A non-zero-sum, sequential detection game

This paper examines a two-player, non-zero-sum, sequential detection game motivated by problems arising in the cyber-security domain. A defender agent seeks to sequentially detect the presence of an attacker agent via the drift of a stochastic process. The attacker strategically chooses the drift of the observed stochastic process, while his payoff increases in both the drift of the stochastic process and the expected time spent undetected by the defender. It is the defender´s objective to minimize a payoff function which is a weighted sum of the expected observation time and both type I and type II detection errors. As such, a best response sequential decision rule for the defender is a continuous-time version of Wald´s Sequential Probability Ratio Test. We prove the existence of pure Nash equilibria and give sufficient conditions for the existence of Stackelberg equilibria with the defender as leader in the special case that the attacker does not discount future payoffs. The equilibria are explored through numerical examples.