Long-Term Bias, Incentives, and Agency Costs

The problem of managerial short-termism has long preoccupied policymakers, researchers, and practitioners. These groups have given much less attention, however, to the converse problem of managerial long-termism. Michal Barzuza and Eric Talley fill this gap in their pioneering article, Long-Term Bias. Relying on the behavioral finance and psychology literatures, the authors provide a novel and thought-provoking analysis of managerial long-term bias, which may be just as detrimental as the more widely condemned short-term bias. This invited Comment to Barzuza and Talley’s article advances three claims. First, it argues that proper incentives— created by executive compensation, heightened risk of early termination, market responses and shareholder pressures— are likely to turn most managers more realistic and thus to mitigate their long-term biases. Second, it explains how, in reality, it could be almost impossible to distinguish between long-term bias and traditional agency theories of empire building and pet projects. Ultimately, both long-termist and self-interested managers systematically harm shareholders; both choose to ignore shareholder interests and waste free cash flow on inferior business investments. This also explains why the cure to both long-term bias and agency costs is similar: reducing the relative insulation of the board from shareholders’ disciplinary power. Finally, this Comment expresses strong support for most of Barzuza and Talley’s normative conclusions, with one important exception: their acceptance of the use of dual-class stock. With a perpetual lock on control and a limited equity stake, corporate leaders will be immune to any “institutional brake” on all forms of long-termist overinvestment. If anything, the analysis of Barzuza and Talley provides an additional strong justification to oppose the use of perpetual dual-class stock.

On the automaticity of sequences defined by the Thue–Morse and period-doubling Stieltjes continued fractions

Continued fraction expansions of automatic numbers have been extensively studied during the last few decades. The research interests are, on one hand, in the degree or automaticity of the partial quotients following the seminal paper of Baum and Sweet in 1976, and on the other hand, in calculating the Hankel determinants and irrationality exponents, as one can find in the works of Allouche–Peyrière–Wen–Wen, Bugeaud, and the first author. This paper is motivated by the converse problem: to study Stieltjes continued fractions whose coefficients form an automatic sequence. We consider two such continued fractions defined by the Thue–Morse and period-doubling sequences, respectively, and prove that they are congruent to algebraic series in [Formula: see text] modulo [Formula: see text]. Consequently, the sequences of the coefficients of the power series expansions of the two continued fractions modulo [Formula: see text] are [Formula: see text]-automatic.

“As Stubble Before the Wind”

Chapter 5 turns to Oklahoma, ground zero of the most violent tornadoes on the planet, where an evangelical Protestant culture meets the frontiers of contemporary meteorological research. Deadly tornadoes in Moore, a suburb of Oklahoma City, have made particularly raw the long-festering question of whether God controls everything that happens. But Oklahomans have also had to confront the converse problem of human complicity in disasters, especially in an era of climate change. Evangelical politicians from Oklahoma have had a disproportionate influence on climate policy in the Trump administration, which has denied the looming crisis of global warming, despite overwhelming evidence to the contrary. At the local level, Oklahomans have also had to reckon with the challenge of disaster preparedness, especially the funding of school storm shelters, in a state that often resists governmental “intrusion.”

Introduction

This chapter provides a background on recent advances in the theory of mean field games (MFGs). MFGs has met an amazing success since pioneering works of more than ten years ago. It gives a self-contained study of the so-called master equation and an answer to the convergence problem. MFGs should be understood as games with a continuum of players, each of them interacting with the whole statistical distribution of the population. In this regard, they are expected to provide an asymptotic formulation for games with finitely many players with mean field interaction. This chapter focuses on the converse problem, which may be formulated by confirming whether the equilibria of the finite games converge to a solution of the corresponding MFG as the number of players becomes very large.

Gamma Factors, Root Numbers, and Distinction

We study a relation between distinction and special values of local invariants for representations of the general linear group over a quadratic extension of p-adic fields. We show that the local Rankin–Selberg root number of any pair of distinguished representation is trivial, and as a corollary we obtain an analogue for the global root number of any pair of distinguished cuspidal representations. We further study the extent to which the gamma factor at 1/2 is trivial for distinguished representations as well as the converse problem.

ISOMORPHIC INDUCED MODULES AND DYNKIN DIAGRAM AUTOMORPHISMS OF SEMISIMPLE LIE ALGEBRAS

Consider a simple Lie algebra $\mathfrak{g}$ and $\overline{\mathfrak{g}}$ ⊂ $\mathfrak{g}$ a Levi subalgebra. Two irreducible $\overline{\mathfrak{g}}$-modules yield isomorphic inductions to $\mathfrak{g}$ when their highest weights coincide up to conjugation by an element of the Weyl group W of $\mathfrak{g}$ which is also a Dynkin diagram automorphism of $\overline{\mathfrak{g}}$. In this paper, we study the converse problem: given two irreducible $\overline{\mathfrak{g}}$-modules of highest weight μ and ν whose inductions to $\mathfrak{g}$ are isomorphic, can we conclude that μ and ν are conjugate under the action of an element of W which is also a Dynkin diagram automorphism of $\overline{\mathfrak{g}}$? We conjecture this is true in general. We prove this conjecture in type A and, for the other root systems, in various situations providing μ and ν satisfy additional hypotheses. Our result can be interpreted as an analogue for branching coefficients of the main result of Rajan [6] on tensor product multiplicities.