Revising the U.S. Vertical Merger Guidelines: Policy Issues and an Interim Guide for Practitioners

Mergers and acquisitions are a major component of antitrust law and practice. The U.S. antitrust agencies spend a majority of their time on merger enforcement. The focus of most merger review at the agencies involves horizontal mergers, that is, mergers among firms that compete at the same level of production or distribution. Vertical mergers combine firms at different levels of production or distribution. In the simplest case, a vertical merger joins together a firm that produces an input (and competes in an input market) with a firm that uses that input to produce output (and competes in an output market). Over the years, the agencies have issued Merger Guidelines that outline the type of analysis carried out by the agencies and the agencies’ enforcement intentions in light of state of the law. These Guidelines are used by agency staff in evaluating mergers, as well as by outside counsel and the courts. Guidelines for vertical mergers were issued in 1968 and revised in 1984. However, the Vertical Merger Guidelines have not been revised since 1984. Those Guidelines are now woefully out of date. They do not reflect current economic thinking about vertical mergers. Nor do they reflect current agency practice. Nor do they reflect the analytic approach taken in the 2010 Horizontal Merger Guidelines. As a result, practitioners and firms lack the benefits of up-to-date guidance from the U.S. enforcement agencies

Bounds on the Automata Size for Presburger Arithmetic

Automata provide a decision procedure for Presburger arithmetic. However, until now only crude lower and upper bounds were known on the sizes of the automata produced by this approach. In this paper, we prove an upper bound on the the number of states of the minimal deterministic automaton for a Presburger arithmetic formula. This bound depends on the length of the formula and the quantifiers occurring in the formula. The upper bound is established by comparing the automata for Presburger arithmetic formulas with the formulas produced by a quantifier elimination method. We also show that our bound is tight, even for nondeterministic automata. Moreover, we provide optimal automata constructions for linear equations and inequations

Some modifications to the SNIP journal impact indicator

The SNIP (source normalized impact per paper) indicator is an indicator of the citation impact of scientific journals. The indicator, introduced by Henk Moed in 2010, is included in Elsevier's Scopus database. The SNIP indicator uses a source normalized approach to correct for differences in citation practices between scientific fields. The strength of this approach is that it does not require a field classification system in which the boundaries of fields are explicitly defined. In this paper, a number of modifications that will be made to the SNIP indicator are explained, and the advantages of the resulting revised SNIP indicator are pointed out. It is argued that the original SNIP indicator has some counterintuitive properties, and it is shown mathematically that the revised SNIP indicator does not have these properties. Empirically, the differences between the original SNIP indicator and the revised one turn out to be relatively small, although some systematic differences can be observed. Relations with other source normalized indicators proposed in the literature are discussed as well

Geometric representations for minimalist grammars

We reformulate minimalist grammars as partial functions on term algebras for strings and trees. Using filler/role bindings and tensor product representations, we construct homomorphisms for these data structures into geometric vector spaces. We prove that the structure-building functions as well as simple processors for minimalist languages can be realized by piecewise linear operators in representation space. We also propose harmony, i.e. the distance of an intermediate processing step from the final well-formed state in representation space, as a measure of processing complexity. Finally, we illustrate our findings by means of two particular arithmetic and fractal representations.Comment: 43 pages, 4 figure