^{Abstract}
In merger enforcement, entry is considered to be a factor that potentially can mitigate otherwise anticompetitive effects of a merger. The current framework for entry analysis evaluates whether potential entrants are likely to have the incentives and ability to enter the industry under the conditions of elevated profitability that are created by an anticompetitive merger. Missing from entry analysis is the notion that incumbent firms may proactively deter entry and how such incumbent incentives may change as a result of a merger. By modeling entry as the outcome of a game between incumbents and potential entrants, we show that a merger can reduce the likelihood of entry even at elevated profit levels by increasing incumbent incentives to invest in entry deterrence. The paper has two policy implications for merger enforcement: First, a merger that is benign by traditional measures may nonetheless have the effect of reducing future entry—entry that would have made the market more competitive relative to status quo. Second, evidence of recent historical entry—which is an important criterion that is used to assess the likelihood of postmerger entry—may be of less evidentiary value than is considered under the current merger enforcement policy.
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Notes
2010 U.S Horizontal Merger Guidelines issued by the Department of Justice and the Federal Trade Commission (“Guidelines”), §9 (https://www.justice.gov/sites/default/files/atr/legacy/2010/08/19/hmg2010.pdf).
These include whether there has been successful prior entry into the relevant market, whether the necessary investments in production assets are not prohibitive, whether technology is freely available to potential entrants, whether a sufficient share of customers can freely choose to buy from a new entrant, etc.
In recent years, the U.S. antitrust agencies have approved a number of mergers—especially in the technology sector—based on evidence of historical entry. See, e.g., the FTC’s closing statements for Google’s acquisition of AdMob (https://www.ftc.gov/sites/default/files/documents/closing_letters/googleinc./admobinc/100521googleadmobstmt.pdf) or the DOJ’s closing statement for Expedia’s acquisition of Orbitz (https://www.justice.gov/opa/pr/justicedepartmentwillnotchallengeexpediasacquisitionorbitz).
The other factor that is considered to mitigate potentially anticompetitive incentives that are due to a merger is efficiencies. Efficiencies are credited when they are of the form that are likely to be passed through to consumers in the form of lower prices. To be credited, efficiencies must also be mergerspecific: not achievable through means that are less anticompetitive relative to a merger. See §10 in Guidelines.
A nonexhaustive list of theoretical treatment of entry deterrence includes Gilbert and Newberry (1982), Gilbert and Vives (1986), Bernheim (1984), and Waldman (1987). In empirical work, among others, Berry and Waldfogel (2001), Ellison and Ellison (2011), Ciliberto and Zhang (2016), and Sweeting et al. (2019) find evidence of entry deterrence efforts by incumbent firms that use a variety of deterrence mechanisms in a variety of industries.
Specifically with regards to regulatory lobbying, Stigler (1971) argued that industry incumbents influence the political process and are able to acquire regulations that reduce entry and increase their profits: “regulation is acquired by the industry and is designed and operated primarily for its benefit … Every industry or occupation that has enough political power to utilize the state will seek to control entry.” Djankov et al. (2002) present data on the regulation of entry in 85 countries and find that “legal entry is extremely cumbersome, timeconsuming, and expensive in most countries in the world.” Djankov et al. argue that the evidence supports the public choice theory over alternative theories of regulation. See also Gutiérrez and Philippon (2018; 2019).
In so far as entry deterrence by incumbents is sought to be achieved by “lobbying” an industry regulator or the legislature, such lobbying may be protected by the NoerrPennington doctrine. In two landmark cases in 1961 and 1965, the U.S. Supreme Court decided that under the First Amendment, businesses who petitioned the government for anticompetitive actions are immune from liability under the antitrust statutes. See, e.g., Paul Gowder (2009). This may potentially limit the ability of a U.S. antitrust agency to oppose a merger purely because it might increase the incentives of the industry incumbents to impede entry by lobbying for the creation of rules or laws that increase entry barriers. At the same time, lobbying is just one of many ways to create entry barriers.
Since the realization of entry is a binary event, and the amount of investment that is needed to prevent entry in our model is uncertain, this article is also related to the provision of discrete public goods with uncertain cost. See, e.g., Nitzan and Romano (1990).
For an overview of issues raised by the merger, see Rogerson (2019).
See Net Neutrality, Public Knowledge, available at https://www.publicknowledge.org/issues/netneutrality.
Comcast and Time Warner ultimately abandoned the proposed merger in the face of serious concerns expressed by the DOJ and the FCC. The DOJ’s Press Release stated that collectively, the two firms would have controlled broadband internet access of more than 30 million subscribers—something that would have made the merged entity “an unavoidable gatekeeper for Internetbased services that rely on a broadband connection to reach consumers”. (See https://www.justice.gov/opa/pr/comcastcorporationabandonsproposedacquisitiontimewarnercableafterjusticedepartment).
In February 2015, the FCC voted to approve the Open Internet Order, which enacted the strongest net neutrality rules in history. The decision faced multiple legal challenges from the wireless and cable industries. Subsequently in December 2017, after the change in administration, the Republican majority of the FCC voted to repeal the Open Internet Order. The repeal in turn faced legal challenges from several states in the U.S. Court of Appeals. The Court of Appeals allowed the repeal to stand but barred the FCC from prohibiting states or local authorities from enforcing net neutrality. See https://en.wikipedia.org/wiki/Net_neutrality_in_the_United_States.
One way in which incumbents can overcome the freeriding problem is by having industry associations coordinate their entry deterrence efforts. For example, the industry association can apportion the optimal entry deterrence investment across incumbent firms, say, in proportion to their private benefits from denying entry. The anticompetitive goal of such coordination is likely to invite prosecution by the antitrust authorities. Moreover, in certain situations, coordination by industry associations may not fully overcome the freeriding problem. As the ComcastTime Warner example illustrates, preventing net neutrality rules from coming into effect would have benefitted both fixed broadband providers (such as Comcast, Time Warner, Charter, etc.) as well as mobile network service providers such as Verizon, AT&T, and TMobile. The two industries have separate trade associations. While the association of, say, fixed broadband providers can help to overcome freeriding among its members, it likely has little ability to dictate the amount of deterrence investments that are made by mobile network service providers.
The analysis can be easily extended to a situation with more than two incumbents, where each operates as a monopolist in a distinct market. Similarly, as a general matter, the analysis can also be extended to a setting in which the merging firms are not monopolists in their respective markets but face withinmarket competition from other firms. (Withinmarket competition is fully discussed in the more general model introduced in Section 3).
Bernheim (1984) and Gilbert and Vives (1986) consider environments with complete information and show that the freerider problem does not cause incumbents to underinvest in entry deterrence. In contrast, Waldman (1987) shows that if the cost of entry deterrence is uncertain, then, for certain investment technologies, incumbents may underinvest.
A referee has pointed out that it is possible for a wellfunded potential entrant to invest in breaking down entry barriers that are created by incumbents (say, by counterlobbying the industry regulator to permit entry). An example may be the lobbying of city officials by a ridehailing service to let it operate in the city over the objections of incumbent taxicab companies. We note that having to make additional upfront investments to neutralize entry barriers also amounts to reducing the likelihood of entry by requiring that the entrant’s profit upon entry cover those (sunk) barrierbreaking investments.
The concavity condition reflects the assumption of diminishing marginal returns from investing in entry deterrence.
If the value of the firstorder condition when \(\sum_{k}{x}_{k}=0\) is negative, then the optimal investment is 0. Note that given the assumption that \(D^{\prime} > 0\) and \(D^{\prime\prime} \le 0\), the profit function is concave in \({x}_{i}\) such that the secondorder profit maximization condition is satisfied.
An equilibrium exists if the derivative \(D^{\prime}\left( x \right)\) converges to zero or \(D\left(x\right)\) converges to infinity as \(x\) goes to infinity.
If firms are asymmetric, only the firm that has the most to lose from entry—the firm with the largest \({\Delta }_{i}\)—invests, while the other firms fully freeride on that investment. See Waldman (1987).
We assume that the effectiveness of the investment to deter entry is not affected by the merger itself. However, it is possible that the merged firm’s investment is more effective: for example, because the merged firm can eliminate duplicative efforts between the two merging firms. In that case, the merger would reduce the likelihood of entry even more than what the model predicts.
The derivative of \(\frac{{D^{\prime}\left( X \right)}}{{\left( {D\left( X \right)} \right)^{2} }}\) with respect to \(X\) is \(\frac{{D^{\prime\prime}\left( X \right) \times \left( {D\left( X \right)} \right)^{2}  2 \times \left( {D^{\prime}\left( X \right)} \right)^{2} \times D\left( X \right)}}{{\left( {D\left( X \right)} \right)^{4} }}\), which is negative because \(D^{\prime} > 0\) and \(D^{\prime\prime} \le 0\).
If multiple firms have the same amount to lose from entry, there are multiple equilibria with the same level of total investment, and any allocation of the total investment across these firms is an equilibrium.
For the merged firm, \({\Omega }_{post}^{merged}=\left({\pi }_{post}^{1}\left(NE\right)+{\pi }_{post}^{2}\left(NE\right){\pi }_{post}^{1}\left(E\right){\pi }_{post}^{2}(E)\right)\)
We can obtain some intuition for why the sufficient condition holds by rewriting (13) as \(\left({\pi }_{post}^{j}\left(NE\right){\pi }_{pre}^{j}\left(NE\right)\right)>\left({\pi }_{post}^{j}\left(E\right){\pi }_{pre}^{j}\left(E\right)\right)\); in words, the effect of a merger on any firm’s profit must be larger when there are fewer firms to begin with.
“The Agencies consider the actual history of entry into the relevant market and give substantial weight to this evidence.” Guidelines §9.
Guidelines §1.
We experimented with alternative bounds for the distributions that we used to generate the model parameters, which did not change the conclusion.
The STATA codes that implement the Monte Carlo simulations in the appendices are available upon request.
We experimented with alternative bounds for the distributions that we used to generate the model parameters, which did not change the conclusion.
We experimented with alternative bounds for the distributions used to generate the model parameters, which did not change the conclusion.
References
Bernheim, B. D. (1984). Strategic deterrence of sequential entry into an industry. RAND Journal of Economics, 15(1), 1–11.
Berry, S., & Waldfogel, J. (2001). Do mergers increase product variety: Evidence from radio broadcasting. The Quarterly Journal of Economics, 116(3), 1009–1025.
Ciliberto, F., & Zhang, Z. (2016). Multiple equilibria and deterrence in airlines markets. Economic Inquiry, 55(1), 319–338.
Cowgill, B., Pratt A., & Valletti, T. (2021). Political power and market power. arXiv working paper arXiv:2106.13612, Available at Retrieved from July 5, 2021, https://arxiv.org/abs/2106.13612
Djankov, S., La Porta, R., LopezdeSilanes, F., & Shleifer, A. (2002). The regulation of entry. The Quarterly Journal of Economics, 117(1), 1–37.
Ellison, G., & Fisher Ellison, S. (2011). Strategic entry deterrence and the behavior of pharmaceutical incumbents prior to patent expiration. American Economic Journal: Microeconomics, 3(1), 1–36.
Gilbert, R., & Newberry, D. (1982). Preemptive patenting and the persistence of monopoly. American Economic Review, 72(3), 514–526.
Gilbert, R., & Vives, X. (1986). Entry deterrence and the free rider problem. Review of Economic Studies, 53(1), 71–83.
Gowder, P. (2009). The first amendment encyclopedia. The Free Speech Center, Available at https://www.mtsu.edu/firstamendment/article/1122/noerrpenningtondoctrine
Gutiérrez, G. & Philippon, T. (2018). How EU markets became more competitive than US markets: A study of institutional drift. NBER Working Paper no. 24700.
Gutiérrez, G. & Philippon, T. (2019). The failure of free entry. NBER Working Paper no. 26001.
Nitzan, S., & Romano, R. (1990). Private provision of a discrete public good with uncertain cost. Journal of Public Economics, 42(3), 357–370.
Rogerson, W. P. (2019). Economic theories of harm raised by the proposed comcast/TWC transaction. In J. E. Kwoka Jr. & L. J. White (Eds.), The antitrust revolution (7th ed.). Oxford University Press.
Scherer, F. M. (1979). Product variety: An application to the readyto eat cereals industry. Journal of Industrial Economics, 28(2), 113–134.
Schmalensee, R. (1978). Entry deterrence in the readytoeat breakfast cereal industry. Bell Journal of Economics, 9(2), 305–327.
Stigler, G. J. (1971). The theory of economic regulation. Bell Journal of Economics and Management Science, 2(1), 3–21.
Sweeting, A., Roberts, J., & Gedge, C. (2020). A model of dynamic limit pricing with an application to the airline industry. Journal of Political Economy, 128(3), 1148–1193.
Waldman, M. (1987). Noncooperative entry deterrence, uncertainty, and the free rider problem. Review of Economic Studies, 54(2), 301–310.
Acknowledgements
Comments from two referees and the Editor greatly improved the paper. For helpful comments on an earlier version, we also thank (without implicating) Andrew Dick, Keler Marku, Joe Podwol, and Greg Vistnes. Any ideas or opinions expressed in this article are solely those of the authors and do not necessarily represent the views of Charles River Associates or its clients.
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Appendices
Appendix 1
Sufficient Condition in Proposition 2
In this appendix, we show that—both under Cournot competition (with linear demand) and under Bertrand competition (with logit demand)—for every firm \(i\), the loss of profit suffered by incumbent \(i\) due to entry is larger postmerger than premerger:
2.1 Cournot
We assume a Cournot model with \(N\) firms, where: (i) each firm has constant marginal cost \({c}_{i}\); and (ii) demand is linear: \(P=ab\times Q\).
Firm \(i\)’s FOC is:
Summing over the FOC of all firms implies that:
where \(\overline{c }\) is the unweighted average cost across all firms: \(\overline{c }=\frac{\sum_{i}{c}_{i}}{N}\). Therefore:
Furthermore, (15) implies that \(P{c}_{i}=ab\times Q{c}_{i}=b\times {q}_{i}\), so that firm \(i\)’s profit is:
We provide an analytic proof under the assumption that \({c}_{i}=\overline{c }\). We then run Monte Carlo simulations that do not impose this restriction.
If \({c}_{i}=\overline{c }\), then \({\pi }_{i}=\frac{1}{b}\times \frac{{\left(a\overline{c }\right)}^{2}}{{\left(N+1\right)}^{2}}\). The condition \(\left({\pi }_{post}^{i}\left(NE\right){\pi }_{post}^{i}\left(E\right)\right)>\left({\pi }_{pre}^{i}\left(NE\right){\pi }_{pre}^{i}\left(E\right)\right)\) translates to (without loss of generality, we normalize \(b\) and \({\left(a\overline{c }\right)}^{2}\) to 1):
To show this, it is sufficient to show that \(\frac{1}{{\left(X\right)}^{2}}\frac{1}{{\left(X+1\right)}^{2}}\) is decreasing in \(X\), for \(X\ge 2\). The derivative of the previous expression with respect to \(X\) is \(\frac{2}{{\left(X\right)}^{3}}+\frac{2}{{\left(X+1\right)}^{3}}\), which is clearly negative.
Now we allow for firms to have different cost \({c}_{i}\). We construct each Monte Carlo experiment as follows^{Footnote 28}:

1.
Each firm’s cost is drawn from a uniform between 0 and 5.

2.
\(a\) is drawn from a uniform between 5 and 50.

3.
The number of firms is between 2 and 10, drawn from a discrete uniform.

4.
The slope \(b\) is normalized to 1.
We ran 50,000 such Monte Carlo experiments. We used only parameter configurations where all firms have a positive quantity both premerger and postmerger. The Monte Carlo results confirm that a merger always increases each incumbent firm’s loss from entry.^{Footnote 29}
2.2 Bertrand
We consider a model where demand is logit and single product firms are Bertrand competitors. Because this model does not have closedform solution, we confirmed that \(\left({\pi }_{post}^{i}\left(NE\right){\pi }_{post}^{i}\left(E\right)\right)>\left({\pi }_{pre}^{i}\left(NE\right){\pi }_{pre}^{i}\left(E\right)\right)\) by running Monte Carlo experiments as follows:
We assume that the latent utility that consumer \(i\) derives from product \(j\) is: \({U}_{ij}={d}_{j}\alpha \times {p}_{j}+{e}_{ij}\), where \({e}_{ij}\) follow an extreme value distribution. It follows that the demand for product \(j\) is: \({q}_{j}=\frac{\mathrm{exp}({d}_{j}\alpha \times {p}_{j})}{1+\sum_{k}\mathrm{exp}({d}_{j}\alpha \times {p}_{j})}\).
In our baseline simulations, we construct each Monte Carlo experiment as follows:

1.
\({d}_{j}\) is drawn from a uniform between 0 and 2.

2.
\(\alpha \) is drawn from a uniform between 0 and 1.

3.
Each firm’s cost is drawn from a uniform between 0 and 2.

4.
The number of firms is between 2 and 10, drawn from a discrete uniform.
We ran 50,000 such Monte Carlo experiments. For each experiment, we find that^{Footnote 30}:

1.
For nonmerging firms \(\left({\pi }_{post}^{i}\left(NE\right){\pi }_{post}^{i}\left(E\right)\right)>\left({\pi }_{pre}^{i}\left(NE\right){\pi }_{pre}^{i}\left(E\right)\right)\): The loss from entry is larger postmerger than premerger.

2.
This may not hold for each individual merging firm, but it holds for the sum of the merging firms’ profits, which is sufficient for our purposes.
Appendix 2
In this appendix we demonstrate analytically that, in the case of a symmetric Cournot model with linear demand and constant marginal cost, a merger always decreases the likelihood of entry when \(D\left(\sum_{k}{x}_{k}\right)=\sum_{k}{x}_{k}\). We also implement Monte Carlo simulations that indicate that the same holds in the case of Bertrand competition with logit demand.
3.1 Cournot
As was derived in Appendix 1, the equilibrium quantity and profits are \({q}_{i}=\frac{\left(ac\right)}{\left(N+1\right)\times b}, \pi \left(N\right)=\frac{{\left(ac\right)}^{2}}{{\left(N+1\right)}^{2}\times b}\). In what follows, we treat \(N\) as the number of incumbent firms premerger. A merger reduces the number of firms to \(N1\): Given symmetry, the merged firm will remove one of the premerger firms from the market. Entry increases the number of firms by 1.
3.1.1 Premerger
Entry increases the number of firms from \(N\) to \(N+1\). Therefore:
3.1.2 Postmerger
Entry increases the number of firms from \(N1\) to \(N\). Therefore:
3.1.3 Comparison of Entry Probabilities
Assume that \(D\left(\sum_{k}{x}_{k}\right)=\sum_{k}{x}_{k}\). Then, for \(l=pre, post\), Eqs. (8) and (11) imply that:
and the likelihood of entry is.
Therefore;
The ratio, which depends only on \(N\), is always less than 1, as Fig. 2 illustrates. For example, when there are four incumbent firms premerger, the ratio of the probabilities is 88.4%; consequently, if the premerger probability of entry is 40%, then the postmerger probability of entry is 35.4% (40% \(\times \) 88.4%).
3.2 Bertrand
For the Bertrand model, we implement Monte Carlo simulations (which were described in Appendix 1) that indicate that, when \(D\left(\sum_{k}{x}_{k}\right)=\sum_{k}{x}_{k}\), the ratio of probabilities \(\frac{{Prob\_Entry}_{post}}{{Prob\_Entry}_{pre}}\) is always less than 1: The entry probability always decreases.^{Footnote 31}
Figure 3 illustrates the relationship between \(\frac{{Prob\_Entry}_{post}}{{Prob\_Entry}_{pre}}\) and number of incumbent firms. It shows that the negative effect on entry probability is greater when the number of incumbent firms is smaller.
Table 1 illustrates the relationship between \(\frac{{Prob\_Entry}_{post}}{{Prob\_Entry}_{pre}}\) and the share of the smaller of the two merging firms, conditional on the number of premerger incumbents. It shows that the reduction in entry probability is greater when the share of the smaller merging firm is smaller.
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Das Varma, G., De Stefano, M. Entry Deterrence, Concentration, and Merger Policy. Rev Ind Organ 61, 199–222 (2022). https://doi.org/10.1007/s1115102209865y
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DOI: https://doi.org/10.1007/s1115102209865y