Discussion Paper

No. 2015-54 | July 24, 2015
On Merger Profitability and the Intensity of Rivalry


This paper considers a general symmetric quantity-setting oligopoly where the "coefficient of cooperation" defined by Cyert and DeGroot (An Analysis of Cooperation and Learning in a Duopoly Context, 1973) is interpreted as the parameter indicating severity of competition. It is obtained that horizontal mergers are more likely to be profitable in a more competitive market structure. Consequently, the results by Salant, Switzer and Reynolds (The Effects of an Exogenous Change in Industry Structure on Cournot-Nash Equilibrium, 1983) about merger profitability are sensitive to the assumption of pre-merger Cournot competition.

JEL Classification:

L13, L40, L41


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Cite As

Marc Escrihuela-Villar (2015). On Merger Profitability and the Intensity of Rivalry. Economics Discussion Papers, No 2015-54, Kiel Institute for the World Economy. http://www.economics-ejournal.org/economics/discussionpapers/2015-54

Comments and Questions

Anonymous - Invited Reader Comment
September 03, 2015 - 11:27

As mentioned in footnote 3 on p. 3, the main result (Proposition 1) has a similarity to that in the related paper discussing strategic delegation (Ziss, 2001). It would be better to discuss the relation between the model in this paper and the related papers.
If you change the ...[more]

... criteria on the incentives of firms to merge in equation (2) to other one (e.g., relative profit, which is the objective of each firm), how does the main result change?
I guess that merger incentives would be related to the steepness of each firm’s reaction function, in other words, the degree of strategic substitutability. If the reaction function of a firm is quite gentle, in other words, if the quantity supplied by a firm is not sensitive to the total quantities supplied by the other firms, the free rider effect of a horizontal merger is weak. In this paper, as the value of λ increases, the reaction function of a firm becomes gentler. This means that an increase in λ weakens the free rider effect, which
implies that the incentives of firms to merge become stronger as shown in Proposition 1. We have already known that merger incentives are stronger when strategic variables are strategic complements (e.g., price competition) than when those are strategic substitutes. Therefore, around the discussion right after Proposition 2 on page 6, it would be useful to briefly mention the relation between the steepness of each firm’s reaction function and the merger incentives.

Marc Escrihuela-Villar - Reply to Reader Comment
September 08, 2015 - 15:04

Thank you very much for your comments. As I mention in the paper, there are several results in the literature on managerial compensation that show that delegation increases merger incentives. In fact these results are related to the one presented here in the sense that, through delegation and similar to ...[more]

... an increase in market competition, pre-merger output is also expanded. In the present note thus an alternative explanation to the existence of a larger set of profitable mergers is provided, which is the existence of pre-merger collusive agreements also in absence of delegation.
Regarding the change in the criteria of the incentives to merge, this is an interesting point that deserves surely future attention. In fact, some papers have already addressed the reversed question by considering for instance the effect of partial cross ownership on firm’s capacity to tacitly collude (for example Gilo, Moshe and Spiegel in the Rand Journal of Economics, 2006). It is generally obtained that cross ownership helps collusion. It seems also plausible to expect that, in the same line and at least to some extent, the previous degree of competition would increase incentives to partially acquire competitors. However, as I mentioned before, this is probably something that deserves future research.
Finally, with respect to the steepness of firms’ reaction function, I especially appreciate this comment and I completely agree with the reader. From Davidson and Deneckere (1985) we know that, under price competition, mergers of any size are beneficial if reaction functions are upward sloping. Therefore, as the reader has pointed out, the present papers establishes a result that goes somewhat in the same line since as λ increases, the reaction function of a firm becomes gentler, roughly speaking, “less decreasing”. Consequently, this reference and the subsequent discussion could help understand and consolidate the intuition of the main result of the present note.

Anonymous - Referee Report 1
September 07, 2015 - 14:38

This paper considers an n‐firm homogeneous product oligopoly model in which the author analyzes the effect of pre‐merger competitive intensity on merger profitability. The way of model the intensity of competition follows some previous works as the author mentions in the introduction. The main results show that the incentive to ...[more]

... merge is increasing in the intensity of competition. Although this is a theoretical work, the references in the paper about empirical evidence indicating that the pre‐merger degree of competition is related to merger incentives add a significant value to this short but interesting contribution. In my opinion, this work shed some light on the relation between two concepts apparently not clearly linked.

Regarding to the analysis, I think that is suitable and correct.

Anonymous - Invited Reader Comment
September 16, 2015 - 08:59

see attached file

Marc Escrihuela-Villar - Reply to Reader Comment
September 18, 2015 - 10:55

Thank you very much for your kind comments. Regarding your first criticism, in this model I basically use a parameter that measures the degree of competition in order to analyze the effect of the pre-merger degree of competition on firms’ merger incentives. To that extent, I use the coefficient of ...[more]

... cooperation approach that has already been extensively used. Admittedly, I have perhaps not properly justified the use of this approach since I considered that their acceptance as a way to parameterise competition was widespread. In this sense, assuming that each firm cares about its own profit plus a weighted average of the profits of the other firms can be observed in, among many others, Symeonidis (2000) and Symeonidis (2008) in the JEMS or Matsumura, Matsushima and Cato (2013) in Economic modelling. Symeonidis (2000) for instance states that a payoff function based on relative performance is justified by reference to some implicit dynamic model of collusion, a reduced-form representation of which being the quantity competition subgame of the present model. The point is that since any individually rational and feasible payoff vector can be sustained as equilibrium of an infinitely repeated game if the players are sufficiently patient, Symeonidis argues that “Alternatively, one can assume that firms always achieve the highest level of collusion that is sustainable given a number of parameters taken as exogenous at the price competition stage; under this interpretation, a fall in the l (a less collusive outcome) might correspond to a lower critical discount factor in an infinitely repeated game.”
Also Kockesen et al.(2000) in the JET studies a model where a subset of players care about their payoffs relative to others and identifies sufficient conditions under which members of this group have a strategic advantage and earn strictly higher material payoffs than do players who seek to maximize their material payoffs.
This formulation has also received attention in the behavioural economics literature like Fehr and Schmidt (1999) in the QJE where people decisions are also driven by fairness considerations based on evidence suggesting that cooperation motives are crucial. In the same line, Charness and Rabin (2002) also in the QJE test in several experimental games that subjects are concerned with reciprocity. Additionally, Vega-Redondo (1997) in Econometrica shows that this relative performance approach is evolutionarily stable.
Regarding the empirical support of this approach, to the best of my knowledge, it is often used in contexts where ownership and management are separated and where by linking management compensation to firm performance, shareholders motivate the manager to exert effort. For instance, Joh (1999) in the Review of Economics and Statistics and using data on Japanese management compensation shows that shareholders in an oligopoly strategically use industry performance information in incentive contracts.
Regarding your second criticism, I really appreciate the value that you give to my paper in the BEJTE but even though it is obviously related to the present paper, I consider that their scope is fairly different. In the former, the equivalence between the coefficient of cooperation and the conjectural variations approaches is analysed while here I basically consider the validity of the merger paradox in more competitive markets. Probably, in the former paper, the use of the coefficient of cooperation approach is better justified which leads us to the previous lines of the present response.
Concerning your last point, in my opinion the present model proves useful to use the coefficient cooperation as a direct “metric” to measure competition as long as conceptually the present model can be directly linked, for instance, to a model where firms' strategy set is a quantity in the interval between perfect competition and full collusion. Then, my point is; why should we consider that horizontal mergers necessarily take place in an environment where the degree of competition is the one from the Cournot assumption? Antitrust authorities are most surely in charge of assessing mergers also in markets where the degree of competition differs from the one close to the standard Cournot allocation. Alternatively, my results could be an explanation to the merger paradox in the sense that if (perhaps expectedly unprofitable) mergers take place is because the per-merger degree of competition was larger than what one believed. On the other hand, the results of the present note might also explain why (in absence of cost synergies) mergers rarely occur in collusive markets. It is important to note that the degree of competition is not endogenous here and I do not pretend to model a situation where firms choose between merging and colluding.
Regarding the minor remarks, the explanation on the first point is much related to what I mentioned above about the contribution of Symmeonidis (2000) where a payoff function based on relative performance can be directly linked to a dynamic model of collusion where the level of collusion directly depends on the value of the discount factor. Indeed, some papers have already parameterised the degree of collusion using the discount factor. As far as I know, the first to do it was Verboven (1997) in the JEBO. As I mentioned above, I do not pretend neither to make endogenous the degree of collusion nor to measure the effect of the coefficient of cooperation on the collusion sustainability cut-off. To some extent, since the discount factor also measures competition, it seems to me a sort of redundancy to analyse the effect of a way to measure the degree of competition on another way to parameterise competition. It is still easy to show that, as the reader correctly anticipated, a lower weight assigned to rivals’ profits increases the interval region in which implicit collaboration can be supported and firms could be, consequently, less willing to merge. Thus, your intuition was completely correct.
Finally, footnote 5 just tries to explain that if l is above zero, it turns out to be the case that you do not (positively) care about your rivals (as you might expect in a collusive market) but on the contrary, your rivals’ profits give you disutility (as you could expect in a market where the parties fiercely compete against each other). In my opinion, this approach makes sense if objective functions are based on relative performance. In this way, the whole range of possible allocations from perfect competition to full collusion can be obtained.

Anonymous - Invited Reader Comment
September 25, 2015 - 09:32

see attached file

Marc Escrihuela-Villar - Reply to Reader Comment
September 28, 2015 - 12:32

Dear reader,
Thank you very much for your comments. The well-known merger paradox stated by Salant et al. (1983), as the reader correctly pointed out, depends on the fact that non-merging firms react to the merger by expanding their production since their reaction functions have a negative slope. The main ...[more]

... intuition of the present paper thus, is that the magnitude of this reaction depends on the degree of competition in such a way that when the market becomes more competitive, the reaction of non-merging firms is "less aggressive". This can be, for instance, easily shown in the linear demand function model by checking that the absolute value of the slope of the reaction function of firms decreases with λ.
Summarizing, my point here is why should we consider merger profitability in a market with the particular competition intensity given by the Cournot conjecture? To that extent, I use one way to parameterize the intensity of competition that has been extensively used in the literature and that allows us to obtain a direct metric for competition. In other words, the use of the 'coefficient of cooperation' is just an instrument to consider whether firms' pre-merger rivalry encourages mergers.

Anonymous - Referee Report 2
October 12, 2015 - 08:57

The paper proposes a quantity-setting oligopoly model where the intensity of competition is modeled according to a ‘coefficient of cooperation,’ which leads to firms taking into account not only their own profit but also a weighted average of the other firms’ profits present in the market. This way of ...[more]

... modeling competition encompasses —depending on the weight given to other firms’ profits— several intensities of competition such as Cournot, perfect collusion and perfect competition. It is shown that in this setting a horizontal merger is more profitable when the market is more competitive, thereby contradicting the ‘merger paradox’ of Salant et al. (1983).

The study is interesting, as it proposes a nice concept to measure competition. Furthermore, while there are other merger models that contradict the famous paper by Salant et al., the idea that more cooperative industries (collusive industries) are less interesting for mergers is appealing.

The paper can be improved though. First and foremost, Kwoka (1989) reached the same conclusion as the current study: mergers are more profitable in more competitive environments. Admittedly, Kwoka (1989) uses a conjectural variations model, which has a different interpretation than this paper’s model. However, the author has recently published another paper (Escrihuela, 2015) where he shows that the ‘coefficient of cooperation’ is in fact equivalent to a conjectural variations model. The paper by Kwoka, therefore, needs to be discussed and compared to the current paper.

An obvious way to distinguish this work from Kwoka is to focus much more on the foundations and interpretation of the coefficient of cooperation. For example, under cross ownership structures a firm may in fact care to some extend about the profit of its rivals. Also the management remuneration being dependent on relative performance is an interesting avenue to explore more.

Furthermore, the empirical evidence on the substitutability between cartels and mergers is quite interesting from a policy point of view, but the evidence and policy implications are not well explained. For example, how can one as policy maker know that an industry is less collusive if cartels are illegal in all important jurisdictions in the world? This needs a more thoughtful reasoning.


Escrihuela-Villar Marc. "A Note on the Equivalence of the Conjectural Variations Solution and the Coefficient of Cooperation," The B.E. Journal of Theoretical Economics, De Gruyter, 15.2 (2015): 473-480.

Kwoka, John E. "The private profitability of horizontal mergers with non-Cournot and maverick behavior." International Journal of Industrial Organization 7.3 (1989): 403-411.

Salant, Stephen W., Sheldon Switzer, and Robert J. Reynolds. "Losses from horizontal merger: the effects of an exogenous change in industry structure on Cournot-Nash equilibrium." The Quarterly Journal of Economics (1983): 185-199.

Marc Escrihuela-Villar - Rey to Referee Report
October 13, 2015 - 17:23

Dear Referee,
Thank you very much for your insightful comments. I also appreciate the reference of the paper from Kwoka (1989). In the present version of my paper, I also acknowledge that in some previous papers it has been obtained that market concentration is increasing in the expected competitive intensity. ...[more]

... For instance, in a closely related paper to Kwoka (1989), Rodrigues (2001) (also in the IJIO) uses numerical simulations with the Conjectural Variations’ approach to confirm the aforementioned relationship.
As the referee opportunely points out, using Conjectural Variations and the Coefficient of Cooperation leads to equivalent closed-form solutions. However, the rationale behind in order to model the degree of competition in the market is fairly different. In my opinion thus, using a wide range of demand functions (unlike Kwoka (1989) and Rodrigues (2001)), the present paper proves the relationship between the degree of competition and firms’ incentives to merge using an approach to the degree of competition that has been often preferred to the Conjectural Variations approach. Admittedly, further explanations to justify the use of the Coefficient of Cooperation could help better understand the paper. For instance, the coefficient of cooperation is also in line with the behavioural economics literature, as well as with experimental games that test that subjects are concerned with reciprocity (some relevant references could be for instance Fehr and Schmidt (1999) and Charness and Rabin (2002) respectively, both in the QJE) or Vega-Redondo (1997) in Econometrica showing that the relative performance approach is evolutionarily stable.
Finally, and regarding the empirical evidence of the results, obviously this paper treats the problem from a theoretical viewpoint but is also motivated by some empirical support as long as merger incentives might be very well related to the pre-merger degree of competition. This could be surely better explained. In this sense, I also appreciate the suggestion to include some references dealing with the most relevant methods used in the empirical literature in order to test the degree of competition since perhaps, in absence of cost synergies, a current market power test might be related to the potential coordinated effects associated to the merger.

Anonymous - Co-editor's Decision Letter
October 22, 2015 - 07:54

see attached file