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Sequential Mergers and Antitrust Authority’s Decisions in Stackelberg Markets

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Abstract

This paper analyses a sequential merger formation game in a setting where: (i) firms compete à la Stackelberg; (ii) mergers may give rise to endogenous efficiency gains; and (iii) every merger has to be submitted for approval to the Antitrust Authority (AA). Two different types of AA are studied: first, we assume a myopic AA, which accepts or rejects a given merger without considering that this merger may be followed by other mergers; and, second, a forward looking AA, which anticipates the final industry structure a merger will give rise to, if approved. We conclude that these two types of AA adopt similar decisions whenever a merger would not trigger the exit of outsider firms. Their decisions are, however, shown to be very different when evaluating exit-inducing merger proposals.

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Notes

  1. The analysis of merger-induced efficiencies was introduced into the US Merger Guidelines in 1997 (Section 4) and into the European Merger Guidelines in 2004 (European Commission Horizontal Merger Guidelines, 2004/03, Article 7).

  2. Other papers also assumed sequential game but with exogenous mergers, such as Nilssen and Søgard (1998) and Salvo (2006).

  3. The inclusion of an efficiency defence argument could bring an asymmetric information problem with respect to the merger’s efficiency gains between the AA and the merging firms. Some papers consider the issue of asymmetric information about merger-specific efficiencies, such as, Gonzalez (2004), Medvedev (2004), Lagerlöf and Heidhues (2005), Cosnita and Tropeano (2009), however, this analysis is far beyond the scope of this paper.

  4. By assuming that the AA evaluates mergers according to a consumer surplus standard this does not mean that this is always better than the total welfare standard. However, as Lyons (2002) argued, the consumer surplus standard is applied in most antitrust jurisdictions. Other papers also study how the AA should apply the consumer surplus standard when challenging a merger, such as Besanko and Spulber (1993), Neven and Röller (2005), Vasconcelos (2010), Nocke and Whinston (2010), Jovanovic and Wey (2012), among others.

  5. See Daughety (1990), Feltovich (2001), Huck et al. (2001), Escrihuela-Villar and Faulí-Oller (2008), Heywood and McGinty (2007, 2008) and Brito and Catalão-Lopes (2011) on the profitability of mergers involving Stackelberg firms operating in a context without merger induced synergies.

  6. Other strands in the literature also tried to solve the Salant et al. (1983)’s merger paradox by adopting Bertrand competition with product differentiation (Deneckere and Davidson 1985), Cournot competition with convex costs (Perry and Porter 1985) or by changing the properties of the demand function (Faulí-Oller 2002).

  7. For details, see Escrihuela-Villar and Faulí-Oller (2008) and the references cited therein.

  8. We assumed that in the market there are only four firms because this allow us to have all the possible merger scenarios and to compare our results with the ones in Motta and Vasconcelos (2005)’s paper.

  9. 9Motta and Vasconcelos (2005)’s cost function is given by \(C(q_{i},k_{i})=\frac {\alpha }{k_{i}}q_{i}+ 4k_{i}f \) which is similar to ours, however we assume that the total capital available in the industry is \(K={\sum }_{i = 1}^{4}k_{i}= 4\), while the authors normalized it to \(K={\sum }_{i = 1}^{4}k_{i}= 1\).

  10. This is the same as in Motta and Vasconcelos (2005).

  11. In Section 5, we discuss the results obtained for other merger cases.

  12. Although the assumption that firms have zero administrative costs from submitting a merger is not very realistic, assuming that these costs are zero does not matter much, since the equilibrium outcome would not change if we assumed positive filing costs.

  13. If we consider that the AA adopts a total Social Welfare (SW) standard, we find that the merger decisions obtained for the myopic AA under SW standard are similar to those obtained under the CS standard. In particular, in both the “exit” and the “no exit” regions, the myopic AA blocks the merger between two leaders, for low levels of the efficiency gains. However, by adopting the SW standard, the myopic AA allows the merger of two leaders for a larger range of the efficiency parameter. Additionally, and contrary to what happened in the benchmark model, the forward looking AA, adopting a SW standard, always approves both mergers in the region where outsider follower firms are constrained to exit the market in case a subsequent merger does not occur. Under a CS standard and in the region of \(\frac {1}{22}<\alpha <\frac { 5}{74}\) and \(\widetilde {f}_{2L}<f<\overline {f}\), the AA blocked the merger between the two leaders because it decreased the CS. However, in the same region and under the SW standard, the AA allows the merger because the induced increase in producers’ surplus more than compensates for the decrease of CS and, therefore, the net effect is an increase in the SW.

  14. For a detailed justification on the assumption that a merger involving two follower firms may give rise to a leader see the justification (based on experimental research and on economic theory) in Brito and Catalão-Lopes (2011) and the references cited therein.

  15. More details on the calculations can be provided upon request to the authors.

  16. If \(\alpha \geq \frac {1}{6}\), the two outsider leader firms are constrained to exit the market since qL = 0. Also if \(f>\widetilde {f}_{2F}\) leader firms are not able to cover the fixed costs and make positive profits. Note that when \(\widetilde {f}_{2F}=\overline {f}\), \(\alpha =\frac {23-3\sqrt {2}}{146} \approx 0.12848\).

  17. If \(\alpha \geq \frac {1}{8}\), the two outsider firms are constrained to exit the market since qL = qF = 0. Also if \(f>\widetilde {f}_{LF}\) outsider leader and follower firms are not able to cover the fixed costs and make positive profits. Note that when \(\widetilde {f}_{LF}=\overline {f}\), \(\alpha =\frac {1}{16} \equiv 0.0625\).

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Acknowledgements

Financial Support from Fundação para a Ciência e Tecnologia (SFRH/BD/70000/2010) is gratefully acknowleged.

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Authors and Affiliations

  1. Católica Porto Business School and CEGE, Universidade Católica Portuguesa, Rua Diogo Botelho, 1327, 4169-005, Porto, Portugal

    Mariana Cunha

  2. CEF.UP and Faculdade de Economia, Universidade do Porto, Rua Dr. Roberto Frias, 4200-464, Porto, Portugal

    Hélder Vasconcelos

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  1. Mariana Cunha
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  2. Hélder Vasconcelos
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Correspondence to Mariana Cunha.

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Cunha, M., Vasconcelos, H. Sequential Mergers and Antitrust Authority’s Decisions in Stackelberg Markets. J Ind Compet Trade 18, 373–394 (2018). https://doi.org/10.1007/s10842-017-0268-x

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