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The antitrust enforcement Agencies' 2020 Vertical Merger Guidelines introduce a nontechnical application of bargaining theory into the assessment of competitive effects from vertical acquisitions. The economics of such bargaining is complex and can produce skepticism among judges, who might regard its mathematics as overly technical, its game theory as excessively theoretical or speculative, or its assumptions as unrealistic.

However, we have been there before. The introduction of concentration indexes, particularly the HHI, in the Merger Guidelines was initially met with skepticism but gradually they were accepted as judges became more comfortable with them. The same thing very largely happened again when unilateral effects theories of mergers were introduced in the 1990s. The bargaining theory that drives so much of vertical merger analysis today has much in common with the theory of unilateral effects. In any event, the value of a particular model depends not on its verisimilitude but rather on its testability.

The theory that relates a concentration index to the risk of competitive harm from horizontal mergers involves as much conjecture as does the bargaining theory that the Nash model for vertical mergers contemplates. The concentration thresholds in the Horizontal Merger Guidelines do no more than capture a rough generalization about a large number of collusive or oligopolistic strategies, many of which are not consistent with each other. What they share in common is belief in a link between the number of firms in a market and their relative sizes, and the likelihood and extent of higher prices.

Double marginalization as a vertical merger defense occurs when two bargaining firms each have market power but are unable to coordinate their output. The result is that each takes a markup without considering the other, and aggregate markups are too high. Both firms as well as their purchasers would be better off if they could coordinate better.

The debate over the elimination of double marginalization bundles two themes that Ronald Coase developed in his two most well-known articles, The Nature of the Firm and The Problem of Social Cost. The first argued that the boundaries of a firm are determined by the firm’s continuous search to procure inputs in the most cost effective way. The second argued that two traders in a well-functioning market will achieve the joint-maximizing solution. This dual relationship is too often ignored.

The debate over elimination of double marginalization reflects more than a little cognitive dissonance. Anti-interventionists rely heavily on Coasean arguments that unless high transaction costs get in the way firms will bargain to joint maximizing results. By contrast, regulation creates inalienability rules that undermine these results. If that is true, then double marginalization will rarely provide a defense to a vertical merger. The law of vertical mergers deals largely with firms that transact with one another routinely, in legally enforceable buy-sell relationships that occur in well established markets.

By contrast, the actors who appear in The Problem of Social Cost do not bargain with each other regularly. They certainly can and do sue one another, but the transaction costs of litigating are extremely high in comparison with transacting in more conventional markets. Those who populate Social Cost are pairs like the doctor and confectioner who share a party wall, the homeowner and the nearby airport, the cattle rancher and neighboring farmer, the spark-emitting chimney and downwind neighbor, or the hotel whose addition blocks light to sunbathers at an adjacent hotel. In all of these cases the parties went to court rather than solve their problem by bargaining. By comparison, joint maximizing contracts in conventional agreements between buyers and seller should be far easier to attain.