Adversarial risk analysis: Borel games

Abstract

Adversarial risk analysis (ARA) offers a new solution concept in game theory. This paper explores its application to a range of simple gambling games, enabling comparison with minimax solutions for similar problems. We find that ARA has several attractive advantages: it is easier to compute, it takes account of asymmetric information, it corresponds better to human behavior, and it reduces to previous solutions in appropriate circumstances.

Adversarial Risk Analysis: The Somali Pirates Case

“…Our objective is to estimate a predictive probability of attack p D A = a 1 d 1 for the type of ship owned by the defender, conditional on each possible initial protective defense d 1 ∈ 1 \ d 3 1 taken. Instead of estimating these probabilities based only on data, as in Carney (2009), which corresponds to a zerolevel analysis, we do so based on a one-level analysis (see Banks et al 2011 and the discussion by Kadane 2011). To do so, we assume the attacker behaves as an expected utility maximizer and derive the defender's uncertainty about the attacker's decision from her uncertainty about the attacker's probabilities and utilities.…”

Adversarial Risk Analysis for Urban Security Resource Allocation

“…Sometimes, such assessments may lead to a hierarchy of nested decision problems, as described in Rios and Rios Insua, similar to the concept of level‐ k thinking; see Stahl and Wilson . Such approach has been applied to several counterterrorism template models including the sequential defend‐attack, the simultaneous defend‐attack, the sequential defend‐attack‐defend, and the sequential defend‐attack model with private information . Note that in contrast with game‐theoretic approaches mentioned above, we do not assume a standard, but unrealistic, common knowledge hypothesis, according to which both agents share information about their utilities and probabilities.…”

Adversarial Risk Analysis with Incomplete Information: A Level‐k Approach

“…They motivate the "mirroring" approach, in part, by analogy to level-k game theory. (9) Our article employs level-k game theory (as developed by Stahl and Wilson and Nagel (10−12) ) more explicitly. We show that it can be used to implement and extend RIRB's and Banks et al's approach in two significant directions.…”