Adversarial Risk Analysis Research Articles

Personalized pricing decisions through adversarial risk analysis

AbstractPricing decisions stand out as one of the most critical tasks a company faces, particularly in today's digital economy. As with other business decision‐making problems, pricing unfolds in a highly competitive and uncertain environment. Traditional analyses in this area have heavily relied on game theory and its variants. However, an important drawback of these approaches is their reliance on common knowledge assumptions, which are hardly tenable in competitive business domains. This paper introduces an innovative personalized pricing framework designed to assist decision‐makers in undertaking pricing decisions amidst competition, considering both buyer's and competitors' preferences. Our approach (i) establishes a coherent framework for modeling competition mitigating common knowledge assumptions; (ii) proposes a principled method to forecast competitors' pricing and customers' purchasing decisions, acknowledging major business uncertainties; and (iii) encourages structured thinking about the competitors' problems, thus enriching the solution process. To illustrate these properties, in addition to a general pricing template, we outline two specifications—one from the retail domain and a more intricate one from the pension fund domain.

On global robustness of an adversarial risk analysis solution

AbstractAdversarial Risk Analysis (ARA) can be a more realistic and practical alternative to traditional game theoretic or decision theoretic approaches for modeling strategic decision‐making in the presence of an adversary. ARA relies on quantifying the decision‐maker's (DM's) uncertainties about the adversary's strategic thinking, choices and utilities via probability distributions to identify the optimal solution for the DM. ARA solution will be sensitive to the choices of prior distributions used for modelling the expert beliefs. Yet, to date, no mathematical results to characterize the robustness of the ARA solution to the misspecification of one or more prior distributions exist. Prior elicitation is known to be challenging. We present the very first mathematical results on the global robustness of the ARA solution. We use the distorted band class of priors and establish the conditions under which an ordering on the ARA solution can be established when modelling the first‐price sealed‐bid auctions using the nonstrategic play and level‐ thinking solution concepts. We illustrate these results using numerical examples and discuss further areas of research.

Forecasting adversarial actions using judgment decomposition-recomposition

In domains such as homeland security, cybersecurity, and competitive marketing, it is frequently the case that analysts need to forecast actions by other intelligent agents that impact the problem of interest. Standard structured expert judgment elicitation techniques may fall short in this type of problem as they do not explicitly take into account intentionality. We present a decomposition technique based on adversarial risk analysis followed by a behavioural recomposition using discrete choice models that facilitate such elicitation process and illustrate its reasonable performance through behavioural experiments.

Manipulating hidden-Markov-model inferences by corrupting batch data

Time-series models typically assume untainted and legitimate streams of data. However, a self-interested adversary may have incentive to corrupt this data, thereby altering a decision maker’s inference. Within the broader field of adversarial machine learning, this research provides a novel, probabilistic perspective toward the manipulation of hidden Markov model inferences via corrupted data. In particular, we provision a suite of corruption problems for filtering, smoothing, and decoding inferences leveraging an adversarial risk analysis approach. Multiple stochastic programming models are set forth that incorporate realistic uncertainties and varied attacker objectives. Three general solution methods are developed by alternatively viewing estimation from frequentist and Bayesian perspectives. The efficacy of each method is illustrated via extensive, empirical testing. The developed methods are characterized by their solution quality and computational effort, resulting in a stratification of techniques across varying problem-instance architectures. This research highlights the weaknesses of hidden Markov models under adversarial activity, thereby motivating the need for robustification techniques to ensure their security.

Interdicting Attack Plans with Boundedly Rational Players and Multiple Attackers: An Adversarial Risk Analysis Approach

Cybersecurity planning supports the selection of and implementation of security controls in resource-constrained settings to manage risk. Doing so requires considering adaptive adversaries with different levels of strategic sophistication in modeling efforts to support risk management. However, most models in the literature only consider rational or nonstrategic adversaries. Therefore, we study how to inform defensive decision making to mitigate the risk from boundedly rational players, with a particular focus on making integrated, interdependent planning decisions. To achieve this goal, we introduce a modeling framework for selecting a portfolio of security mitigations that interdict adversarial attack plans that uses a structured approach for risk analysis. Our approach adapts adversarial risk analysis and cognitive hierarchy theory to consider a maximum-reliability path interdiction problem with a single defender and multiple attackers who have different goals and levels of strategic sophistication. Instead of enumerating all possible attacks and defenses, we introduce a solution technique based on integer programming and approximation algorithms to iteratively solve the defender’s and attackers’ problems. A case study illustrates the proposed models and provides insights into defensive planning. Funding: A. Peper and L. A. Albert were supported in part by the National Science Foundation [Grant 2000986].

First Price Sealed-Bid Auctions with Bidders’ Heterogeneous Risk Behavior: An Adversarial Risk Analysis Approach

Bidders’ bidding behavior is analyzed in first price sealed-bid (FPSB) auctions using an adversarial risk analysis (ARA) framework. However, using nonstrategic play and level-k thinking solution concepts, modeling is performed by assuming only two bidders. Also, the aleatory and concept uncertainties have not been yet taken into account by using an ARA framework for these auctions. In this paper, we apply an ARA approach to model bidders’ bidding behavior in a more realistic way for FPSB auctions. We assume n bidders that may have different wealth and heterogeneous risk behaviors. We use nonstrategic play and level-k thinking solution concepts, and we take into account aleatory uncertainty in addition to epistemic uncertainty. Finally, concept uncertainty is taken into account to find ARA solutions for these auctions. We also provide numerical examples to illustrate our methodology.

Multipolar Security Cooperation Planning: A Multiobjective, Adversarial-Risk-Analysis Approach

In an increasingly competitive environment, defense organizations are met with more difficult decisions than in years past. This problem is especially apparent in security cooperation, that is, defense diplomacy, conducted by the United States. Both the United States and its competitors offer military assistance to third-party nations who, in turn, select an offer based on their own self-interest. Unfortunately, current security cooperation planning practices adopt an ad hoc approach to such problems. Therefore, we set forth herein a decision-analytic-planning framework by (1) provisioning a generic utility model for security cooperation planning applicable to myriad stakeholders and (2) developing a Bayesian solution that allows the stakeholder to select an action that maximizes their expected utility. This combination of value-focused thinking and adversarial risk analysis improves upon standard U.S. defense practices; it tractably encodes planning assumptions and more comprehensively considers the relevant uncertainties. The efficacy of this planning approach is illustrated on a notional U.S. Air Force case study in which a host nation must choose between security assistance from the United States or a competing nation. Funding: This work was supported by the National Science Foundation [Grant DMS-1638521] and Air Force Office of Scientific Research [Grant 21RT0867].

Defense and security planning under resource uncertainty and multi‐period commitments

AbstractThe public sector is characterized by hierarchical and interdependent organizations. For defense and security applications in particular, a higher authority is generally responsible for allocating resources among subordinate organizations. These subordinate organizations conduct long‐term planning based on both uncertain resources and an uncertain operating environment. This article develops a modeling framework and multiple solution methodologies for subordinate organizations to use under such conditions. We extend the adversarial risk analysis approach to a stochastic game via a decomposition into a Markov decision process. This allows the subordinate organization to encode its beliefs in a Bayesian manner such that long‐term policies can be built to maximize its expected utility. The modeling framework we develop is illustrated in a realistic counter‐terrorism use case, and the efficacy of our solutions are evaluated via comparisons to alternatively constructed policies.

Augmented probability simulation methods for sequential games

We present a robust framework with computational algorithms to support decision makers in sequential games. Our framework includes methods to solve games with complete information, assess the robustness of such solutions and, finally, approximate adversarial risk analysis solutions when lacking complete information. Existing simulation based approaches can be inefficient when dealing with large sets of feasible decisions; the game of interest may not even be solvable to the desired precision for continuous decisions. Hence, we provide a novel alternative solution method based on the use of augmented probability simulation. While the proposed framework conceptually applies to multi-stage sequential games, the discussion focuses on two-stage sequential defend-attack problems.

Adversarial risk analysis for auctions using non-strategic play and level-k thinking: A general case of n bidders with regret

First-price sealed-bid auctions have been modeled using a utility function that takes into account bidders’ regret in case of winning or losing the auctioned item. However, that modeling does not consider bidders’ wealth which is an important determinant of bidders’ behavior in these auctions. In this paper, we apply an adversarial risk analysis approach for these auctions and find solutions using non-strategic play and level-k thinking solution concepts assuming n bidders. We define new regret parameters and a modified utility function to incorporate the effect of bidders’ wealth on their bidding behavior. In our modeling, we assume that the auctioned item is a normal item and has a reserve price. We give numerical examples to illustrate our methodology for each solution concept.

Adversarial Risk Analysis for Auctions Using Mirror Equilibrium and Bayes Nash Equilibrium

In this paper, we use the adversarial risk analysis (ARA) methodology to model first-price sealed-bid auctions under quite realistic assumptions. We extend prior work to find ARA solutions for mirror equilibrium and Bayes Nash equilibrium solution concepts, not only for risk-neutral but also for risk-averse and risk-seeking bidders. We also consider bidders having different wealth and assume that the auctioned item has a reserve price.

Deterrence against Terrorist Attacks in Sports-Mega Events: A Method to Identify the Optimal Portfolio of Defensive Countermeasures.

Sports mega-events, such as the Olympic Games or the Super Bowl, are attractive targets for terrorist organizations, due to their visibility, size, and number of people involved. Two characteristics of sports mega-events, however, make them distinctive in comparison with other well-studied target protection problems in counterterrorism analysis (such as transportation hubs or infrastructure facilities). First, defensive measures are often publicly known. Second, their finite horizon means that deterrence against any attack must be prioritized. In this article we thus propose a method that identifies the best portfolio of defensive measures the defense may adopt, given a fixed budget, to minimize the chances of suffering a terrorist attack during a sports mega-event. The method makes some relevant contributions to adversarial risk analysis: (i) it represents attackers that can choose among multiple attack scenarios and the no-attack scenario; (ii) it measures the deterrence effect caused by synergic portfolios of defensive measures; and (iii) it proposes an algorithm that identifies dominated portfolios and may, thus, overcome the scalability problems inherent to this portfolio optimization. We apply this method to a real-world defense problem, revisiting the defensive countermeasure planning for the 2016 Brazilian Olympic Games in Rio de Janeiro, Brazil. In the case study, we find a nonlinear relationship between budget expenditure and deterrence, as well as a decreasing marginal effectiveness use of resources after a given budget threshold, which would support a more efficient allocation of investments in the Gamesdefense.

Adversarial risk analysis for first‐price sealed‐bid auctions

SummaryAdversarial risk analysis (ARA) is an upcoming methodology that is considered to have advantages over the traditional decision‐theoretic and game‐theoretic approaches. ARA solutions for first‐price sealed‐bid (FPSB) auctions have been found but only under strong assumptions which make the model somewhat unrealistic. In this paper, we use ARA methodology to model FPSB auctions using more realistic assumptions. We define a new utility function that considers bidders’ wealth, we assume a reserve price and find solutions not only for risk‐neutral but also for risk‐averse as well as risk‐seeking bidders. We model the problem using ARA for non‐strategic play and level‐k thinking solution concepts.

An Adversarial Risk Analysis Framework for Batch Acceptance Problems

We provide an adversarial risk analysis framework for batch acceptance problems in which a decision maker relies exclusively on the size of the batch to accept or reject its admission to a system, albeit being aware of the presence of an opponent. The adversary acts as a data-fiddler attacker perturbing the observations perceived by the decision maker through injecting faulty items and/or modifying the existing items to faulty ones. We develop optimal policies against this combined attack strategy and illustrate the methodology with a review spam example.

Perspectives on Adversarial Classification

Adversarial classification (AC) is a major subfield within the increasingly important domain of adversarial machine learning (AML). So far, most approaches to AC have followed a classical game-theoretic framework. This requires unrealistic common knowledge conditions untenable in the security settings typical of the AML realm. After reviewing such approaches, we present alternative perspectives on AC based on adversarial risk analysis.

Insider Threat Modeling: An Adversarial Risk Analysis Approach

Insider threats entail major security issues in many organizations. Game theoretic models of insider threats so far proposed do not take into account important factors such as the organizational culture and whether the attacker was detected or not. They also fail to model defensive mechanisms already put in place by an organization to mitigate insider attacks. We propose two new models which incorporate these settings and, hence, are more realistic, and use adversarial risk analysis to find their solutions. Our models and solutions are general and can be applied to most insider threat scenarios. A data security example illustrates the discussion.

Adversarial risk analysis: An overview

AbstractAdversarial risk analysis (ARA) is a relatively new area of research that informs decision‐making when facing intelligent opponents and uncertain outcomes. It is a decision‐theoretic alternative to game theory. ARA enables an analyst to express her Bayesian beliefs about an opponent's utilities, capabilities, probabilities, and the type of strategic calculations that the opponent is using to make his decision. Within that framework, the analyst then solves the problem from the perspective of the opponent. This calculation produces a distribution over the actions of the opponent that permits the analyst to maximize her expected utility. This review covers conceptual, modeling, computational, and applied issues in ARA as well as interesting open research issues.This article is categorized under: Statistical and Graphical Methods of Data Analysis > Bayesian Methods and Theory Applications of Computational Statistics > Defense and National Security

Protecting From Malware Obfuscation Attacks Through Adversarial Risk Analysis.

Malware constitutes a major global risk affecting millions of users each year. Standard algorithms in detection systems perform insufficiently when dealing with malware passed through obfuscation tools. We illustrate this studying in detail an open source metamorphic software, making use of a hybrid framework to obtain the relevant features from binaries. We then provide an improved alternative solution based on adversarial risk analysis which we illustrate describe with anexample.

Adversarial Risk Analysis (Overview)

Adversarial risk analysis (ARA) is a relatively new area of research that informs decision-making when facing intelligent opponents and uncertain outcomes. It enables an analyst to express her Bayesian beliefs about an opponent's utilities, capabilities, probabilities and the type of strategic calculation that the opponent is using. Within that framework, the analyst then solves the problem from the perspective of the opponent while placing subjective probability distributions on all unknown quantities. This produces a distribution over the actions of the opponent that permits the analyst to maximize her expected utility. This overview covers conceptual, modeling, computational and applied issues in ARA.

Adversarial risk analysis under partial information

Adversarial risk analysis provides one-sided decision support to decision makers faced with risks due to the actions of other parties who act in their own interest. It is therefore relevant for the management of security risks, because the likely actions of the adversary can, to some extent, be forecast by formulating and solving decision models which explicitly capture the adversary’s objectives, actions, and beliefs. Yet, while the development of these decision models sets adversarial risk analysis apart from other approaches, the exact specification of the adversary’s decision model can pose challenges. In response to this recognition, and with the aim of facilitating the use of adversarial risk analysis when the parameters of the decision model are not completely known, we develop methods for characterizing the adversary’s likely actions based on concepts of partial information, stochastic dominance and decision rules. Furthermore, we consider situations in which information about the beliefs and preferences of all parties may be incomplete. We illustrate our contributions with a realistic case study of military planning in which the Defender seeks to protect a supply company from the Attacker who uses unmanned aerial vehicles for surveillance and the acquisition of artillery targets.