Most of congestion control schemes require users to behave in a cooperative way, so that they respect some "social responsible" rules. However, without forcing end users to adopt a centralized mandated algorithm controlling their behavior (which is not advisable), it is not possible to guarantee that they will not act in a selfish manner. Consequently, a fundamental issue is to evaluate the impact of having users that act in such a manner. In such a scenario, having a Nash equilibrium guarantees that no selfish user has incentive to unilaterally deviate from its current state (i.e., it guarantees that we are in a stable state in the presence of selfish users). However, here we formally prove that an efficient Nash equilibrium can not be reached in practice for any oblivious control policy.