencies (i.e., marginal cost reductions and/or product quality improvements) would have on the effect of a merger-induced entry on consumer surplus and merger profitability. They define an entrant that leaves consumer surplus unchanged following a merger with no efficiencies as a “compensating entrant.” It is worth noting while the compensating entrant restores pre-merger consumer surplus, it does not eliminate the merging firm’s price increases. Some of the consumer-surplus restoration of entry relate to an increase in product variety rather than lower prices. This implies if a merger without efficiencies induced entry by a “high-type” entrant as compared to a “compensating entrant,” then consumer surplus will increase post-merger. An entrant is considered to be a “high-type” as compared to a compensating entrant if it has lower marginal costs, a broader product portfolio, higher product quality or some combination of these three type factors. Conversely, with a “low-type” entrant, consumer surplus will fall.
Elimination of a merging firm’s price increases all together would require a large-scale entry by a “high-type” entrant sufficient to enable the entrant to capture a market share possibly larger than those of all incumbents combined. However, the analysis based on IIA and nested IIA demand presented above suggests entry by such high-type entrant is unlikely to occur in equilibrium. That analysis demonstrated that a merger-induced entry alone may not always be sufficient to restore pre-merger consumer surplus in equilibrium. However, the authors show there exists a combination of efficiency and merger-induced entry that results in a profitable merger that also increases consumer surplus, even though neither entry induced by a profitable merger nor efficiency can eliminate consumer surplus loss on its own. This suggests it may be more appropriate to analyze efficiencies and entry jointly as there is little reason to consider merger-induced entry alone as a justification for an otherwise anticompetitive merger in most circumstances.
To illustrate how entry in the real-world settings can be assessed using these models, the authors apply the empirical framework they developed in the paper (including the notion of compensating, high-type and low-type entrants) to analyze the possibility and the effect of merger-induced entry following the T-Mobile/Sprint merger. At the time, the satellite video provider DISH was considered to be a potential cellular entrant, as it had already acquired significant portfolio of spectrum licenses in prior Federal Communications Commission (FCC) auctions and that status as a potential entrant is the focus of the simulation. The authors calibrate the model based on publicly available data and information on market shares, prices, markup and market elasticity under the assumption of merger-induced entry by DISH. Simulating the T-Mobile/Sprint merger with merger-induced entry by DISH, the authors find the consumer surplus would increase due to product variety that DISH introduces. However, there is no SPE that coincides with merger-induced entry by DISH. This is primarily driven by DISH type, which is too high, as it is calibrated relative to that of one of the merging parties (i.e., Sprint) based on the Court’s determination that DISH is well positioned to become a fourth player in the market. This, in turn, bounds the efficiencies necessary to produce a merger-induced entry sufficient to restore the pre-merger consumer surplus. Specifically, with small efficiencies, a merger would induce entry by DISH, but it would make the merger unprofitable. With large efficiencies, the merger would be profitable with DISH entry, but it would reduce the profitability of its entry. Thus, in neither case does merger and merger-induced entry ensue in equilibrium. That DISH has not entered the market two years after the merger closed is consistent with the analysis presented in this paper: the merger is profitable, and entry is not. However, as the authors acknowledge, the simulation model used here is more stylized in that (among other simplifications) it does not incorporate the divestiture of the Boost brand to DISH as required by the FCC because the publicly available data were insufficient to calibrate the “type” associated with Boost. More retrospective analyses of mergers with entry using the framework developed in this paper will indeed be very helpful.
This paper contributes to the existing literature on countervailing factors, such as entry and efficiencies, that can overcome the adverse effects of an anticompetitive merger (e.g., Werden (1996) and Werden and Froeb (1998)). The authors draw on the aggregative games framework to derive analytical results that were until now not obtainable. Specifically, they show that any merger that does not yield efficiencies is unprofitable if it induces entry sufficient to preserve pre-merger consumer surplus. As a result, mergers occur in equilibrium only if barriers restrain entry, highlighting the importance of assessing the presence (or absence) of entry barriers in a merger analysis, as stressed in the merger guidelines. These findings are largely consistent with those of Werden and Froeb (1998), but extend their simulation-based findings analytically to a broader class of demand functions. Werden’s (1996) influential CMCR expression is widely used by antitrust practitioners as it does not require assumptions about the underlying demand functional form. However, in instances where merger-related efficiencies alone are not sufficient to overcome the anticompetitive effects of a merger, the authors show that a profitable merger can nonetheless increase consumer surplus if it generates both efficiencies and merger-induced entry even if neither is sufficient in isolation. Therefore, they conclude “as a matter of economic theory, there may be little reason, outside of exceptional cases, to consider merger-induced entry as a standalone justification for an otherwise anticompetitive merger. . . . A more nuanced role for entry in merger review may nonetheless be appropriate for cases in which merger profitability derives in part from efficiencies, such as fixed cost savings, marginal cost savings, or quality improvements.” As the authors conclude, in these cases, entry and efficiencies should be considered jointly not separately.
