  We extend the adversarial/non-stochastic multi-play multi-armed bandit
(MPMAB) to the case where the number of arms to play is variable. The work is
motivated by the fact that the resources allocated to scan different critical
locations in an interconnected transportation system change dynamically over
time and depending on the environment. By modeling the malicious hacker and the
intrusion monitoring system as the attacker and the defender, respectively, we
formulate the problem for the two players as a sequential pursuit-evasion game.
We derive the condition under which a Nash equilibrium of the strategic game
exists. For the defender side, we provide an exponential-weighted based
algorithm with sublinear pseudo-regret. We further extend our model to
heterogeneous rewards for both players, and obtain lower and upper bounds on
the average reward for the attacker. We provide numerical experiments to
demonstrate the effectiveness of a variable-arm play.
