Adversarial risk analysis: An overview

Abstract

Adversarial 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 TheoryApplications of Computational Statistics > Defense and National Securityauctions, Bayes Nash equilibrium, decision theory, game theory, level-k thinking | INTRODUCTIONAdversarial risk analysis (ARA) guides decision-making when there are intelligent opponents who reason strategically about each other in the context of uncertain outcomes. It is a decision-theoretic alternative to classical game theory that uses Bayesian subjective distributions to model the goals, resources, beliefs, and reasoning of the opponent. Within this framework, the analyst solves the problem from the perspective of her opponent while placing subjective probability distributions on all unknown quantities. This structure provides a distribution over the actions of the opponent that enables her to maximize her expected utility, accounting for the uncertainty she has about the opponent. ARA applications include convoy routing through an insurgent city with improvised explosive devices (Banks, Petralia, & Wang, 2011), managing Somali piracy (Sevillano, Insua, & Rios, 2012), dealing with crime in a public transportation system (Banks, Aliaga, & Insua, 2015), Emile Borel's game La Relance (Banks et al., 2011), and cybersecurity (Rios Insua et al., 2019). It is relevant whenever one party is trying to model the decision-making process of one or more other parties, in order to achieve an outcome sought by the first party. The mathematics behind ARA can be quite complicated, but the essential idea is very natural. When asking the boss for a raise, one has a mental model for what the boss values (e.g., performance, flattery, punctual paperwork) and his likely response to various pitches. If the model is correct, one has a good chance of obtaining a raise; if not, then success is unlikely.

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

“…Consider ARA's canonical, simultaneous defend‐attack example (Banks et al, 2020). The defender (female) and attacker (male) each have a finite set of available actions, $$$ \mathcal{D} $$$ and $$$ \mathcal{A} $$$, respectively.…”

“…However, as discussed elsewhere (Banks et al, 2015), this is the most challenging quantity to assess in ARA. Although difficult, there are well‐established methods for doing so in normal‐form and extensive‐form games (e.g., see Banks et al, 2020; Rios Insua et al, 2016; Sevillano et al, 2012; Wang & Banks, 2011). Frameworks exist in which the decision maker believes opponents will act nonstrategically, seek a Nash‐equilibrium, perform k levels of iterative reasoning, or perform an analysis mirroring that of her own.…”

“…ARA provides decision support to a player, whereas epistemic game theory adopts a Bayesian perspective to analyze and develop solution concepts. Consider ARA's canonical, simultaneous defend-attack example (Banks et al, 2020). The defender (female) and attacker (male) each have a finite set of available actions,  and , respectively.…”

“…However, as discussed elsewhere (Banks et al, 2015), this is the most challenging quantity to assess in ARA. Although difficult, there are well-established methods for doing so in normal-form and extensive-form games (e.g., see Banks et al, 2020;Rios Insua et al, 2016;Sevillano et al, 2012;.…”

“…Therefore, we find that existing analyses are inappropriate from a decision-analytic perspective. Our goal is to provide decision support to a single player based upon their subjective beliefs regarding the aleatory, epistemic and concept uncertainties surrounding the strategic interaction (Banks et al, 2020). To do so, we must extend ideas previously developed in adversarial risk analysis (ARA) to a stochastic game setting akin to the threatened Markov decision processes (TMDPs) developed by Gallego et al (2019).…”