Bridge trisections in rational surfaces

We study smooth isotopy classes of complex curves in complex surfaces from the perspective of the theory of bridge trisections, with a special focus on curves in $\mathbb{CP}^2$ and $\mathbb{CP}^1\times\mathbb{CP}^1$. We are especially interested in bridge trisections and trisections that are as simple as possible, which we call "efficient". We show that any curve in $\mathbb{CP}^2$ or $\mathbb{CP}^1\times\mathbb{CP}^1$ admits an efficient bridge trisection. Because bridge trisections and trisections are nicely related via branched covering operations, we are able to give many examples of complex surfaces that admit efficient trisections. Among these are hypersurfaces in $\mathbb{CP}^3$, the elliptic surfaces $E(n)$, the Horikawa surfaces $H(n)$, and complete intersections of hypersurfaces in $\mathbb{CP}^N$. As a corollary, we observe that, in many cases, manifolds that are homeomorphic but not diffeomorphic have the same trisection genus, which is consistent with the conjecture that trisection genus is additive under connected sum. We give many trisection diagrams to illustrate our examples.Comment: 46 pages, 28 color figure

Social Reciprocity

We define social reciprocity as the act of demonstrating one's disapproval, at some personal cost, for the violation of widely-held norms (e.g., don't free ride). Social reciprocity differs from standard notions of reciprocity because social reciprocators intervene whenever a norm is violated and do not condition intervention on potential future payoffs, revenge, or altruism. Instead, we posit that social reciprocity is a triggered normative reponse. Our experiment confirms the existence of social reciprocity and demonstrates that more socially efficient outcomes arise when reciprocity can be expressed socially. Too provide theoretical foundations for social reciprocity, we show that generalized punishment norms survive in one of the two stable equilibria of an evolutionary game with selection drift.reciprocity, norm, experiment, public good, learning, evolution

What Norms Trigger Punishment

Many experiments have demonstrated the power of norm enforcement-peer monitoring and punishment-to maintain, or even increase, contributions in social dilemma settings, but little is known about the underlying norms that monitors use to make punishment decisions. Using a large sample of experimental data, we empirically recover the set of norms used most often by monitors and show ?rst that the decision to punish should be modeled separately from the decision of how much to punish. Second, we show that absolute norms often ?t the data better than the group average norm often assumed in related work. Third, we ?nd that di?erent norms seem to in?uence the decisions about punishing violators inside and outside one’s own group.public good, experiment, punishment, social norm, norm enforcement.

No Switchbacks: Rethinking Aspiration-Based Dynamics in the Ultimatum Game

Aspiration-based evolutionary dynamics have recently been used to model the evolution of fair play in the ultimatum game showing that incredible threats to reject low offers persist in equilibrium. We focus on two extensions of this analysis: we experimentally test whether assumptions about agent motivations (aspiration levels) and the structure of the game (binary strategy space) reflect actual play, and we examine the problematic assumption embedded in the standard replicator dynamic that unhappy agents who switch strategies may return to a rejected strategy without exploring other options. We find that the resulting "no switchback" dynamic predicts the evolution of play better than the standard dynamic and that aspirations are a significant motivator for our participants. In the process, we also construct and analyze a variant of the ultimatum game in which players can adopt conditional (on their induced aspirations) stategies.ultimatum game, learning, aspirations, replicator dynamics, experiment

What Determines BITs?

Bilateral investment treaties (BITs) have proliferated over the past 50 years such that the number of pairs of countries with BITs is roughly as large as the number of country-pairs that belong to bilateral or regional preferential trade agreements (PTAs). The purpose of this study is to provide the first systematic empirical analysis of the economic determinants of BITs and of the likelihood of BITs between pairs of countries using a qualitative choice model, and in a manner consistent with explaining PTAs. We develop the econometric specification for explaining the two based upon a general equilibrium model of world trade and foreign direct investment with three factors, two products, and explicit natural as well as policy trade and investment costs among multiple countries in the presence of national and multinational firms. The empirical model for BITs and PTAs is bivariate in nature and supports a set of hypotheses drawn from the general equilibrium model. Using the preferred empirical model, we correctly predict approximately 85 (75) percent of all BITs (PTAs) correctly, relative to an unconditional probability of only 11 (16) percent.bilateral investment treaties, foreign direct investment, multinational firms, free trade agreements, international trade

False-alarm probability in relation to over-sampled power spectra, with application to Super-Kamiokande solar neutrino data

The term "false-alarm probability" denotes the probability that at least one out of M independent power values in a prescribed search band of a power spectrum computed from a white-noise time series is expected to be as large as or larger than a given value. The usual formula is based on the assumption that powers are distributed exponentially, as one expects for power measurements of normally distributed random noise. However, in practice one typically examines peaks in an over-sampled power spectrum. It is therefore more appropriate to compare the strength of a particular peak with the distribution of peaks in over-sampled power spectra derived from normally distributed random noise. We show that this leads to a formula for the false-alarm probability that is more conservative than the familiar formula. We also show how to combine these results with a Bayesian method for estimating the probability of the null hypothesis (that there is no oscillation in the time series), and we discuss as an example the application of these procedures to Super-Kamiokande solar neutrino data

Crying Over Spilt Milk: Sunk Costs, Fairness Norms and the Hold-Up Problem*

This paper explores a possible connection between two behavioral anomalies in economics, the observed responsiveness of individual decision-makers to sunk costs, and the apparent failure of backward induction to predict outcomes in experimental bargaining games. In particular, we show that under some conditions, a "sunk cost sensitive" fairness norm can evolve in such environments. Under this norm, a fair distribution allows all parties to recoup whatever each has invested in their relationship before the net surplus is then divided into equal shares. The establishment of such a norm would have important consequences for the hold-up problem, which we characterize in terms of ultimatum bargaining in the presence of an outside option. We then conclude with a brief discussion of the possible labor market implications of our results.sunk costs, norms, fairness, trust, hold-up problem, human capital