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This paper presents a new framework for vulnerability analysis. Under this framework, we can identify the vulnerable components and the critical components of a power grid. Distinct from previous work, our model considers the interaction between the components of the power system, and models the dynamic evolving process of cascading failures. The impact of a component failure on the system is dynamically changing as the failure propagates. We analyze the vulnerability of a power grid using an optimization model based on game theory, and use linear programming method to solve it. Since instability is the reason of power outage, we use an instability index to measure the negative impact to the system. The results from this optimization problem suggest which component of the system is critical since its failure can most negatively impact the cyber-physical system.