Sensor selection in adversarial setting

We consider the problem of sensor selection for a binary hypothesis testing problem when the conditional density of the sensor readings can be affected by an adversary. A typical application of the proposed setup is surveillance with spatially distributed sensors, where the adversary is changing locations to evade detection. We consider a zero-sum game model where the primary and the adversary are choosing open loop randomized strategies and the payoffs are specified by the asymptotic detection probability under a false alarm constraint. We prove the existence of the Nash equilibrium of this surveillance game and characterize the optimal min-max strategies and the value of the game. A computed example of decentralized detection with sensors providing binary valued observations is given to illustrate the results.