On global robustness of an adversarial risk analysis solution

Abstract

Adversarial 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.