Optimal Sequential Investigation Rules in Competition Law

Although both in US antitrust and European competition law there is a clear evolution to a much broader application of "rule of reason" (instead of per-se rules), there is also an increasing awareness of the problems of a case-by-case approach. The "error costs approach" (minimizing the sum of welfare costs of decision errors and administrative costs) allows not only to decide between these two extremes, but also to design optimally differentiated rules (with an optimal depth of investigation) as intermediate solutions between simple per-se rules and a fullscale rule of reason. In this paper we present a decision-theoretic model that can be used as an instrument for deriving optimal rules for a sequential investigation process in competition law. Such a sequential investigation can be interpreted as a step-by-step sorting process into ever smaller subclasses of cases that help to discriminate better between pro- and anticompetitive cases. We analyze both the problem of optimal stopping of the investigation and optimal sequencing of the assessment criteria in an investigation. To illustrate, we show how a more differentiated rule on resale price maintenance could be derived after the rejection of its per-se prohibition by the US Supreme Court in the "Leegin" case 2007.Law Enforcement, Decision-Making, Competition Law, Antitrust Law

Sequential stopping for high-throughput experiments

In high-throughput experiments, the sample size is typically chosen informally. Most formal sample-size calculations depend critically on prior knowledge. We propose a sequential strategy that, by updating knowledge when new data are available, depends less critically on prior assumptions. Experiments are stopped or continued based on the potential benefits in obtaining additional data. The underlying decision-theoretic framework guarantees the design to proceed in a coherent fashion. We propose intuitively appealing, easy-to-implement utility functions. As in most sequential design problems, an exact solution is prohibitive. We propose a simulation-based approximation that uses decision boundaries. We apply the method to RNA-seq, microarray, and reverse-phase protein array studies and show its potential advantages. The approach has been added to the Bioconductor package gaga

The Sequencing Problem in Sequential Investigation Processes

Many decision problems in various fields of application can be characterized as diagnostic problems trying to assess the true state (of the world) of given cases. The investigation of assessment criteria improves the initial information according to observed signal outcomes, which are related to the possible states. Such sequential investigation processes can be analyzed within the framework of statistical decision theory, in which prior probability distributions of classes of cases are updated, allowing for a sorting of particular cases into ever smaller subclasses. However, receiving such information causes investigation costs. Besides the question about the set of relevant criteria, this defines two additional problems of statistical decision problems: the optimal stopping of investigations and the optimal sequence of investigating a given set of criteria. Unfortunately, no solution exists with which the optimal sequence can generally be determined. Therefore, the paper characterizes the associated problems and analyzes existing heuristics trying to approximate an optimal solution.Decision-Making, Uncertainty, Information, Bayesian Analysis, Statistical Decision Theory

DYNAMIC INVESTMENT STRATEGIES FOR INFORMATION SYSTEMS DEVELOPMENT

This paper presents an analytical model for choosing optimal investment schedules for the development of new systems under various types of risk. Two modes of risk reduction are considered. In the first mode, risk is reduced by gathering information through prototype building or sequential development, where risky parameters are assumed to have unknown but fixed values. The second mode involves an increase in systems development and usage skills through experience and learning, which may reduce the development cost and increase the acceptance of the system among the potential users. The second mode of risk reduction changes the true values of the parameters. Starting with a conceptual multi-dimensional framework for analyzing systems risk, a dynamic decisiontheoretic model for guiding the investment process is developed. The model specifies the level of investment in development activities at any stage, depending on the information gathered from prototypes or parts of the actual system developed to that point. Some properties of global and myopic investment policies are derived. The sensitivity of the level of investment to the accuracy of information is characterized. Experience and learning effects are considered in a simple two-period setting, where familiarity with the development process in the first period reduces the cost of developing the remaining part of the system in the second period. Extensions, testing, and implementation of the model are discussed

Optimal treatment allocations in space and time for on-line control of an emerging infectious disease

A key component in controlling the spread of an epidemic is deciding where, whenand to whom to apply an intervention.We develop a framework for using data to informthese decisionsin realtime.We formalize a treatment allocation strategy as a sequence of functions, oneper treatment period, that map up-to-date information on the spread of an infectious diseaseto a subset of locations where treatment should be allocated. An optimal allocation strategyoptimizes some cumulative outcome, e.g. the number of uninfected locations, the geographicfootprint of the disease or the cost of the epidemic. Estimation of an optimal allocation strategyfor an emerging infectious disease is challenging because spatial proximity induces interferencebetween locations, the number of possible allocations is exponential in the number oflocations, and because disease dynamics and intervention effectiveness are unknown at outbreak.We derive a Bayesian on-line estimator of the optimal allocation strategy that combinessimulation–optimization with Thompson sampling.The estimator proposed performs favourablyin simulation experiments. This work is motivated by and illustrated using data on the spread ofwhite nose syndrome, which is a highly fatal infectious disease devastating bat populations inNorth America