An oblivious active queue management scheme is one which does not differentiate between packets belonging to different flows. In this paper, we study the existence and the quality of Nash equilibria imposed by oblivious AQM schemes on selfish agents. Oblivious AQM schemes are of obvious importance because of the ease of implementation and deployment, and Nash equilibrium offers valuable clues into network performance under noncooperative user behavior. Specifically, we ask the following three questions: 1) do there exist oblivious AQM schemes that impose Nash equilibria on selfish agents? 2) Are the imposed equilibria, if they exist, efficient in terms of the goodput obtained and the drop probability experienced at the equilibrium? 3) How easy is it for selfish users to reach the Nash equilibrium state? We assume that the traffic sources are Poisson but the users can control the average rate. We show that drop-tail and RED do not impose Nash equilibria. We modify RED slightly to obtain an oblivious scheme, VLRED, that imposes a Nash equilibrium, but is not efficient. We then present another AQM policy, EN-AQM, that can impose an efficient Nash equilibrium. Finally, we show that for any oblivious AQM, the Nash equilibrium imposed on selfish agents is highly sensitive as the number of agents increases, thus making it hard for the users to converge to the Nash equilibrium, and motivating the need for equilibria-aware protocols.