When two companies merge, they sometimes achieve efficiencies of scope or of scale, but where they were previously competitors, the merger may reduce competition. If the former effect dominates the latter, the merger may benefit consumers, but if the latter dominates the former, consumers will be harmed, and frequently the net harm to consumers is likely to exceed the net benefit to other parties (e.g. stockholders). Even where this last inequality does not hold, it is frequently within the ambit of regulators only to consider the effect on consumers, and this may be a defensible principle. Regulators may, however, have less knowledge about the likely effects of the merger than industry sources. It would be nice if there were a way to induce industry sources to reveal useful information to the regulators.
Mankiw pointed out a couple years ago that, where a merger is likely to benefit consumers, it will do so by lowering prices and raising quality for consumers, while where it hurts consumers, the opposite will be true. Regardless of how it plays out, competitors of the prospective merger partners will be helped or harmed exactly inversely to the effect on consumers, thus, in this narrow context at least, the anti-business instincts of certain populists are actually well-justified; if competing businesses are lobbying in favor of a merger, Mankiw suggested, block it, while if they lobby against it, approve it. He noted, though, that it is necessary to keep such a policy quiet; if the companies know their lobbying actions have these perverse effects, they will no longer lobby in a way that reveals the relevant information. The policy is not, in this sense, incentive compatible.
On the other hand, what just occurred to me is that one might well be able to, openly and publicly, follow the evolution of the stock prices of competitors that are publicly traded. A potential shareholder in a competitor to the prospective merger partners will wish for the regulator to see a drop in share prices on the announcement of the potential merger when the merger would in fact benefit the company, but he still finds it in his own interest to buy ahead of other potential shareholders; similarly, if he would like regulators to see an increase, he may still wish to sell before others do. If all buyers and sellers in a particular stock could form a cartel, they would jointly find an advantage in acting to confuse the regulator; what they might narrowly view as a "tragedy of the commons" may in fact serve, in this case, to enhance the public good.
While there is a tendency to think of coordination problems as a bad thing, in fact they are frequently quite useful, if usually in combating the effects of other coordination problems (or private information problems). Most of forensic accounting, in fact, involves asking different parties to keep track of essentially redundant information; while a single agent might be able to forge all of its own records in a consistent way, getting all of its business associates to forge their records in the same way is more difficult, such that accountants can subpoena everyone's records and find inconsistency in the combined dataset. Indeed, perhaps the most famous illustration of a coordination problem, with the possible exception of the aforementioned tragedy of the commons, is the prisoner's dilemma, in which a mechanism designer has, according to the usual story, explicitly designed the coordination problem in order to turn the agents against themselves.
In the case of two agents, cooperation is more likely to obtain, especially where they know each other, than it is with multiple, anonymous agents; "incentive compatibility" as it is usually treated in the literature requires only that each agent find it unprofitable to unilaterally deviate from the prospective equilibrium supposing that nobody else does so. In actual practice, it seems likely that this condition is insufficient as long as the sets of agents required to coordinate to block such an outcome are both small and in a variety of senses are known to each other in such a way that they can solve their internal coordination problems — possibly creating what manifests itself as a coordination problem on a larger scale.