Sensor-Reveal Games

We introduce two-player nonzero-sum partial information games, called sensor-reveal games, in which one of the players (which we call the attacker) decides whether or not to engage in an illegal activity and the other player (which we call the defender) wants to detect the attacker's action based on noisy sensor measurements. The partial information character of the game arises from the fact that the attacker controls which sensor provides the measurements that will be revealed to the defender, with the understanding that it may be costly to the attacker to reveal non-informative sensors, rather than sensors that carry useful information about the attack. Such games arise in several areas including computer security and law enforcement. We show that, for a very general sensor model, this game admits a closed form solution and provide explicit formulas for the Nash policies for both players. For scenarios in which the defender may not know the parameters that determine the cost function of the attacker, we provide a data-driven approach for the defender to compute an optimal policy based on fictitious play. The resulting algorithm is guaranteed to converge to a Nash equilibrium when both players rely on fictitious play. A brief numerical example illustrates the use of fictitious play.