Vicki M. Bier

Balancing Terrorism and Natural Disasters---Defensive Strategy with Endogenous Attacker Effort

In this paper, we apply game theory to identify equilibrium strategies for both attacker and defender in a fully endogenous model of resource allocation for countering terrorism and natural disasters. The key features of our model include balancing protection from terrorism and natural disasters, and describing the attacker choice by a continuous level of effort rather than a discrete choice (i.e., attack or not). Interestingly, in a sequential game, increased defensive investment can lead an attacker to either increase his level of effort (to help compensate for the reduced probability of damage from an attack), or decrease his level of effort (because attacking has become less profitable). This can either reduce or increase the effectiveness of investments in protection from intentional attack, and can therefore affect the relative desirability of investing in protection from natural disasters.

Choosing What to Protect: Strategic Defensive Allocation Against an Unknown Attacker

We study a strategic model in which a defender must allocate defensive resources to a collection of locations and an attacker must choose a location to attack. In equilibrium, the defender sometimes optimally leaves a location undefended and sometimes prefers a higher vulnerability at a particular location even if a lower risk could be achieved at zero cost. The defender prefers to allocate resources in a centralized (rather than decentralized) manner, the optimal allocation of resources can be non-monotonic in the value of the attackers outside option, and the defender prefers her defensive allocation to be public rather than secret.

Protection of simple series and parallel systems with components of different values

We apply game theory, optimization, and reliability analysis to identify optimal defenses against intentional threats to system reliability. The goals are to identify optimal strategies for allocating resources among possible defensive investments, and to develop qualitative guidelines that reflect those strategies. The novel feature of the approach is the use of reliability analysis together with game theory and optimization to study optimal management of intentional threats to system reliability. Thus, this work extends and adapts the existing body of game-theoretic work on security to systems with series or parallel structures. The results yield insights into the nature of optimal defensive investments that yield the best tradeoff between investment cost and security. In particular, the results illustrate how the optimal allocation of defensive investments depends on the structure of the system, the cost-effectiveness of infrastructure protection investments, and the adversarys goals and constraints.

On the state of the art: risk communication to the public

Abstract This paper reviews the state of the art on risk communication to the public, with an emphasis on summarizing relevant empirical findings. In particular, the paper reviews empirical results regarding the format of risk communication messages, the use of risk comparisons, audience differences, and the use of mental models as an aid in crafting effective risk communication messages. Later sections discuss the issue of credibility and trust in risk communication, and the use of stakeholder participation processes — important areas in which not as much rigorous empirical information is available. Due to the breadth of the topic, the paper is not intended to be a comprehensive review, but rather an overview of the voluminous literature in this area.

Modeling secrecy and deception in a multiple-period attacker-defender signaling game

In this paper, we apply game theory to model strategies of secrecy and deception in a multiple-period attacker-defender resource-allocation and signaling game with incomplete information. At each period, we allow one of the three possible types of defender signals--truthful disclosure, secrecy, and deception. We also allow two types of information updating--the attacker updates his knowledge about the defender type after observing the defenders signals, and also after observing the result of a contest (if one occurs in any given time period). Our multiple-period model provides insights into the balance between capital and expense for defensive investments (and the effects of defender private information, such as defense effectiveness, target valuations, and costs), and also shows that defenders can achieve more cost-effective security through secrecy and deception (possibly lasting more than one period), in a multiple-period game. This paper helps to fill a significant gap in the literature. In particular, to our knowledge, no past work has studied defender secrecy and deception in a multiple-period game. Moreover, we believe that the solution approach developed and applied in this paper would prove useful in other types of multiple-period games.

A critique of current practice for the use of expert opinions in probabilistic risk assessment

Abstract This paper critically reviews and evaluates the elicitation and use of expert opinion in probabilistic risk assessment (PRA) of nuclear power plants in light of the available empirical and theoretical results on expert opinion use. PRA practice is represented by four case studies selected to represent a variety of aspects of the problem: 1. ⊗ Assessments of component failure rates and maintenance data. 2. ⊗ An assessment of seismic hazard rates. 3. ⊗ Assessments of containment phenomenology. 4. ⊗ Accident precursor studies. The review has yielded mixed results. On the negative side, there appears to be little reliance on normative expertise in structuring the process of expert opinion elicitation and use; most applications instead rely primarily on the common sense of the experts involved in the analysis, which is not always an adequate guide. On the positive side, however, there is evidence that expert opinions can, in fact, be used well in practical settings.

Optimal Resource Allocation for Defense of Targets Based on Differing Measures of Attractiveness

This article describes the results of applying a rigorous computational model to the problem of the optimal defensive resource allocation among potential terrorist targets. In particular, our study explores how the optimal budget allocation depends on the cost effectiveness of security investments, the defenders valuations of the various targets, and the extent of the defenders uncertainty about the attackers target valuations. We use expected property damage, expected fatalities, and two metrics of critical infrastructure (airports and bridges) as our measures of target attractiveness. Our results show that the cost effectiveness of security investment has a large impact on the optimal budget allocation. Also, different measures of target attractiveness yield different optimal budget allocations, emphasizing the importance of developing more realistic terrorist objective functions for use in budget allocation decisions for homeland security.

A study of expert overconfidence

Overconfidence is one of the most common (and potentially severe) problems in expert judgment. To assess the extent of expert overconfidence, we analyzed a large data set on expert opinion compiled by Cooke and colleagues at the Technical University of Delft and elsewhere. This data set contains roughly five thousand 90% confidence intervals of uncertain quantities for which the true values are now known. Our analysis assesses the overall extent of overconfidence in the data set. Significant differences in the extent of overconfidence were found among studies, among experts, and among questions within a study. Moreover, replications (multiple realizations for the same question) allowed a preliminary assessment of whether the question effect is due largely to question difficulty, or merely to random noise in the realizations of the uncertain quantities. The results of this analysis suggest that much of the apparent question effect may be due to noise rather than systematic differences in the difficulty of achieving good calibration for different questions. The results support the differential weighting of experts, since there are significant differences in expert calibration within studies.

Game Theoretic Risk Analysis of Security Threats

Why Both Game Theory and Reliability Theory Are Important in Defending Infrastructure against Intelligent Attacks.- Game Theory Models of Intelligent Actors in Reliability Analysis: An Overview of the State of the Art.- Optimizing Defense Strategies for Complex Multi-State Systems.- Defending Against Terrorism, Natural Disaster, and All Hazards.- A Bayesian Model for a Game of Information in Optimal Attack/Defense Strategies.- Search for a Malevolent Needle in a Benign Haystack.- Games and Risk Analysis: Three Examples of Single and Alternate Moves.- Making Telecommunications Networks Resilient against Terrorist Attacks.- Improving Reliability through Multi-Path Routing and Link Defence: An Application of Game Theory to Transport.

Methodology for identifying near-optimal interdiction strategies for a power transmission system

Abstract Previous methods for assessing the vulnerability of complex systems to intentional attacks or interdiction have either not been adequate to deal with systems in which flow readjusts dynamically (such as electricity transmission systems), or have been complex and computationally difficult. We propose a relatively simple, inexpensive, and practical method (“Max Line”) for identifying promising interdiction strategies in such systems. The method is based on a greedy algorithm in which, at each iteration, the transmission line with the highest load is interdicted. We apply this method to sample electrical transmission systems from the Reliability Test System developed by the Institute of Electrical and Electronics Engineers, and compare our method and results with those of other proposed approaches for vulnerability assessment. We also study the effectiveness of protecting those transmission lines identified as promising candidates for interdiction. These comparisons shed light on the relative merits of the various vulnerability assessment methods, as well as providing insights that can help to guide the allocation of scarce resources for defensive investment.