Approximate dispersion relations for waves on arbitrary shear flows

An approximate dispersion relation is derived and presented for linear surface waves atop a shear current whose magnitude and direction can vary arbitrarily with depth. The approximation, derived to first order of deviation from potential flow, is shown to produce good approximations at all wavelengths for a wide range of naturally occuring shear flows as well as widely used model flows. The relation reduces in many cases to a 3D generalization of the much used approximation by Skop [1987], developed further by Kirby & Chen [1989], but is shown to be more robust, succeeding in situations where the Kirby & Chen model fails. The two approximations incur the same numerical cost and difficulty. While the Kirby & Chen approximation is excellent for a wide range of currents, the exact criteria for its applicability have not been known. We explain the apparently serendipitous success of the latter and derive proper conditions of applicability for both approximate dispersion relations. Our new model has a greater range of applicability. A second order approximation is also derived. It greatly improves accuracy, which is shown to be important in difficult cases. It has an advantage over the corresponding 2nd order expression proposed by Kirby \& Chen that its criterion of accuracy is explicitly known, which is not currently the case for the latter to our knowledge. Our 2nd order term is also arguably significantly simpler to implement, and more physically transparent, than its sibling due to Kirby & Chen.Comment: 22 pages, 5 figure

Anticipated verbal feedback induces altruistic behavior

A distinctive feature of humans compared to other species is the high rate of cooperation with non-kin. One explanation is that humans are motivated by concerns for social esteem. In this paper we experimentally investigate the impact of anticipated verbal feedback on altruistic behavior. We study pairwise interactions in which one subject, the “divider”, decides how to split a sum of money between herself and a recipient. Thereafter, the recipient can send an unrestricted anonymous message to the divider. The subjects’ relationship is anonymous and one-shot to rule out any reputation effects. Compared to a control treatment without feedback messages, donations increase substantially when recipients can communicate. With verbal feedback, the fraction of zero donations decreases from about 40% to about 20%, and there is a corresponding increase in the fraction of equal splits from about 30% to about 50%. Recipients who receive no money almost always express disapproval of the divider, sometimes strongly and in foul language. Following an equal split, almost all recipients praise the divider. The results suggest that anticipated verbal rewards and punishments play a role in promoting altruistic behavior among humans.Punishment; Approval; Disapproval; Dictator game; Altruism; Communication; Verbal feedback

Generosity

We develop a simple model of generous behavior. It is based on the premise that some people are generous, but everyone wants to appear generous. Although non-monetary donations are always inefficient, our model predicts donors to favor non-monetary donations when the inefficiency is relatively small and when the recipient is sufficiently rich. The model helps to explain the prevalence of volunteering, the nature of Christmas gifts, and the taboo against paying cash in return for friendly favors. The model also explains why it is socially more acceptable to ask for favors than for money.Altruism; Non-monetary gifts; Volunteering

Organizational Structure as the Channeling of Boundedly Rational Pre-play Communication

We model organizational decision making as costless pre-play communication. Decision making is called authoritarian if only one player is allowed to speak and consensual if all players are allowed to speak. Players are assumed to have limited cognitive capacity and we characterize their behavior under each decision making regime for two different cognitive hierarchy models. Our results suggest that authoritarian decision making is optimal when players have conflicting preferences over the set of Nash equilibrium outcomes, whereas consensual decision making is optimal when players have congruent preferences over this set. The intuition is that authoritarian decision making avoids conflict, but sometimes creates insufficient mutual trust to implement socially optimal outcomes.Organizational decision making; coordination games; communication; cognitive hierarchy models

Foreign direct investment and the political economy of protection

Trade Barriers;Foreign Investment