Every conformal class contains a metric of bounded geometry

We show that on every manifold, every conformal class of semi-Riemannian metrics contains a metric $g$ such that each $k$-th-order covariant derivative of the Riemann tensor of $g$ has bounded absolute value $a_k$. This result is new also in the Riemannian case, where one can arrange in addition that $g$ is complete with injectivity and convexity radius greater than 1. One can even make the radii rapidly increasing and the functions $a_k$ rapidly decreasing at infinity. We prove generalizations to foliated manifolds, where curvature, second fundamental form and injectivity radius of the leaves can be controlled similarly. Moreover, we explain a general principle that can be used to obtain analogous results for Riemannian manifolds equipped with arbitrary other additional geometric structures instead of foliations.Comment: 22 pages, 1 figure. The journal article differs from this version only by marginal adaptations required by the publisher's style guidelines, and by one minor typ

Mechanism design for decentralized online machine scheduling

Traditional optimization models assume a central decision maker who optimizes a global system performance measure. However, problem data is often distributed among several agents, and agents take autonomous decisions. This gives incentives for strategic behavior of agents, possibly leading to sub-optimal system performance. Furthermore, in dynamic environments, machines are locally dispersed and administratively independent. Examples are found both in business and engineering applications. We investigate such issues for a parallel machine scheduling model where jobs arrive online over time. Instead of centrally assigning jobs to machines, each machine implements a local sequencing rule and jobs decide for machines themselves. In this context, we introduce the concept of a myopic best response equilibrium, a concept weaker than the classical dominant strategy equilibrium, but appropriate for online problems. Our main result is a polynomial time, online mechanism that |assuming rational behavior of jobs| results in an equilibrium schedule that is 3.281-competitive with respect to the maximal social welfare. This is only lightly worse than state-of-the-art algorithms with central coordination

The Google Book search settlement: A law and economics analysis

Beginning in December 2004 Google has pursued a new project to create a book search engine (Google Book Search). The project has released a storm of controversy around the globe. While the supporters of Google Book Search conceive the project as a first reasonable step towards unlimited access to knowledge in the information age, its opponents fear profound negative effects due to an erosion of copyright law. Our law and economics analysis of the Book Search Project suggests that – from a copyright perspective – the proposed settlement may be beneficial to right holders, consumers, and Google. For instance, it may provide a solution to the still unsolved dilemma of orphan works. From a competition policy perspective, we stress the important aspect that Google’s pricing algorithm for orphan and unclaimed works effectively replicates a competitive Nash-Bertrand market outcome under post-settlement, third-party oversight.Book Rights Registry; Competition Policy; Copyright; Fair Use; Google Book Search; Library Program; Orphan Works

Games and Mechanism Design in Machine Scheduling – An Introduction

In this paper, we survey different models, techniques, and some recent results to tackle machine scheduling problems within a distributed setting. In traditional optimization, a central authority is asked to solve a (computationally hard) optimization problem. In contrast, in distributed settings there are several agents, possibly equipped with private information that is not publicly known, and these agents need to interact in order to derive a solution to the problem. Usually the agents have their individual preferences, which induces them to behave strategically in order to manipulate the resulting solution. Nevertheless, one is often interested in the global performance of such systems. The analysis of such distributed settings requires techniques from classical Optimization, Game Theory, and Economic Theory. The paper therefore briefly introduces the most important of the underlying concepts, and gives a selection of typical research questions and recent results, focussing on applications to machine scheduling problems. This includes the study of the so-called price of anarchy for settings where the agents do not possess private information, as well as the design and analysis of (truthful) mechanisms in settings where the agents do possess private information.computer science applications;

Characterization of revenue equivalence

The property of an allocation rule to be implementable in dominant strategies by a unique payment scheme is called \emph{revenue equivalence}. In this paper we give a characterization of revenue equivalence based on a graph theoretic interpretation of the incentive compatibility constraints. The characterization holds for any (possibly infinite) outcome space and many of the known results are immediate consequences. Moreover, revenue equivalence can be identified in cases where existing theorems are silent

Decentralization and Mechanism Design for Online Machine Scheduling

We study the online version of the classical parallel machine scheduling problem to minimize the total weighted completion time from a new perspective: We assume a strategic setting, where the data of each job j, namely its release date r(j) , its processing time p(j) and its weight w(j) is only known to the job itself, but not to the system. Furthermore, we assume a decentralized setting, where jobs choose the machine on which they want to be processed themselves. We study this setting from the perspective of algorithmic mechanism design and present a polynomial time decentralized online scheduling mechanism that induces rational jobs to select their machine in such a way that the resulting schedule is 3.281-competitive. The mechanism deploys an online payment scheme that induces rational jobs to truthfully report about their private data: with respect to release dates and processing times, truthfully reporting is a dominant strategy equilibrium, whereas truthfully reporting the weights is a myopic best response equilibrium. We also show that the local scheduling policy used in the mechanism cannot be extended to a mechanism where truthful reports with respect to weights constitute a dominant strategy equilibrium.operations research and management science;

Equity valuation of Zalando SE

his dissertation covers the equity valuation of the German online fashion retail company, Zalando SE. The objective of the valuation is to determine Zalando’s fair share price as of 6 th May 2021 and to provide an investment recommendation. To justify the forecasting assumptions, an overview of the firm as well as of the external environment is presented. In the valuation process two different methods are applied: The Discounted Cash Flow Model (DCF) and the Relative Valuation. Furthermore, to account for the current economic uncertainties, a sensitivity analysis on the estimated share value was conducted. Finally, the results are compared with the assessment made in the Bank of America report. Overall, this leads to a target price per share of EUR 129, which corresponds to a 51.9% upside compared to its current share price of EUR 85. My recommendation for Zalando SE is, therefore, a buy.Esta dissertação apresenta a avaliação patrimonial da empresa alemã de retalho de moda online, Zalando SE. O objetivo da avaliação é determinar o preço justo das ações da Zalando a partir de 6 de maio de 2021 e fornecer uma recomendação de investimento. Para justificar as hipóteses de previsão, é apresentada uma visão geral da empresa, bem como do ambiente externo. No processo de avaliação, são aplicados dois métodos diferentes: O Modelo de Fluxo de Caixa Descontado (DCF) e a Avaliação Relativa. Além disso, para ter em conta as atuais incertezas económicas, foi realizada uma análise de sensibilidade sobre o valor estimado das ações. Finalmente, os resultados são comparados com a avaliação feita no relatório do Bank of America. Globalmente, isto conduz a um preço-alvo por ação de EUR 129, o que corresponde a um aumento de 51.9% em relação ao seu preço atual por ação de EUR 85. A minha recomendação para Zalando SE é, portanto, uma compra

Characterization of Revenue Equivalence

The property of an allocation rule to be implementable in dominant strategies by a unique payment scheme is called revenue equivalence. In this paper we give a characterization of revenue equivalence based on a graph theoretic interpretation of the incentive compatibility constraints. The characterization holds for any (possibly infinite) outcome space and many of the known results are immediate consequences. Moreover, revenue equivalence can be identified in cases where existing theorems are silent.computer science applications;