Cost of Equity in Homeland Security Resource Allocation in the Face of a Strategic Attacker

Hundreds of billions of dollars have been spent in homeland security since September 11, 2001. Many mathematical models have been developed to study strategic interactions between governments (defenders) and terrorists (attackers). However, few studies have considered the tradeoff between equity and efficiency in homeland security resource allocation. In this article, we fill this gap by developing a novel model in which a government allocates defensive resources among multiple potential targets, while reserving a portion of defensive resources (represented by the equity coefficient) for equal distribution (according to geographical areas, population, density, etc.). Such a way to model equity is one of many alternatives, but was directly inspired by homeland security resource allocation practice. The government is faced with a strategic terrorist (adaptive adversary) whose attack probabilities are endogenously determined in the model. We study the effect of the equity coefficient on the optimal defensive resource allocations and the corresponding expected loss. We find that the cost of equity (in terms of increased expected loss) increases convexly in the equity coefficient. Furthermore, such cost is lower when: (a) government uses per‐valuation equity; (b) the cost‐effectiveness coefficient of defense increases; and (c) the total defense budget increases. Our model, results, and insights could be used to assist policy making.     

Adversarial Risk Analysis with Incomplete Information: A Level‐k Approach

This article proposes, develops, and illustrates the application of level‐k game theory to adversarial risk analysis. Level‐k reasoning, which assumes that players play strategically but have bounded rationality, is useful for operationalizing a Bayesian approach to adversarial risk analysis. It can be applied in a broad class of settings, including settings with asynchronous play and partial but incomplete revelation of early moves. Its computational and elicitation requirements are modest. We illustrate the approach with an application to a simple defend‐attack model in which the defender's countermeasures are revealed with a probability less than one to the attacker before he decides on how or whether to attack.     

Risk Preferences,Probability Weighting,and Strategy Tradeoffs in Wildfire Management

Wildfires present a complex applied risk management environment, but relatively little attention has been paid to behavioral and cognitive responses to risk among public agency wildfire managers. This study investigates responses to risk, including probability weighting and risk aversion, in a wildfire management context using a survey‐based experiment administered to federal wildfire managers. Respondents were presented with a multiattribute lottery‐choice experiment where each lottery is defined by three outcome attributes: expenditures for fire suppression, damage to private property, and exposure of firefighters to the risk of aviation‐related fatalities. Respondents choose one of two strategies, each of which includes “good” (low cost/low damage) and “bad” (high cost/high damage) outcomes that occur with varying probabilities. The choice task also incorporates an information framing experiment to test whether information about fatality risk to firefighters alters managers' responses to risk. Results suggest that managers exhibit risk aversion and nonlinear probability weighting, which can result in choices that do not minimize expected expenditures, property damage, or firefighter exposure. Information framing tends to result in choices that reduce the risk of aviation fatalities, but exacerbates nonlinear probability weighting.     

On the Existence of Monotone Pure‐Strategy Equilibria in Bayesian Games

We generalize Athey's (2001) and McAdams' (2003) results on the existence of monotone pure‐strategy equilibria in Bayesian games. We allow action spaces to be compact locally complete metric semilattices and type spaces to be partially ordered probability spaces. Our proof is based on contractibility rather than convexity of best‐reply sets. Several examples illustrate the scope of the result, including new applications to multi‐unit auctions with risk‐averse bidders.     

An Optimization‐Based Framework for the Identification of Vulnerabilities in Electric Power Grids Exposed to Natural Hazards

This article proposes a novel mathematical optimization framework for the identification of the vulnerabilities of electric power infrastructure systems (which is a paramount example of critical infrastructure) due to natural hazards. In this framework, the potential impacts of a specific natural hazard on an infrastructure are first evaluated in terms of failure and recovery probabilities of system components. Then, these are fed into a bi‐level attacker–defender interdiction model to determine the critical components whose failures lead to the largest system functionality loss. The proposed framework bridges the gap between the difficulties of accurately predicting the hazard information in classical probability‐based analyses and the over conservatism of the pure attacker–defender interdiction models. Mathematically, the proposed model configures a bi‐level max‐min mixed integer linear programming (MILP) that is challenging to solve. For its solution, the problem is casted into an equivalent one‐level MILP that can be solved by efficient global solvers. The approach is applied to a case study concerning the vulnerability identification of the georeferenced RTS24 test system under simulated wind storms. The numerical results demonstrate the effectiveness of the proposed framework for identifying critical locations under multiple hazard events and, thus, for providing a useful tool to help decisionmakers in making more‐informed prehazard preparation decisions.     

Risk–Risk Tradeoff Analysis of Nuclear Explosives for Asteroid Deflection

To prevent catastrophic asteroid–Earth collisions, it has been proposed to use nuclear explosives to deflect away earthbound asteroids. However, this policy of nuclear deflection could inadvertently increase the risk of nuclear war and other violent conflict. This article conducts risk–risk tradeoff analysis to assess whether nuclear deflection results in a net increase or decrease in risk. Assuming nonnuclear deflection options are also used, nuclear deflection may only be needed for the largest and most imminent asteroid collisions. These are low‐frequency, high‐severity events. The effect of nuclear deflection on violent conflict risk is more ambiguous due to the complex and dynamic social factors at play. Indeed, it is not clear whether nuclear deflection would cause a net increase or decrease in violent conflict risk. Similarly, this article cannot reach a precise conclusion on the overall risk–risk tradeoff. The value of this article comes less from specific quantitative conclusions and more from providing an analytical framework and a better overall understanding of the policy decision. The article demonstrates the importance of integrated analysis of global risks and the policies to address them, as well as the challenge of quantitative evaluation of complex social processes such as violent conflict.     

Understanding Gaps Between the Risk Perceptions of Wildland–Urban Interface (WUI) Residents and Wildfire Professionals

Research across a variety of risk domains finds that the risk perceptions of professionals and the public differ. Such risk perception gaps occur if professionals and the public understand individual risk factors differently or if they aggregate risk factors into overall risk differently. The nature of such divergences, whether based on objective inaccuracies or on differing perspectives, is important to understand. However, evidence of risk perception gaps typically pertains to general, overall risk levels; evidence of and details about mismatches between the specific level of risk faced by individuals and their perceptions of that risk is less available. We examine these issues with a paired data set of professional and resident assessments of parcel‐level wildfire risk for private property in a wildland–urban interface community located in western Colorado, United States. We find evidence of a gap between the parcel‐level risk assessments of a wildfire professional and numerous measures of residents’ risk assessments. Overall risk ratings diverge for the majority of properties, as do judgments about many specific property attributes and about the relative contribution of these attributes to a property's overall level of risk. However, overall risk gaps are not well explained by many factors commonly found to relate to risk perceptions. Understanding the nature of these risk perception gaps can facilitate improved communication by wildfire professionals about how risks can be mitigated on private lands. These results also speak to the general nature of individual‐level risk perception.     

Dose–Response Modeling: Extrapolating From Experimental Data to Real‐World Populations

Dose–response modeling of biological agents has traditionally focused on describing laboratory‐derived experimental data. Limited consideration has been given to understanding those factors that are controlled in a laboratory, but are likely to occur in real‐world scenarios. In this study, a probabilistic framework is developed that extends Brookmeyer's competing‐risks dose–response model to allow for variation in factors such as dose‐dispersion, dose‐deposition, and other within‐host parameters. With data sets drawn from dose–response experiments of inhalational anthrax, plague, and tularemia, we illustrate how for certain cases, there is the potential for overestimation of infection numbers arising from models that consider only the experimental data in isolation.     

A Production–Inventory Model for a Push–Pull Manufacturing System with Capacity and Service Level Constraints

We study a hybrid push–pull production system with a two‐stage manufacturing process, which builds and stocks tested components for just‐in‐time configuration of the final product when a specific customer order is received. The first production stage (fabrication) is a push process where parts are replenished, tested, and assembled into components according to product‐level build plans. The component inventory is kept in stock ready for the final assembly of the end products. The second production stage (fulfillment) is a pull‐based assemble‐to‐order process where the final assembly process is initiated when a customer order is received and no finished goods inventory is kept for end products. One important planning issue is to find the right trade‐off between capacity utilization and inventory cost reduction that strives to meet the quarter‐end peak demand. We present a nonlinear optimization model to minimize the total inventory cost subject to the service level constraints and the production capacity constraints. This results in a convex program with linear constraints. An efficient algorithm using decomposition is developed for solving the nonlinear optimization problem. Numerical results are presented to show the performance improvements achieved by the optimized solutions along with managerial insights provided.     

Ambiguity,Risk, and Asset Returns in Continuous Time

Models of utility in stochastic continuous–time settings typically assume that beliefs are represented by a probability measure, hence ruling out a priori any concern with ambiguity. This paper formulates a continuous–time intertemporal version of multiple–priors utility, where aversion to ambiguity is admissible. In a representative agent asset market setting, the model delivers restrictions on excess returns that admit interpretations reflecting a premium for risk and a separate premium for ambiguity.     

Inference in Arch and Garch Models with Heavy–Tailed Errors

ARCH and GARCH models directly address the dependency of conditional second moments, and have proved particularly valuable in modelling processes where a relatively large degree of fluctuation is present. These include financial time series, which can be particularly heavy tailed. However, little is known about properties of ARCH or GARCH models in the heavy–tailed setting, and no methods are available for approximating the distributions of parameter estimators there. In this paper we show that, for heavy–tailed errors, the asymptotic distributions of quasi–maximum likelihood parameter estimators in ARCH and GARCH models are nonnormal, and are particularly difficult to estimate directly using standard parametric methods. Standard bootstrap methods also fail to produce consistent estimators. To overcome these problems we develop percentile–t, subsample bootstrap approximations to estimator distributions. Studentizing is employed to approximate scale, and the subsample bootstrap is used to estimate shape. The good performance of this approach is demonstrated both theoretically and numerically.     

Informed Public Preferences for Electricity Portfolios with CCS and Other Low‐Carbon Technologies

Public perceptions of carbon capture and sequestration (CCS) and other low‐carbon electricity‐generating technologies may affect the feasibility of their widespread deployment. We asked a diverse sample of 60 participants recruited from community groups in Pittsburgh, Pennsylvania to rank 10 technologies (e.g., coal with CCS, natural gas, nuclear, various renewables, and energy efficiency), and seven realistic low‐carbon portfolios composed of these technologies, after receiving comprehensive and carefully balanced materials that explained the costs and benefits of each technology. Rankings were obtained in small group settings as well as individually before and after the group discussions. The ranking exercise asked participants to assume that the U.S. Congress had mandated a reduction in carbon dioxide emissions from power plants to be built in the future. Overall, rankings suggest that participants favored energy efficiency, followed by nuclear power, integrated gasification combined‐cycle coal with CCS and wind. The most preferred portfolio also included these technologies. We find that these informed members of the general public preferred diverse portfolios that contained CCS and nuclear over alternatives once they fully understood the benefits, cost, and limitations of each. The materials and approach developed for this study may also have value in educating members of the general public about the challenges of achieving a low‐carbon energy future.     

Issues in Qualitative and Quantitative Risk Analysis for Developmental Toxicology1

The qualitative and quantitative evaluation of risk in developmental toxicology has been discussed in several recent publications.(^1–3) A number of issues still are to be resolved in this area. The qualitative evaluation and interpretation of end points in developmental toxicology depends on an understanding of the biological events leading to the end points observed, the relationships among end points, and their relationship to dose and to maternal toxicity. The interpretation of these end points is also affected by the statistical power of the experiments used for detecting the various end points observed. The quantitative risk assessment attempts to estimate human risk for developmental toxicity as a function of dose. The current approach is to apply safety (uncertainty) factors to die no observed effect level (NOEL). An alternative presented and discussed here is to model the experimental data and apply a safety factor to an estimated risk level to achieve an “acceptable” level of risk. In cases where the dose-response curves upward, this approach provides a conservative estimate of risk. This procedure does not preclude the existence of a threshold dose. More research is needed to develop appropriate dose-response models that can provide better estimates for low-dose extrapolation of developmental effects.     

Risk‐Cost‐Benefit Analysis for Transportation Corridors with Interval Uncertainties of Heterogeneous Data

Access management, which systematically limits opportunities for egress and ingress of vehicles to highway lanes, is critical to protect trillions of dollars of current investment in transportation. This article addresses allocating resources for access management with incomplete and partially relevant data on crash rates, travel speeds, and other factors. While access management can be effective to avoid crashes, reduce travel times, and increase route capacities, the literature suggests a need for performance metrics to guide investments in resource allocation across large corridor networks and several time horizons. In this article, we describe a quantitative decision model to support an access management program via risk‐cost‐benefit analysis under data uncertainties from diverse sources of data and expertise. The approach quantifies potential benefits, including safety improvement and travel time savings, and costs of access management through functional relationships of input parameters including crash rates, corridor access point densities, and traffic volumes. Parameter uncertainties, which vary across locales and experts, are addressed via numerical interval analyses. This approach is demonstrated at several geographic scales across 7,000 kilometers of highways in a geographic region and several subregions. The demonstration prioritizes route segments that would benefit from risk management, including (i) additional data or elicitation, (ii) right‐of‐way purchases, (iii) restriction or closing of access points, (iv) new alignments, (v) developer proffers, and (vi) etc. The approach ought to be of wide interest to analysts, planners, policymakers, and stakeholders who rely on heterogeneous data and expertise for risk management.     

Spatial and Temporal Variation in Evacuee Risk Perception Throughout the Evacuation and Return‐Entry Process

Developing effective evacuation and return‐entry plans requires understanding the spatial and temporal dimensions of risk perception experienced by evacuees throughout a disaster event. Using data gathered from the 2008 Cedar Rapids, Iowa Flood, this article explores how risk perception and location influence evacuee behavior during the evacuation and return‐entry process. Three themes are discussed: (1) the spatial and temporal characteristics of risk perception throughout the evacuation and return‐entry process, (2) the relationship between risk perception and household compliance with return‐entry orders, and (3) the role social influences have on the timing of the return by households. The results indicate that geographic location and spatial variation of risk influenced household risk perception and compliance with return‐entry plans. In addition, sociodemographic characteristics influenced the timing and characteristics of the return groups. The findings of this study advance knowledge of evacuee behavior throughout a disaster and can inform strategies used by emergency managers throughout the evacuation and return‐entry process.     

A Data‐Driven Approach to Assessing Supply Inadequacy Risks Due to Climate‐Induced Shifts in Electricity Demand

The U.S. electric power system is increasingly vulnerable to the adverse impacts of extreme climate events. Supply inadequacy risk can result from climate‐induced shifts in electricity demand and/or damaged physical assets due to hydro‐meteorological hazards and climate change. In this article, we focus on the risks associated with the unanticipated climate‐induced demand shifts and propose a data‐driven approach to identify risk factors that render the electricity sector vulnerable in the face of future climate variability and change. More specifically, we have leveraged advanced supervised learning theory to identify the key predictors of climate‐sensitive demand in the residential, commercial, and industrial sectors. Our analysis indicates that variations in mean dew point temperature is the common major risk factor across all the three sectors. We have also conducted a statistical sensitivity analysis to assess the variability in the projected demand as a function of the key climate risk factor. We then propose the use of scenario‐based heat maps as a tool to communicate the inadequacy risks to stakeholders and decisionmakers. While we use the state of Ohio as a case study, our proposed approach is equally applicable to all other states.     

The Mirrlees Approach to Mechanism Design with Renegotiation (with Applications to Hold‐up and Risk Sharing)

The paper studies the implementation problem, first analyzed by Maskin and Moore (1999), in which two agents observe an unverifiable state of nature and may renegotiate inefficient outcomes following play of the mechanism. We develop a first‐order approach to characterizing the set of implementable utility mappings in this problem, paralleling Mirrlees's (1971) first‐order analysis of standard mechanism design problems. We use this characterization to study optimal contracting in hold‐up and risk‐sharing models. In particular, we examine when the contracting parties can optimally restrict attention to simple contracts, such as noncontingent contracts and option contracts (where only one agent sends a message).     

Context,Cultural Bias,and Health Risk Perception: The “Everyday” Nature of Pesticide Policy Preferences in London,Calgary, and Halifax

Risk perception and the cultural theory of risk have often been contrasted in relation to risk‐related policy making; however, the local context in which risks are experienced, an important component of everyday decision making, remains understudied. What is unclear is the extent to which localized community beliefs and behaviors depend on larger belief systems about risk (i.e., worldviews). This article reports on a study designed to understand the relative importance of health risk perceptions (threat of harm); risk‐related worldviews (cultural biases); and the experiences of local context (situated risk) for predicting risk‐related policy preferences regarding cosmetic pesticides. Responses to a random telephone questionnaire are used to compare residents’ risk perceptions, cultural biases, and pesticide bylaw preferences in Calgary (Alberta), Halifax (Nova Scotia), and London (Ontario), Canada. Logistic regression shows that the most important determinants of pesticide bylaw preference are risk perception, lack of benefit, and pesticide “abstinence.” Though perception of health risk is the best single predictor of differences in bylaw preferences, social factors such as gender and situated risk factors like conflict over chemical pesticides, are also important. Though cultural biases are not important predictors of pesticide bylaw preference, as in other studies, they are significant predictors of health risk perception. Pesticide bylaw preference is therefore more than just a health risk perception or worldview issue; it is also about how health risk becomes situated—contextually—in the experiences of residents’ everyday lives.