Asymptotic Nash Equilibrium for the Sequential Adversarial Hypothesis Testing Game

In this paper, we formulate the sequential binary hypothesis testing problem in which an adversary is active under both hypotheses. This problem is formulated as a sequential adversarial hypothesis testing game played between the decision maker and the adversary and it is a zero-sum and strategic one. The goal of the decision maker is to minimize the expectation of stopping time to make the test more efficient, while the adversary’s goal is to maximize it. We obtain the pair of strategies under which the asymptotic Nash equilibrium of the game is attained.