Comments and Questions

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 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.