liberalism on security declares that cooperation, and security is possible under anarchy 

Despite some differences, Classical Realism and Neo-realism as a whole body of Realist paradigm share some common assumptions that are key in understanding security in international politics. First, the Realism points out that international system is anarchic. Second, power is the defining notion of state behaviors in the anarchic international environment (Ibid: 33-34). Third, states are the most important units/ actors in international politics. Fourth, states are unitary and rational actors.