Ecosystem Competition and the Antitrust Laws

I. Introduction II. Three Examples of Ecosystem Competition ... A. Middleware and Operating Systems ... B. E-Books and Tablets … C. Connected and Automated Vehicles III. How Ecosystem Competition Enhances Consumer Welfare IV. Implications for Antitrust Law and Polic

The singular value expansion for compact and non-compact operators

Given any bounded linear operator T : X → Y between separable Hilbert spaces X and Y , there exists a measure space (M, Α, µ) and isometries V : L2(M) → X, U : L2(M) → Y and a nonnegative, bounded, measurable function σ : M → [0, ∞) such that T = UmσV †, with mσ : L2(M ) → L2(M ) defined by mσ(f ) = σf for all f ∈ L2(M ). The expansion T = UmσV † is called the singular value expansion (SVE) of T . The SVE is a useful tool for analyzing a number of problems such as the computation of the generalized inverse T† of T , understanding the inverse problem Tx = y and, regularizing Tx = y using methods such as Tikhonov regularization. In fact, many standard Tikhonov regularization results can be derived by making use of the SVE. The expansion T = UmσV † can also be compared to the SVE of a compact operator T : X → Y which has the form T = Σ σnun ⊗ vn where the above sum may be finite or infinite depending on the rank of T . The set {σn} is a sequence of positive real numbers that converge to zero if T has infinite rank. Such σn are the singular values of T . The sets {vn} ⊂ X and {un} ⊂ Y are orthonormal sets of vectors that satisfy Tvn = σnun for all n. The vectors vn and un are the right and left singular vectors of T, respectively. If the essential range, denoted Ress(σ), forms a sequence of positive real numbers converging to zero (or is merely a finite set of nonnegative real numbers) and for each nonzero s ∈ Ress(σ), the essential preimage of the singleton set s , denoted σess−1( {s} ), is finite, then the bounded operator T = UmσV † is in fact compact. The converse of this statement is also true. If the operator T is compact, the singular values and vectors of T may be approximated by discretizing the operator and finding the singular value decomposition of a scaled Galerkin matrix. In general, the approximated singular values and vectors converge at the same rate, which is governed by the error (in the operator norm) in approximating T by the discretized operator. However, when the discretization is accomplished by projection (variational approximation), the computed singular values converge at an increased rate; the typical case is that the errors in the singular values are asymptotically equal to the square of the errors in the singular vectors (this statement must be modified if the approximations to the left and right singular vectors converge at different rates). Moreover, in the case of variational approximation, the error in the singular vectors can be compared with the optimal approximation error, with the two being asymptotically equal in the typical case

After Search Neutrality: Drawing a Line between Promotion and Demotion

The Federal Trade Commission\u27s (“FTC” or “the commission”) January 3, 2013 decision to close its longstanding investigation of Google1 brings to a close a flurry of discussion over the possibility that Google could become subject to a “search neutrality” principle in the United States. Although the Commission found against Google on several grounds, it rejected petitions from Google\u27s critics to create a search neutrality principle as a matter of antitrust law. This essay briefly analyzes what remains of U.S. antitrust scrutiny of Internet search bias after the Google settlement. In particular, it suggests that a sensible line can be drawn between promotion of a search engine\u27s own properties and demotion of rival properties. Although distinctions of this kind are inherently slippery, in this case the distinction should serve well enough. As of this writing, the wild card remains the European Commission, which may yet upset the applecart

The Future of Law and Mobility

With the launch of the new Journal of Law and Mobility, the University of Michigan is recognizing the transformative impact of new transportation and mobility technologies, from cars, to trucks, to pedestrians, to drones. The coming transition towards intelligent, automated, and connected mobility systems will transform not only the way people and goods move about, but also the way human safety, privacy, and security are protected, cities are organized, machines and people are connected, and the public and private spheres are defined. Law will be at the center of these transformations, as it always is. There has already been a good deal of thinking about the ways that law must adapt to make connected and automated mobility feasible in areas like tort liability, insurance, federal preemption, and data privacy. But it is also not too early to begin pondering the many implications for law and regulation arising from the technology’s spillover effects as it begins to permeate society. For better or worse, connected and automated mobility will disrupt legal practices and concepts in a variety of ways additional to the obvious “regulation of the car.” Policing practices and Fourth Amendment law, now so heavily centered on routine automobile stops, will of necessity require reconsideration. Notions of ownership of physical property (i.e., an automobile) and data (i.e., accident records) will be challenged by the automated sharing economy. And the economic and regulatory structure of the transportation network will have to be reconsidered as mobility transitions from a largely individualistic model of drivers in their own cars pursuing their own ends within the confines of general rules of the road to a model in which shared and interconnected vehicles make collective decisions to optimize the system’s performance. In these and many other ways, the coming mobility revolution will challenge existing legal concepts and practices with implications far beyond the “cool new gadget of driverless cars.” Despite the great importance of the coming mobility revolution, the case for a field of study in “law and mobility” is not obvious. In this inaugural essay for the Journal of Law and Mobility, I shall endeavor briefly to make that case

Market Power Without Market Definition

Antitrust law has traditionally required proof of market power in most cases and has analyzed market power through a market definition/market share lens. In recent years, this indirect or structural approach to proving market power has come under attack as misguided in practice and intellectually incoherent. If market definition collapses in the courts and antitrust agencies, as it seems poised to do, this will rupture antitrust analysis and create urgent pressures for an alternative approach to proving market power through direct evidence. None of the leading theoretic approaches—such as the Lerner Index or a search for supracompetitive profits—provides a robust solution. Further, one of the core premises in modern antitrust analysis—that the presence of high entry barriers is necessary to market power—is deeply flawed. Counterintuitively, the higher the entry barriers, the less likely it is that (1) the accused firm engaged in anticompetitive conduct and (2) the market would have been more competitive but for the alleged conduct. A robust approach to market power would require a tight nexus between the challenged conduct and a plausible competitive counterfactual. This Article articulates first principles of market power, diagnoses sources of confusion in the current caselaw, and scrutinizes the recognized methods of proving market power without reliance on market definition and market shares

Is More Antitrust the Answer to Wealth Inequality?

Wealth inequality has reemerged as a major political issue and may become one of the defining themes of the 2016 presidential election. Progressives claim a broad set of causes for wealth inequality, from tax loopholes favoring the wealthy to the decline of private sector unionization. Recently, a number of high-profile public intellectuals have begun to finger an additional culprit - lax antitrust enforcement. According to prominent progressives such as Nobel economics laureates Joseph Stiglitz and Paul Krugman, former labor secretary Robert Reich, and Oxford economist Anthony Atkinson, weak enforcement of the antitrust laws has permitted the flourishing of anticompetitive mergers, monopolistic conduct, and other exclusionary and collusive behavior, with the effect of redistributing wealth upward to corporate shareholders and senior executives and away from the less wealthy strata of society. This monopoly regressivity claim is increasingly being repeated in legal and economic scholarship and in the media. The monopoly regressivity claim may have considerable political appeal, but it is vastly overstated. Althought htere are surely some violations of the antitrust laws that exacerbate wealth inequality, the generalization that more antitrust enforcement would lead to a more equitable distribution of wealth misunderstands the actual incidence and effects of antitrust enforcement. Exercises of market power have complex, cross-cutting effects, some of which may be regressive, but many of which may also be progressive or distributively neutral. More antitrust is not the answer to wealth inequality

Antitrust and the Judicial Virtues

Although commentators frequently debate how judges should decide antitrust cases substantively, little attention has been paid to theories of judicial virtue in antitrust decision making. This essay considers four pairings of virtues: (1) striving for substantive purity versus conceding to institutional realism; (2) incrementalism versus generalism; (3) presenting a unified face versus candidly conceding differences among judges on an appellate panel; and (4) adhering strictly to stare decisis versus freely updating precedents to reflect evolving economic learning or conditions. While recognizing the complexities that sometimes pull judges in the opposite direction, this Article gives the nod to institutional realism, incrementalism, candor, and relatively unconstrained updating of precedent

After Search Neutrality: Drawing a Line Between Promotion and Demotion

The Federal Trade Commission\u27s (“FTC” or “the commission”) January 3, 2013 decision to close its longstanding investigation of Google1 brings to a close a flurry of discussion over the possibility that Google could become subject to a “search neutrality” principle in the United States. Although the Commission found against Google on several grounds, it rejected petitions from Google\u27s critics to create a search neutrality principle as a matter of antitrust law. This essay briefly analyzes what remains of U.S. antitrust scrutiny of Internet search bias after the Google settlement. In particular, it suggests that a sensible line can be drawn between promotion of a search engine\u27s own properties and demotion of rival properties. Although distinctions of this kind are inherently slippery, in this case the distinction should serve well enough. As of this writing, the wild card remains the European Commission, which may yet upset the applecart