Robust Adversarial Risk Analysis: A Level-<i>k</i> Approach

Abstract

Adversarial risk analysis is an active and important area of decision analytic research. Both single-actor decision analysis and multiple-actor game theory have been applied to this problem, with game theoretic methods being particularly popular. Although game theory models do explicitly capture strategic interactions between attackers and defenders, two of the key assumptions—decision making based on subjective expected utility maximization and common knowledge of rationality—are known to be descriptively inaccurate in some situations. This paper addresses these shortcomings by proposing, formulating, and illustrating the application of robust optimization methodologies to a level-k game theory model for adversarial risk analysis. Level-k game theory provides a practical method for modeling bounded rationality. Robust optimization provides an alternative way to model the actions of conservative players facing “deep” uncertainties about their environment—uncertainties that are possible to bound but that are difficult or impossible to represent using probability distributions. Our approach thus combines level-k and robust optimization insights to provide a computationally tractable model of boundedly rational players who are faced with significant and difficult to quantify uncertainties.