Bounded Rationality in Byzantine Sensors Under Attacks

Abstract

In this article, we investigate the behavior of agents with bounded rationality, attacking a set of stochastic sensors measuring the state of a binary event. The coordination problem between the attackers is formulated as a multiplayer non-zero-sum one-shot game. The objective of each attacker is to maximize the probability that a certain detector will produce an erroneous estimate of the true event, while they remain stealthy. To better predict the outcome of this game, we categorize the players based on the number of strategic thinking steps they will take. Each level- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$k$</tex-math></inline-formula> attacker behaves based on subjective beliefs of the others’ behaviors, which are quantified via a Poisson distribution over the lower levels. The expected best responses for the type of each attacker are derived. The limiting conditions as the cognitive levels increase, as well as when the attackers fully coordinate, are shown to converge to the Nash equilibrium.