Availability of low cost sensor nodes has made Wireless Sensor Networks (WSNs) a viable choice for monitoring critical infrastructure such as power grid, civil structures and others. There are quite a few approaches in the literature that use WSN to monitor pipelines (water, gas, oil, and various other types of pipelines). The primary goal of all these protocols is to detect device malfunctions such as pipe leakage, oil spillage etc. However, none of these protocols are specifically designed to handle a malicious active adversary such as terrorist attacks. In this paper, we present a game theoretic approach to monitoring pipeline infrastructures using WSNs in the adversarial context. More specifically, we use Stackelberg competition to model attacker-defender interaction and derive the equilibrium condition of such a game under appropriate utility functions. Finally, we show that a monitoring system can do no better by deviating from its equilibrium strategy if the adversary acts rationally.